Methods and devices comprising flexible seals, flexible microchannels, or both for modulating or controlling flow and heat

Abstract

Claims

2. The device of claim 1, wherein the mobile and inflexible substrate is capable of movement in the normal direction due to expansion or contraction of the flexible seal or flexible complex seal.

3. The device of claim 2, wherein a change in the volumetric space of the microchannel occurs upon movement of the mobile and inflexible substrate.

4. The device of claim 1, wherein the flexible seal or the flexible complex seal separates the immobile and inflexible substrate and the mobile and inflexible substrate by a distance.

5. The device of claim 1, wherein the mobile and inflexible substrate has a thermal conductivity that is about equal to or greater than the thermal conductivity of copper.

6. The device of claim 1, wherein the flexible seal has an elastic modulus lower than about 10.sup.7 N/m.sup.2.

7. The device of claim 1, wherein the flexible seal connects the immobile and inflexible substrate and the mobile and flexible substrate.

8. The device of claim 1, wherein one of the substrates is heated.

9. The device of claim 1, and further comprising at least one heated substrate.

10. The device of claim 1, wherein the substrates separate a plurality of fluid layers.

11. The device of claim 10, wherein the direction of the fluid flow of the fluid layers is the same or different.

12. The device of claim 10, wherein the rate of the fluid flow of the fluid layers is the same or different.

13. The device of claim 4, wherein the distance between the substrates increases when the average pressure between the substrates increases.

14. The device of claim 3, wherein the volumetric space of the microchannel comprises a coolant and a super dispersive media.

15. The device of claim 14, wherein the super dispersive media comprises at least one metallic nanoparticle, at least one carbon nanoparticle, at least one nanotube, at least one flexible nanostring, or a combination thereof.

16. The device of claim 14, wherein the distribution of the super dispersive media is not uniform.

17. The device of claim 16, wherein the distribution is minimum in the regions of the volumetric space of the microchannel having least transverse convection heat transfer.

18. The device of claim 16, wherein the distribution is maximum in the regions of the volumetric space of the microchannel having maximum transverse convection heat transfer.

Description

[0001] This application is a continuation-in-part of U.S. patent application Ser. No. 10/840,303, filed 7 May 2004, pending, which claims the benefit of U.S. Provisional Patent Application No. 60/470,850 filed 16 May 2003, which names Kambiz Vafai and Abdul Rahim A. Khaled as inventors, which are herein incorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention generally relates to thin film channels, microfluidic devices, biosensors, electronic cooling, control of fuel flow prior combustion and insulating assemblies.

[0004] 2. Description of the Related Art

[0005] Thin films are used in a variety of devices, including electrical, electronic, chemical, and biological devices, for modulating or controlling flow and heat characteristics in the devices. See e.g. Vafai & Wang (1992) Int. J. Heat Mass Transfer 35:2087-2099, Vafai et al. (1995) ASME J Heat Transfer 117:209-218, Zhu & Vafai (1997) Int. J. Heat Mass Transfer 40:2887-2900, and Moon et al. (2000) Int. J. Microcircuits and Electronic Packaging 23:488-493 for flat heat pipes; Fedorov & Viskanta (2000) Int. J. Heat Mass Transfer 43:399-415, Lee and Vafai (1999) Int. J. Heat Mass Transfer 42:1555-1568, and Vafai & Zhu (1999) Int. J. Heat Mass Transfer 42; 2287-2297 for microchannel heat sinks; Lavrik et al. (2001) Biomedical Microdevices 3(1):35-44, and Xuan & Roetzel (2000) Int. J. Heat Mass Transfer 43:3701-3707 for biosensors and nanodevices.

[0006] For many of these applications, modulation and control of the flow and heat characteristics in the devices is desired. Unfortunately, the prior art methods for modulating and controlling the flow and heat are difficult or problematic. For example, a two phase flow in a microchannel is capable of removing maximum heat fluxes generated by electronic packages, but instability occurs near certain operating conditions. See Bowers & Mudwar (1994) ASME J. Electronic Packaging 116:290-305. Further, the use of porous medium for cooling electronic devices enhances heat transfer via the increase in the effective surface area, but the porous medium results in a substantial increase in the pressure drop inside the thin film. See Huang & Vafai (1993) Int. J. Heat Mass Transfer 36:4019-4032, Huang & Vafai (1994) AIAA J. Thermophysics and Heat Transfer 8:563-573, Huang & Vafai (1994) Int. J. Heat and Fluid Flow 15:48-61, and Hadin (1994) ASME J. Heat Transfer 116:465-472.

[0007] Therefore, a need still exists for methods of modulating or controlling heat and flow characteristics in thin films.

SUMMARY OF THE INVENTION

[0008] The present invention generally relates to thin film channels, microfluidic devices, biosensors, electronic cooling, control of fuel flow prior to combustion and insulating assemblies.

[0009] The present invention provides methods to modulate flow and heat in a variety of thermal systems including thin film channels, microfluidics, insulating assemblies, and the like with no need for external cooling or flow controlling devices.

[0010] The present invention provides several devices for modulating flow and heat. Several devices provided herein reduce the temperature as the thermal load increases as related to electronic cooling and cooling of engine applications. Several devices provided herein reduce the flow rate as the thermal load increases which are important to internal combustion applications where fuel rate needs to be reduced as the engine gets overheated. Several devices provided herein conserve thermal energy as the temperature increases and to reduce leakage from microfluidics. These devices have applications related to thermal insulations and biosensor devices among others.

[0011] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are intended to provide further explanation of the invention as claimed. The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute part of this specification, illustrate several embodiments of the invention, and together with the description serve to explain the principles of the invention.

DESCRIPTION OF THE DRAWINGS

[0012] This invention is further understood by reference to the drawings wherein:

[0013] FIG. 1 shows an insulating assembly comprising the flexible seals of the present invention.

[0014] FIG. 2 shows primary fluid layer expansion versus its temperature.

[0015] FIG. 3 shows the percentage volumetric thermal expansion for the conditions of isobaric expansion and expansion using a linearized model under linearly varying pressure.

[0016] FIG. 4 shows dimesionless change in the equivalent resistance of the fluid layers for two different fluids.

[0017] FIG. 5 shows enhanced insulating properties using xenon and an insulating assembly using the flexible seals according to the present invention.

[0018] FIG. 6 shows deteriorated insulating properties using helium and an insulating assembly using the flexible seals according to the present invention.

[0019] FIG. 7 shows reduction of thermal losses at large operating temperatures using xenon and an insulating assembly using the flexible seals according to the present invention.

[0020] FIG. 8 shows deterioration of thermal losses at large operating temperatures using helium and an insulating assembly using the flexible seals according to the present invention.

[0021] FIG. 9 shows advanced assemblies with enhanced insulating properties comprising the flexible seals according to the present invention.

[0022] FIG. 10 shows the schematic diagram for a thin film and the coordinate system.

[0023] FIG. 11 shows the effects of the fixation parameter on the thin film thickness.

[0024] FIG. 12 shows the effects of the fixation parameter on the fluctation at the upper substrate.

[0025] FIG. 13 shows the effects of the frequency of internal pressure pulsations on the fluctation at the upper substrate.

[0026] FIG. 14 shows the effects of the squeezing number on the thin film thickness.

[0027] FIG. 15 shows the effects of the squeezing number on the fluctation at the upper substrate.

[0028] FIG. 16 shows the effects of the phase shift of the internal pressure on the thin film thickness.

[0029] FIG. 17 shows the effects of the thermal squeezing paremeter and the fixation parameter on the mean bulk temperature.

[0030] FIG. 18 shows the effects of the thermal squeezing paremeter and the fixation parameter on the average lower substrate temperature.

[0031] FIG. 19 shows the effects of the fixation parameter on the Nusselt number for constant wall temperature conditions.

[0032] FIG. 20 shows the effects of the fixation parameter on the Nusselt number for uniform wall heat flux conditions.

[0033] FIG. 21 shows the axial development of the Nusselt number vesrus the fixation parameter.

[0034] FIG. 22 shows the effects of the frequency of pulsations on the average heat transfer.

[0035] FIG. 23 shows the effects of the frequency of pulsations on the average lower substrate temperature.

[0036] FIG. 24 shows the effects frequency of pulsations on the fluctuation in the average heat transfer and the average lower substrate temperature.

[0037] FIG. 25A is a 3D view of a schematic diagram for a two-layered thin film supported by flexible seals and flexible complex seals of the present invention.

[0038] FIG. 25B shows the front and side views including the main boundary conditions of the schematic diagram for a two-layered thin film supported by flexible seals and flexible complex seals of the present invention.

[0039] FIG. 26A shows the effects of E* on .PSI..sub.X=0.5 and dH.sub.1/d.tau.*(H.sub.t=2.0, E.sub.1*=E.sub.2*=E*, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0040] FIG. 26B shows the effects of E* on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0041] FIG. 27A shows the effects of F.sub.T on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (H.sub.1=2.0, E.sub.1*=0.3, E.sub.2*=0.003, P.sub.S1=1.0, P.sub.S2=0.012, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=6.0, .sigma..sub.2=1.0).

[0042] FIG. 27B shows the effects of F.sub.T on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (H.sub.t=2.0, E.sub.1*=0.3, E.sub.2*=0.003, P.sub.S1=1.0, P.sub.S2=0.012, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=6.0, .sigma..sub.2=1.0).

[0043] FIG. 28 shows the effects of F.sub.T on Nusselt numbers for primary and secondary flows: (primary flow maintained at a CIF condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0044] FIG. 29A shows the effects of .sigma..sub.1 on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.2=6.0).

[0045] FIG. 29B shows the effects of .sigma..sub.1 on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.2=6.0).

[0046] FIG. 30A shows the effects of P.sub.S2 on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=5.0, .sigma..sub.2=6.0).

[0047] FIG. 30B shows the effects of P.sub.S2 on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=5.0, .sigma..sub.2=6.0).

[0048] FIG. 31 shows the effects of P.sub.S2 on Nusselt numbers for primary and secondary flows: (primary flow maintained at a CIF condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=5.0, .sigma..sub.2=6.0).

[0049] FIG. 32A shows the effects of .lamda..sub.2 on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (primary flow maintained at a CIP condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=0, .sigma..sub.1=3.0, .sigma..sub.22=6.0).

[0050] FIG. 32B shows the effects of .lamda..sub.2 on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (primary flow maintained at a CIP condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0051] FIG. 33A shows the effects of .lamda..sub.2 on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (primary flow maintained at a CIF condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0052] FIG. 33B shows the effects of .lamda..sub.2 on .THETA..sub.AVG and (.theta..sub.u).sub.AVG (primary flow maintained at a CIF condition, H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0053] FIG. 34 shows the effects of .gamma..sub.p on .DELTA..PSI..sub.X=0.5 and .DELTA.(.theta..sub.u).sub.AVG for the CIP condition (H.sub.t=2.0, E.sub.1*=E.sub.2*=E*=0.3, F.sub.T=0.3, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0054] FIG. 35 shows the effects of H.sub.t on .PSI..sub.X=0.5 and dH.sub.1/d.tau.* (primary flow maintained at a CIP condition, E.sub.1*=E.sub.2*=E*=0.2, F.sub.T=0.15, P.sub.S1=P.sub.S2=1.0, .beta..sub.p=0.3, .beta..sub.q=0.2, .phi..sub.p=.pi./2, .gamma.=3.0, .gamma..sub.p=6.0, .lamda..sub.1=.lamda..sub.2=0, .sigma..sub.1=3.0, .sigma..sub.2=6.0).

[0055] FIG. 36A is a front view of a schematic diagram for a thin film with flexible complex seal according to the present invention and the corresponding coordinate system.

[0056] FIG. 36B is a side view of a schematic diagram for a thin film with flexible complex seal according to the present invention and the corresponding coordinate system.

[0057] FIG. 36C is a 3D diagram of a schematic diagram for a thin film with flexible complex seal according to the present invention and the corresponding coordinate system.

[0058] FIG. 37A shows the effects of the dimensionless thermal expansion parameter F.sub.T on dimensionless thin film thickness H.

[0059] FIG. 37B shows the effects of the dimensionless thermal expansion parameter F.sub.T on dimensionless average lower substrate temperature (.theta..sub.W).sub.AVG.

[0060] FIG. 37C shows the effects of the dimensionless thermal expansion parameter F.sub.T on dH/d.tau..

[0061] FIG. 37D shows the effects of the dimensionless thermal expansion parameter F.sub.T on exit Nusselt number Nu.sub.L

[0062] FIG. 38A shows the effects of the dimensionless thermal dispersion parameter .lamda. on dimensionless average lower substrate temperature (.theta..sub.W).sub.AVG.

[0063] FIG. 38B shows the effects of the dimensionless thermal dispersion parameter .lamda. on dimensionless thickness H.

[0064] FIG. 38C shows the effects of the dimensionless thermal dispersion parameter .lamda. on temperature profile.

[0065] FIG. 38D shows the effects of the dimensionless thermal dispersion parameter .lamda. on exit Nusselt number Nu.sub.L

[0066] FIG. 39 shows effects of the dimensionless dispersion parameter .lamda. on the time variation of the dimensionless thin film thickness dH/d.tau..

[0067] FIG. 40A shows effects of the thermal squeezing parameter P.sub.S and the squeezing number .sigma. on dimensionless average lower substrate temperature (.theta..sub.W).sub.AVG.

[0068] FIG. 40B shows effects of the thermal squeezing parameter P.sub.S and the squeezing number .sigma. on dimensionless thin film thickness H.

[0069] FIG. 40C shows effects of the thermal squeezing parameter P.sub.S and the squeezing number .sigma. on dH/d.tau..

[0070] FIG. 41A shows effects of the fixation parameter F.sub.n and the dimensionless thermal load amplitude .beta..sub.q on dimensionless average lower substrate temperature (.theta..sub.W).sub.AVG.

[0071] FIG. 41B shows effects of the fixation parameter F.sub.n and the dimensionless thermal load amplitude .beta..sub.q on dimensionless thin film thickness H.

[0072] FIG. 42 shows effects of the dimensionless thermal expansion parameter F.sub.T on the average dimensionless pressure inside the thin film .PI..sub.AVG.

[0073] FIG. 43A is a schematic diagram of a symmetrical fluidic cell (it has a uniform variation in the film thickness under disturbed conditions and can be used for multi-detection purposes).

[0074] FIG. 43B is a schematic diagram of corresponding coordinate systems with leakage illustration.

[0075] FIG. 44A shows effects of the dimensionless leakage parameter M.sub.L on the dimensionless thin film thickness H, the film thickness decreases with an increase in the leakage.

[0076] FIG. 44B shows effects of the dimensionless leakage parameter M.sub.L on the inlet pressure gradient.

[0077] FIG. 45 shows effects of the fixation parameter F.sub.n on the fluctuation rate at the upper substrate dH/d.tau.. The fluctuation rate increases as the seal becomes softer.

[0078] FIG. 46 shows effects of the squeezing number .sigma. on the fluctuation rate at the upper substrate dH/d.tau.. The fluctuation rate decreases as the order of the inlet velocity decreases compared to the axial squeezed velocity due to pressure pulsations.

[0079] FIG. 47A shows the effects of the dimensionless slip parameter .beta..sub.P/h.sub.o on the dimensionless wall slip velocity U.sub.slip.

[0080] FIG. 47B shows the effects of the dimensionless slip parameter .beta..sub.P/h.sub.o on the dimensionless normal velocity V (the dimensionless time .tau.*=3.pi./2 corresponds to the time at which the fluctuation rate at the upper substrate is maximum while .tau.*=11.pi./6 corresponds to the time at which the fluctuation rate at the upper substrate is minimum).

[0081] FIG. 48A shows the effects of the power law index n on the dimensionless wall slip velocity U.sub.slip.

[0082] FIG. 48B shows the effects of the power law index n on the dimensionless normal velocity V (the dimensionless time .tau.*=3.pi./2 corresponds to the time at which the fluctuation rate at the upper substrate is maximum while .tau.*=11.pi./6 corresponds to the time at which the fluctuation rate at the upper substrate is minimum).

[0083] FIG. 49 shows the effects of the dimensionless leakage parameter M.sub.L on the average dimensionless lower substrate temperature .theta..sub.W. The cooling increases with an increase in the leakage rate.

[0084] FIG. 50 shows the effects of the fixation parameter F.sub.n on the average dimensionless lower substrate temperature .theta..sub.W. The cooling increases as the seal becomes softer.

[0085] FIG. 51 shows the effects of the squeezing number .sigma. on the average dimensionless lower substrate temperature .theta..sub.W. The cooling increases as the order of the inlet velocity increases.

[0086] FIG. 52 shows a multi-compartment fluidic cell.

[0087] FIG. 53A shows systems with increased cooling capacity as thermal load increases utilizing a flexible complex seal according to the present invention.

[0088] FIG. 53B shows systems with increased cooling capacity as thermal load increases utilizing a bimaterial upper substrate.

[0089] FIG. 54A shows systems with decreased cooling capacity as thermal load increases utilizing flexible complex seals according to the present invention and two layered thin films.

[0090] FIG. 54B shows systems with decreased cooling capacity as thermal load increases utilizing a bimaterial upper substrate.

[0091] FIG. 55A shows an insulating assembly arrangement for low temperature applications.

[0092] FIG. 55A shows an insulating assembly arrangement for high temperature applications.

[0093] FIG. 56 shows expected sample results for xenon with and without the flexible seals of the present invention.

[0094] FIG. 57 shows a thin film supported by flexible complex seals of the present invention with one inlet port and two exit ports.

[0095] FIG. 59B is a schematic for an open ended cell supported by flexible complex seals.

[0096] FIG. 60A is a front view of a schematic diagram and the coordinate system for a single layer flexible microchannel heat sink of the present invention.

[0097] FIG. 60B is a side view of a schematic diagram and the coordinate system for a single layer flexible microchannel heat sink of the present invention.

[0098] FIG. 61A is a front view of a schematic diagram and the coordinate system for a double layered flexible microchannel heat sink of the present invention

[0099] FIG. 61B is a side view of a schematic diagram and the coordinate system for a double layer flexible microchannel heat sink of the present invention.

[0100] FIG. 62 show effects of the pressure drop ( Re o = .rho. 12 .times. .times. 2 .times. .DELTA. .times. .times. p B .times. H o 3 ) on the dimensionless exit mean bulk temperature for a single layer flexible microchannel heat sink.

[0101] FIG. 63 shows effects of the pressure drop ( Re o = .rho. 12 .times. .times. 2 .times. .DELTA. .times. .times. p B .times. H o 3 ) on the dimensionless average lower plate temperature for a single layer flexible microchannel heat sink.

[0102] FIG. 64 shows effects of the pressure drop ( Re o = .rho. 12 .times. .times. 2 .times. .DELTA. .times. .times. p B .times. H o 3 ) on the dimensionless average convective heat transfer coefficient for a single layer flexible microchannel heat sink.

[0103] FIG. 65 shows effects of the pressure drop ( Re o = .rho. 12 .times. .times. 2 .times. .DELTA. .times. .times. p B .times. H o 3 ) on U.sub.Reo and U.sub.F for a single layer flexible microchannel heat sink.

[0104] FIG. 66 shows effects of the fixation parameter on the fully developed heated plate temperature at the exit for a single layer flexible microchannel heat sink.

[0105] FIG. 67 shows effects of Prandtl number on the dimensionless average lower plate temperature for a single layer flexible microchannel heat sink.

[0106] FIG. 68 shows effects of Prandtl number on the average convective heat transfer coefficient for a single layer flexible microchannel heat sink.

[0107] FIG. 69 shows effects of the fixation parameter on the mean bulk temperature inside the double layered flexible microchannel heat sink

[0108] FIG. 70 shows effects of the pressure drop ( Re o = .rho. 12 .times. .times. 2 .times. .DELTA. .times. .times. p B .times. H o 3 ) on .kappa..sub.m and .kappa..sub.W

[0109] FIG. 71 shows effects of the pressure drop ( ( Re o ) DL = .rho. 12 .times. .times. 2 .times. ( .DELTA. .times. .times. p ) DL B .times. H o 3 ) on the pressure drop ratio and the friction force ratio between single and double layered flexible microchannel heat sinks.

[0110] FIG. 72 shows effects of the delivered coolant mass flow rate on the average heated plate temperature for both single and double layered flexible microchannel heat sinks.

[0111] FIG. 73 is a schematic diagram and the coordinate system.

[0112] FIG. 74 shows different arrangements for the thermal dispersion region: (a) central arrangement, and (b) boundary arrangement.

[0113] FIG. 75 shows effects of the thermal dispersion parameter E.sub.o and the dimensionless thickness .LAMBDA. on the Nusselt number at thermally fully developed conditions for the central arrangement (the number of the dispersive elements is the same for each arrangement).

[0114] FIG. 76 shows effects of the thermal dispersion parameter E.sub.o and the dimensionless thickness .LAMBDA. on the Nusselt number at thermally fully developed conditions for the boundary arrangement (the number of the dispersive elements is the same for each arrangement).

[0115] FIG. 77 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the Nusselt number at the exit for central arrangement (the number of the dispersive elements is the same for each arrangement).

[0116] FIG. 78 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the average dimensionless plate temperature .theta..sub.W for central arrangement (the number of the dispersive elements is the same for each arrangement, Pe.sub.f=670).

[0117] FIG. 79 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the average dimensionless plate temperature .theta..sub.W for central arrangement (the number of the dispersive elements is the same for each arrangement, Pe.sub.f=1340).

[0118] FIG. 80 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the Nusselt number at the exit for the boundary arrangement (the number of the dispersive elements is the same for each arrangement).

[0119] FIG. 81 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the average dimensionless plate temperature .theta..sub.W for boundary arrangement (the number of the dispersive elements is the same for each arrangement, Pe.sub.f=670).

[0120] FIG. 82 shows effects of the dispersion coefficient C* and the dimensionless thickness .LAMBDA. on the average dimensionless plate temperature .theta..sub.W for boundary arrangement (the number of the dispersive elements is the same for each arrangement, Pe.sub.f=340).

[0121] FIG. 83 shows effects of D.sub.e on the volume fraction distribution of the dispersive element (the number of the dispersive elements is the same for each distribution).

[0122] FIG. 84 shows effects of D.sub.c on the volume fraction distribution of the dispersive elements (the number of the dispersive elements is the same for each distribution).

[0123] FIG. 85 shows effects of D.sub.e on the fully developed value for the Nusselt number (exponential distribution, the number of the dispersive elements is the same for each distribution).

[0124] FIG. 86 shows effects of D.sub.c on the fully developed value for the Nusselt number (parabolic distribution, the number of the dispersive elements is the same for each distribution).

[0125] FIG. 87 is a graph that shows that the excess in Nusselt number .kappa. is always greater than one for the boundary arrangement while it is greater than one for the exponential distribution when the velocity is uniform.

DETAILED DESCRIPTION OF THE INVENTION

[0126] The present invention provides methods for modulating or controlling heat and flow characteristics in a variety of devices. In particular, the present invention provides flexible seals for modulating or controlling heat and flow characteristics in devices comprising thin films, such as thin film channels, microchannels, microfluidics and the like. The present invention also provides a method to control heat and flow inside other thermal systems, such as insulating assemblies and fuel flow passages. As used herein, a "flexible seal" refers to a material that can be deformed significantly according to the load acting upon it. Examples of these materials include elastmors, polymers, natural rubber, closed rubber cell foams, and the like. In some embodiments, the present invention provides flexible complex seals for modulating or controlling heat and flow characteristics in devices comprising thin films, such as microchannels and microfluidics. As used herein, a "flexible complex seal" refers to a flexible seal comprising at least one closed cavity of stagnant fluid. In preferred embodiments, the stagnant fluid has at least one point of contact with the heated surface of the device. In preferred embodiments, the stagnant fluid has a large value of the volumetric thermal coefficient. As used herein, a "fluid" refers to a continuous amorphous substance that tends to flow and to conform to the outline of a container, such as a liquid or a gas, and may be used in accordance with the present invention. As used herein, "stagnant fluid" refers to a fluid that is not circulating or flowing and in preferred embodiments of the present invention, the stagnant fluid is surrounded by a flexible seal of the present invention and/or the surfaces of a device such that the average translational velocity of the fluid is zero.

[0127] As used herein, "primary fluid" refers to the fluid that the devices of the present invention control or modulate its flow rate or its temperature. As used herein, "secondary fluid" refers to an auxiliary fluid utilized in the present invention to achieve additional control and modulation features for the primary fluid flow rate and temperature. As provided herein, the stagnant fluid in the complex flexible seals can have characteristics that are the same as or different from the characteristics of the primary fluid, the secondary fluid, or both. As used herein, "biofluid" refers to the fluid that contains at least one species of a biological substance that needs to be measured. As provided herein, the primary fluid can be a biofluid.

[0128] The flexible seals and flexible complex seals of the present invention are typically found between a first substrate and a second substrate of a thin film or other thermal systems such as the insulating assemblies. As used herein, "substrate" includes plates which may be inflexible or flexible according to part 6 herein below. In some preferred embodiments, the elastic modulus for the seals of the present invention, the ratio of the applied stress on the seal to the induced strain, range from about 10.sup.3N/m.sup.2 to about 10.sup.7N/m.sup.2. The seals of the present invention may comprise at least one closed cavity of a fluid such as air or the like in order to minimize their effective elastic modulus. The deformation of the flexible seals of the present invention can be guided by special guiders to attain maximum or desired deformations. In preferred embodiments, the flexible seals comprise different cross-sectional geometries, such as circular cross-section, rectangular cross-section and the like. As used herein, "thin films" include fluidic devices that have the thickness of their fluidic layers of an order of about a millimeter or less such as, microchannels and microfluidic devices. Thin films comprise at least two substrates, lower and upper substrates, and at least one fluidic layer. As used herein, an "insulating assembly" means an assembly of at least two insulating substrates and at least one fluid layer placed consecutively in series.

[0129] The flexible seals and flexible complex seals of the present invention are typically found between a first substrate and a second substrate of a thin film or other thermal systems such as the insulating assemblies. As used herein, "substrate" includes plates which may be inflexible or flexible according to part 6 herein below. In some preferred embodiments, the elastic modulus for the seals of the present invention, the ratio of the applied stress on the seal to the induced strain, range from about 10.sup.3N/m.sup.2 to about 10.sup.7N/m.sup.2. The seals of the present invention may comprise at least one closed cavity of a fluid such as air or the like in order to minimize their effective elastic modulus. The deformation of the flexible seals of the present invention can be guided by special guiders to attain maximum or desired deformations. In preferred embodiments, the flexible seals comprise different cross-sectional geometries, such as circular cross-section, rectangular cross-section and the like. As used herein, "thin films" include fluidic devices that have the thickness of their fluidic layers of an order of about a millimeter or less such as, microchannels and microfluidic devices. Thin films comprise at least two substrates, lower and upper substrates, and at least one fluidic layer. As used herein, an "insulating assembly" means an assembly of at least two insulating substrates and at least one fluid layer placed consecutively in series.

[0130] As disclosed herein, modulating the thermal characteristics of a device may be conducted by modifying the thin film thickness, the thermal load, the flow rate, or a combination thereof. For example, additional cooling can be achieved if the thin film thickness is allowed to increase by an increase in the thermal load, pressure gradient or both which will cause the coolant flow rate to increase. As provided herein, the enhancement in the cooling due to the flexible complex seals used is substantial at larger thermal loads for stagnant liquids while this enhancement is much larger at lower temperatures for stagnant fluids, especially ideal gases. This is because the volumetric thermal expansion coefficient increases for liquids and decreases for gases as the temperature increases. Moreover, the enhancement in the cooling due to flexible seals is substantial at larger pressure gradients for single layered thin films while it is significant for double layered thin films at lower pressure gradients.

[0131] Khaled and Vafai analyzed the enhancement in the heat transfer inside thin films supported by flexible complex seals. See Khaled & Vafai (2003) ASME J. of Heat Transfer 125:916-925, which is herein incorporated by reference. Specifically, the applied thermal load was considered to vary periodically with time in order to investigate the behavior of expandable thin film systems in the presence of a noise in the applied thermal load. As provided herein, a noticeable enhancement in the cooling capacity can be achieved for large thermal loads especially in cooling of high flux electronic components (q.apprxeq.700 kW/m.sup.2) since they produce elevated working temperatures. Also, the generated squeezing effects at the mobile and inflexible substrate can be minimized when nanofluids are employed in the coolant flow. As used herein, "nanofluids" are mixtures of a working fluid, such as water, and suspended ultrafine particles in the fluid such as copper, aluminum, or the like with diameters of an order of about the nanometer range. See Eastman et al. (2001) Applied Physics Letters 78: 718-720, which is herein incorporated by reference.

[0132] The flexible seals, flexible complex seals, or both of the present invention may be used in two-layered thin films in order to regulate the flow rate of the primary fluid layer such that excessive heating in the secondary fluid layer results in a reduction in the primary fluid flow rate. For example, the flexible seals, flexible complex seals, or both of the present invention may be applied in the internal combustion industry where the fuel flow rate should be reduced as the engine gets overheated. In this example, the primary fluid flow is the fuel flow while the secondary fluid flow can be either flow of combustion products, flow of engine coolant or flow of any other auxiliary fluid. The flexible seals, flexible complex seals, or both of the present invention may be used to modulate or control exit thermal conditions in devices comprising two-layered thin films. For example, the flexible seals, flexible complex seals, or both of the present invention may be used to minimize bimaterial effects of various biosensors, including microcantilever based biosensors, which are sensitive to flow temperatures. See Fritz et al. (2000) Science 288:316-318, which is herein incorporated by reference. In this example, the primary fluid flow is flow of a biofluid while the secondary fluid flow can be either flow of the external surrounding fluid or flow of any auxiliary fluid.

[0133] As provided herein, thin films comprising flexible seals, flexible complex seals, or both are modeled and designed in order to alleviate the thermal load or modulate the flow. These systems according to the present invention provide noticeable control of the flow rate, reduce thermal gradients within the primary fluid layer at relatively large external thermal loads, and minimize fluctuation at the mobile and inflexible substrate in the presence of nanofluids.

1. Control of Insulating Properties Using Flexible Seals

[0134] As disclosed herein, the present invention provides a method for modulating or controlling the insulating properties of a device, an insulating assembly having insulating substrates separated by fluid layers and flexible seals. The fluid layers were supported by flexible seals in order to allow for volumetric thermal expansion of the primary fluid layers while the secondary fluid layers are vented to the atmosphere such that the secondary fluid pressure remains constant. The volumetric thermal expansion of the primary fluid layers within the insulating assembly were determined taking into consideration the variation in the fluid pressure due to the elastic behavior of the supporting flexible seals. The volumetric thermal expansion of the primary fluid layers was correlated to the increase in the equivalent thermal resistance of the fluid layers. The volumetric thermal expansion of the primary fluid was found to approach its isobaric condition value as the primary fluid layer thickness decreases. Also, the insulating properties were found to be enhanced when the primary fluid had a minimum thermal conductivity and when relatively high temperatures were experienced. The insulating properties deteriorate at large temperatures when the primary fluid has a relatively large thermal conductivity.

[0135] The following Table 1 provides the various symbols and meanings used in this section: TABLE-US-00001 TABLE 1 A.sub.S surface area of the intermediate insulating substrate C.sub.F volumetric thermal expansion efficiency h.sub.c convective heat transfer coefficent at the upper surface h.sub.o reference thickness of the primary fluid layer K* stiffness of the supporting seal k.sub.ins thermal conductivity of insulating substrates k.sub.1 thermal conductivity of the primary fluid k.sub.2 thermal conductivity of the secondary fluid m.sub.1 mass of the primary fluid p.sub.atm pressure of the surrounding q heat flux R.sub.1 primary fluid layer fluid constant R.sub.th thermal resistance of the fluid layers R.sub.tho orginal thermal resistance of the fluid layers T average temperature of the primary fluid layer T.sub.1 temperature at the lower surface of the primary fluid layer T.sub.o orginal primary fluid temperature T.sub.e temperature of the upper surface facing of the surroundings .DELTA.h.sub.1 expansion of the primary fluid layer .eta..sub.R dimensionless increase in the resistance of the fluid layers

[0136] Generally, thermal losses increase at large working temperatures. The present invention provides a device that has desirable insulative attributes even at high working temperatures. That is, the present invention better conserves thermal energy especially at high temperatures as compared to similar devices that do not comprise flexible seals. An example of a device of the present invention is shown in FIG. 1. The device shown in FIG. 1 comprises the following from bottom to top: (1) a heated substrate (generally due to contact with or proximity to a heat source), (2) a first layer of fluid that has a very low thermal conductivity such as xenon (the primary fluid layer), (3) a thin layer of an insulating substrate, (4) a secondary fluid layer comprising a second fluid that has a lower thermal conductivity like air (needs to be larger than that of the first layer and is open to the outside environment), and (5) a top insulating substrate. The first and the second fluid layers along with the intermediate insulating substrate are connected together by flexible seals. Both the heated substrate and the upper insulating substrate are fixed (immobile and inflexible substrates) while the intermediate insulating substrate is capable of moving as it is supported by flexible complex seals (mobile and inflexible substrate). In preferred embodiments, the flexible seals are made of a material resistant to melting at high temperatures. In order to avoid melting the seals at high temperatures, ordinary homogenous flexible seals may be replaced with flexible complex seals, a flexible seal comprising at least one closed cavity containing a fluid, such as a gas.

1A. Operational Principle

[0137] When the operating temperature (high temperature source) increases, the average fluid temperature of the primary fluid layer increases. Accordingly, the volume of the primary fluid layer expands accompanied by a shrinkage in the secondary fluid layer. As such, an increase in the equivalent thermal resistance of the insulating assembly can be attained as long as the thermal conductivity of the primary fluid layer is smaller than that for the secondary fluid layer. Preferably, the heated substrate has a relatively small thickness and a relatively large thermal conductivity so that the thermal expansion of the primary fluid layer is maximized.

1B. Volumetric Expansion in the Primary Fluid Layer

[0138] Forces on elastic materials, such as seals, are usually proportional to the elongation of this material. See R. L. Norton (1998) MACHINE DESIGN: AN INTEGRATED APPROACH Prentice-Hall, NJ, which is herein incorporated by reference. Accordingly, a force balance on the intermediate insulating substrate results as provided in Equation 1 as follows: m 1 .times. R 1 .times. T A S .function. ( h o + .DELTA. .times. .times. h 1 ) - p atm = K * A S .times. .DELTA. .times. .times. h 1 Eq . .times. 1 wherein

[0139] T is the average temperature of the primary fluid layer

[0140] K* is the stiffness of the supporting seals

[0141] A.sub.s is the surface area of the intermediate insulating substrate.

[0142] h.sub.o is the reference thickness of the primary fluid layer

[0143] .DELTA.h.sub.1 is the corresponding expansion in the primary fluid layer thickness

[0144] m.sub.1 is the mass of the primary fluid

[0145] R.sub.1 is the primary fluid constant

[0146] The first term on the left hand side of Equation 1 represents the pressure inside the primary fluid layer. The reference thickness h.sub.o corresponds to the thickness of the primary fluid layer when the primary fluid pressure is equal to the atmospheric pressure. Equation 1 can be solved for .DELTA.h.sub.1 and the expansion is found to be: .DELTA. .times. .times. h 1 h o = C 1 .function. ( C 2 C 1 2 + 1 - 1 ) .times. .times. where Eq . .times. 2 C 1 = ( p atm .times. A S ) / ( K * .times. h o ) + 1 2 .times. .times. and Eq . .times. 3 C 2 = ( m 1 .times. R 1 .times. T ) / ( K * .times. h o 2 ) - ( p atm .times. A S ) / ( K * .times. h o ) Eq . .times. 4

[0147] In order to maximize the expansion in the primary fluid layer which in turn results in better insulating properties, i.e. increased effective thermal resistance of the insulating assembly, the parameter C.sub.2 needs to be maximized. This can be accomplished by considering minimum values of K*h.sub.o while the following relationship provided in Equation 5 is preferred to be satisfied: m 1 .times. R 1 .times. T p atm .times. A S .times. h o >> 1 Eq . .times. 5

[0148] The following parameters were considered for studying the flexible seals of the present invention: K*=48000 N/m, A.sub.S=0.0036 m.sup.2 and p.sub.atm=0.1 Mpa. The parameter m.sub.1R.sub.1 was evaluated at the reference condition when the primary fluid pressure was equal to the atmospheric pressure. This condition which causes the expansion to be zero in Equation 1 was assumed to be at T=T.sub.o=283 K and h.sub.o=0.004 m. This leads to m.sub.1R.sub.1=5.088.times.10.sup.-3 J/K. Accordingly, the relation between the volumetric thermal expansion of the primary fluid layer and its average temperature is illustrated in FIG. 2.

[0149] Equation 2 reduces to the following linearized model for relatively low volumetric thermal expansion levels ( .DELTA. .times. .times. h 1 h o < 0.2 ) .times. : .DELTA. .times. .times. h 1 h o .apprxeq. 0.5 .times. C 2 C 1 + O .function. ( .DELTA. .times. .times. h 1 2 ) = T - T o T o + K * .times. h o 2 m 1 .times. R 1 + O .function. ( .DELTA. .times. .times. h 1 2 ) Eq . .times. 6 where T.sub.o is the average temperature of the primary fluid layer at the reference condition. The reference condition corresponds to the condition that produces a zero net force on the seals. That is, thermal expansion is zero when the primary fluid layer is kept at T.sub.o. At this condition, the primary fluid layer thickness is h.sub.o. The relative volumetric thermal expansion, .DELTA.h.sub.l/h.sub.o, approximated by Equation 6 is similar to that for isobaric expansion with the average primary fluid temperature being increased by the parameter K * .times. h o 2 m 1 .times. R 1 . This parameter is denoted as .DELTA.T.sub.o.

[0150] The error associated with Equation 6 is further reduced if m 1 .times. R 1 .times. T o K * .times. h o 2 > 1. The latter inequality means that the insulating system exhibits relatively large volumetric thermal expansion by having a small increase in the primary fluid pressure due to the elastic behavior of the flexible seal. FIG. 3 illustrates the difference between the relative volumetric expansion expressed by Equation 6 and that obtained when the expansion is at a constant pressure. FIG. 3 shows that isobaric conditions provide favorable volumetric thermal expansion when compared to volumetric thermal expansion under linearly varying pressure as when flexible seals are present.

[0151] The efficiency of the volumetric thermal expansion C.sub.F of the primary fluid layer is defined as the ratio of the expansion in the primary fluid layer when the flexible seal is present to the expansion when under constant pressure as expressed in the following Equation 7: C F = .DELTA. .times. .times. h 1 ( .DELTA. .times. .times. h 1 ) Isobaric Eq . .times. 7 where (.DELTA.h.sub.1).sub.1sobaric/h.sub.o=(T-T.sub.o)/T.sub.o. For the linearized model shown in Equation 6, the efficiency C.sub.F will be: C F .apprxeq. T o T o + .DELTA. .times. .times. T o Eq . .times. 8

[0152] According to Equation 8, the values of C.sub.F which approaches unity as .DELTA.T.sub.o decreases are provided for various .DELTA.T.sub.o in Table 2 as follows: TABLE-US-00002 TABLE 2 Volumetric thermal expansion efficiency C.sub.F of the primary fluid layer versus .DELTA.T.sub.o .DELTA.T.sub.o (K) C.sub.F (T.sub.o = 283 K) 10 0.966 50 0.850 100 0.739 150.88 0.652

1C. Equivalent Thermal Resistance of Fluid Layers

[0153] The equivalent thermal resistance of the fluid layers during volumetric thermal expansion is given by the following Equation 9: R th = h o k 1 + h o k 2 + .DELTA. .times. .times. h 1 .function. ( 1 k 1 - 1 k 2 ) Eq . .times. 9 where

[0154] k.sub.1 is the thermal conductivity of the primary fluid

[0155] k.sub.2 is the thermal conductivity of the secondary fluid.

[0156] Both fluid layers are assumed to have a similar thickness prior to thermal expansion equal to h.sub.o. Based on Equation 1 and Equation 3, the increase in the equivalent thermal resistance .DELTA.R.sub.th, the third part on the right of Equation 9, was correlated to the relative expansion in the primary fluid layer according to the following Equation 10: .eta. R .ident. .DELTA. .times. .times. R th R tho = .DELTA. .times. .times. h 1 h o .times. ( k 2 - k 1 ) ( k 1 + k 2 ) Eq . .times. 10 where R.sub.tho is the equivalent thermal resistance of both layers prior to thermal expansion.

[0157] The parameter R.sub.tho is the sum of the first two terms on the right of Equation 9. When the parameter .eta..sub.R is positive, the thermal resistance of the insulating assembly increases while it decreases as it becomes negative. Therefore, R.sub.tho represents the dimensionless increase in the thermal resistance. Various properties of different gases are provided in the following Table 3: TABLE-US-00003 TABLE 3 Various Properties of Proposed Different Gases at T = 373 K and p = 1 atm Primary fluid k (W/mK) .rho.(kg/m.sup.3) R(J/kg K) (k.sub.air - k)/(k.sub.air + k) Xenon 0.0068 4.3 64.05 0.609 Krypton 0.011 2.75 99.78 0.4359 Helium 0.181 0.13 2077 -0.732 Neon 0.0556 0.66 412.1 -0.33 Argon 0.0212 1.3 209 0.138 Air 0.028 1.2 287 0

[0158] According to Table 3, xenon can be used to enhance the insulating properties while helium is preferable to deteriorate the insulating properties especially at large operating temperatures as can be noticed from the last column in Table 3.

[0159] FIG. 4 shows the dimensionless increase in the fluid layers equivalent thermal resistance when the primary fluid layer is charged with xenon or helium while the secondary fluid layer is open to the atmosphere. Charging the primary fluid layer with xenon can provide about a 20 percent increase in the effective thermal resistance of the fluid layers with an increase of the primary fluid layer temperature by about 165 K. However, helium can produce a deterioration in the insulating properties by about 25 percent with about a 165 K increase in the primary fluid layer temperature.

1D. Heat Transfer Analysis

[0160] In the following analysis, the temperature at the lower side of the primary fluid layer was assumed to be kept under T.sub.1. See FIG. 1. The insulating substrates were assumed to have equal thicknesses and thermal conductivities which were equal to the reference thickness for the primary fluid layer h.sub.o and k.sub.ins, respectively. Accordingly, the thermal energy balance on the insulating assembly shown in FIG. 1 reveals the following relation for the temperature at the surface of the lower temperature side T.sub.e and the heat transfer q, respectively: T e = ( T 1 - T .infin. ) / h c ( 1 h c + 2 .times. h o k ins + R tho .function. ( 1 + .DELTA. .times. .times. R th R tho ) ) + T .infin. Eq . .times. 11 q = ( T 1 - T .infin. ) ( 1 h c + 2 .times. h o k ins + R tho .function. ( 1 + .DELTA. .times. .times. R th R tho ) ) Eq . .times. 12 where

[0161] h.sub.c is the convective heat transfer coefficient at the lower temperature side

[0162] T.sub..infin. is the temperature of environment facing the lower temperature side

[0163] The surface area of the insulating assembly that faces the seal is relatively small. Therefore, the heat transfer through the seal portion is neglected in Equation 11 and Equation 12. For the previous example along with h.sub.c=5 W/m.sup.2K, T.sub..infin.=275 K and k.sub.ins=0.04 W/mK, the temperature T.sub.e as a function of T.sub.1 is illustrated in FIG. 5 and FIG. 6, respectively. These figures also compare the temperature T.sub.e for the case when the thermal expansion is encountered due to the presence of flexible seals with the case where thermal expansion is not present (both fluid layer thicknesses are equal to h.sub.o for all values of T.sub.1). FIG. 5 shows that insulating properties are enhanced when xenon and flexible seals are used and that T.sub.e for this case is departing away down from the values corresponding to the case where the thermal expansion is not present. Also, this figure shows that the departure rates compared to the case where the thermal expansion is not present, increase as the temperature levels increase.

[0164] FIG. 6 shows that insulating properties are deteriorated when helium and flexible seals are used. As shown in FIG. 6 the departure of T.sub.e for this case from the results corresponding to the case with no thermal expansion is in the direction of an increase in T.sub.e. Thus, insulating properties are deteriorated at larger rates when helium and flexible seals are used especially at large operating temperatures. The thermal expansion of the primary fluid layer was computed at its average temperature. As such, an iterative procedure was implemented in generating FIG. 5 and FIG. 6 so that the obtained temperatures produce the employed thermal expansion of the primary fluid layer. Also, the volumetric thermal expansion that were used to develop FIG. 5 and FIG. 6 were evaluated from Equation 2.

[0165] FIG. 7 shows a comparison of heat flux of the insulating assembly with xenon as the primary fluid under the following two conditions: (1) in the presence of flexible seals, and (2) when thermal expansion is not present and the thickness of the fluid layers is h at all working temperatures. FIG. 7 shows a reduction in the heat flux when flexible seals are introduced. FIG. 7 also shows that the reduction rate in the heat flux increases as the working temperatures increase indicating better insulating characteristics are achieved when flexible seals are used to support the primary fluid layer while the secondary fluid layer is vented. On the other hand, an increase in the heat flux is attained when flexible seals are used to support a fluid layer comprising a fluid with relatively large thermal conductivity, such as helium, as shown in FIG. 8.

1E. Simplified Correlation

[0166] For the insulating assembly shown in FIG. 1, heat transfer can be expressed by the following Equation 13a: q = ( T 1 - T e ) ( i = 1 2 .times. ( h ins ) i ( k ins ) i + ( h o .times. .times. 1 k 1 + h o .times. .times. 2 k 2 ) ( 1 + ( k 2 - k 1 ) ( k 2 + h o .times. .times. 2 .times. k 1 / h o .times. .times. 1 ) .times. ( .DELTA. .times. .times. h 1 h o .times. .times. 1 ) ) ) Eq . .times. 13 .times. a where .DELTA.h.sub.1/h.sub.o1 can be shown to be equal to the following Equation 13b: .DELTA. .times. .times. h 1 h o .times. .times. 1 = ( T o + .DELTA. .times. .times. T o 2 .times. .times. .DELTA. .times. .times. T o ) .function. [ 4 .times. ( T 1 * - T o ) .times. .DELTA. .times. .times. T o ( T o + .DELTA. .times. .times. T o ) 2 + 1 - 1 ] Eq . .times. 13 .times. b where

[0167] h.sub.o1 is the reference primary fluid layer thickness

[0168] h.sub.o2 is the reference secondary fluid layer thickness

[0169] (h.sub.ins).sub.i is the thickness of the i.sup.th insulating substrate

[0170] (k.sub.ins).sub.i is the thermal conductivity of the i.sup.th insulating substrate

[0171] T.sub.o is the primary fluid layer temperature that causes the primary fluid pressure to be equal to the atmospheric pressure

[0172] T.sub.1* represents the average primary fluid layer temperature

[0173] The parameter T.sub.1* can be measured experimentally or determined theoretically using an iterative scheme. Equation 13a is based on the assumption that the heat transfer through the flexible seals is negligible when compared to the total heat transferred through the insulating assembly.

[0174] The solution of Equation 13a and Equation 13b can be used to produce pertinent engineering correlations. For example, percentage difference between the heat flux including thermal expansion effects and the heat flux at reference condition, q.sub.ref, where thermal expansion is ignored, and correlated to T.sub.1, T.sub.e, T.sub.o, k.sub.1 and .DELTA.T.sub.o. The obtained family of correlations has the following functional form: ( q ref - q ) q ref 100 .times. % = [ a - b .function. ( T o ) - c .function. ( .DELTA. .times. .times. T o ) - d .function. ( k 1 ) + e .function. ( T e .times. T o .times. .DELTA. .times. .times. T o .times. k 1 ) ] .times. ( T 1 - T o ) m .times. ( T e 270 ) n Eq . .times. 14

[0175] where a, b, c, d, e, m, n and the correlation coefficient R.sup.2 for different values of h.sub.o1 are listed in Table 4 as follows: TABLE-US-00004 TABLE 4 Coefficients of Equation 14 for different h.sub.o1 h.sub.o1 (m) Coefficients R.sup.2 0.004 a = 0.559, b = 1.08 .times. 10.sup.-3, c = 5.14 .times. 10.sup.-4, 0.980 d = 11.572, e = 2.74 .times. 10.sup.-7, m = 0.850, n = 0.1.789 0.006 a = 0.591, b = 1.17 .times. 10.sup.-3, c = 5.26 .times. 10.sup.-4, 0.983 d = 11.399, e = 2.71 .times. 10.sup.-7, m = 0..847, n = 1.880 0.008 a = 0.610, b = 1.23 .times. 10.sup.-3, c = 5.32 .times. 10.sup.-4, 0.984 d = 11.295, e = 2.69 .times. 10.sup.-7, m = 0.845, n = 1.934

This correlation was obtained over the following range of parameter variations:

[0176] 310<T.sub.1<400 K, 270<T.sub.o<290 K, 50<.DELTA.T.sub.o<150 K, 270<T.sub.e<300 K, 0.001<k.sub.1<0.017 W/m K , h o .times. .times. 2 = h 0 .times. .times. 1 , i = 1 2 .times. ( h ins ) i ( k ins ) i = 0.2 .times. .times. m 2 .times. K / W , and .times. .times. k 2 = 0.028 .times. .times. W / m .times. .times. K . 1F. Examples of Insulating Assemblies with Maximum Enhanced Insulating Properties

[0177] FIG. 9 shows a more advanced insulating assembly comprising an array of primary and secondary fluid layers supported by flexible seals. The secondary fluid layers are vented to the external atmosphere in order to provide maximum volumetric thermal expansion of primary fluid layers. Accordingly, the insulating properties are enhanced for the assembly provided that the primary fluid possesses relatively lower thermal conductivity than the secondary fluid which is the air. The insulating assembly of FIG. 9A shows the frame of the insulating assembly supported by a flexible seal, thereby allowing for additional volumetric thermal expansion for the primary fluids, thereby resulting in further enhancements of insulating properties, an increase in the effective thermal resistance of the assembly. In an alternative embodiment, soft elastic balloons having minimized stiffness and containing fluids with minimized thermal conductivities within the secondary fluid layer may be used and placed in a vented layer as shown in FIG. 9B and FIG. 9C. In this arrangement the primary fluid layer is eliminated and is suitable for lower heat flux applications. The degree of enhancements in the insulating properties of the insulating assemblies of the present invention are governed by the temperature levels that the flexible seals can sustain before melting. Thus, flexible seals having high melting points are preferably used for insulating assemblies for high temperature applications. The compositions and thus the melting points of the flexible seals of the present invention suitable for desired temperature conditions may be readily selected by one skilled in the art using known methods.

2. Flow and Heat Transfer Inside Thin Films Supported by Flexible Seals in the Presence of Internal and External Pressure Pulsations

[0178] As provided herein, the effects of both external squeezing and internal pressure pulsations were studied on flow and heat transfer inside non-isothermal and incompressible thin films supported by flexible seals. The laminar governing equations were non-dimensionalized and reduced to simpler forms. The upper substrate (mobile and inflexible substrate) displacement was related to the internal pressure through the elastic behavior of the supporting seals. The following parameters: squeezing number, squeezing frequency, frequency of pulsations, fixation number (for the seal) and the thermal squeezing parameter are the main controlling parameters. Accordingly, their influences on flow and heat transfer inside disturbed thin films were determined and analyzed. As provided herein, an increase in the fixation number results in more cooling and a decrease in the average temperature values of the primary fluid layer. Also, an increase in the squeezing number decreases the turbulence level at the upper substrate. Furthermore, fluctuations in the heat transfer and the fluid temperatures may be maximized at relatively lower frequency of internal pressure pulsations.

[0179] The following Table 5 provides the various symbols and meanings used in this section: TABLE-US-00005 TABLE 5 B Thin film length c.sub.p specific heat of the fluid d.sub.s effective diameter of the seal E modulus of elasticity for the seal's material F.sub.n fixation number H, h, h.sub.o dimensionless, dimensional and reference thin film thickness h.sub.c convective heat transfer coefficient k thermal conductivity of the fluid Nu.sub.L, Nu.sub.U lower and upper substrates Nusselt numbers P.sub.S thermal squeezing parameter p fluid pressure q reference heat flux at the lower substrate for UHF T, T.sub.1 temperature in fluid and the inlet temperature T.sub.2 temperature at the lower and the upper substrates for CWT t time V.sub.o reference axial velocity U, u dimensionless and dimensional axial velocities V, v dimensionless and dimensional normal velocities X, x dimensionless and dimensional axial coordinates Y, y dimensionless and dimensional normal coordinates .alpha. thermal diffusivity for the fluid .beta., .beta..sub.p dimensionless squeezing motion and pressure pulsation amplitudes .epsilon. perturbation parameter .gamma., .gamma..sub.p dimensionless squeezing motion and pressure pulsation frequencies .mu. dynamic viscosity of the fluid .theta., .theta..sub.m dimensionless temperature and dimensionless mean bulk temperature .theta..sub.W dimensionless temperature at the lower substrate (UHF) .rho. density of the fluid .tau. dimensionless time .sigma. squeezing number .omega. reciprocal of a reference time (reference squeezing frequency) .eta. variable transformation for the dimensionless Y-coordinate .THETA. dimensionless heat transfer parameter (CWT) .PI. dimensionless pressure .PI..sub.i, .PI..sub.o dimensionless inlet pressure and dimensionless mean pressure

[0180] In certain thin film applications, external disturbances, such as unbalances in rotating machines or pulsations in external ambient pressures due to many disturbances, can result in an oscillatory motion at the upper substrate boundary. In addition to external disturbances, internal pressure pulsations such as irregularities in the pumping process, can produce similar oscillatory motion. Even small disturbances on the substrates of the thin film can have a substantial impact on the cooling process as the thickness of thin films is very small. These disturbances are even more pronounced if the thin film is supported by flexible seals. Accordingly, the dynamics and thermal characterization of thin films will be altered.

[0181] The chambers for chemical and biological detection systems such as fluidic cells for chemical or biological microcantilever probes are examples of thin films. See Lavrik et al. (2001) Biomedical Devices 3(12):35-44, which is herein incorporated by reference.

[0182] Small turbulence levels that can be introduced into these cells by either flow pulsating at the inlet or external noise that may be present at the boundaries which result in a vibrating boundary can produce flow instabilities inside the fluidic cells. These disturbances substantially effect the measurements of biological probes, such as microcantilevers which are very sensitive to flow conditions.

[0183] The flow inside squeezed thin films, such as the flow inside isothermal oscillatory squeezed films with fluid density varying according to the pressure, has been studied. See Langlois (1962) Quarterly of Applied Math. XX:131-150, which is herein incorporated by reference. The heat transfer inside squeezed thin films (not oscillatory type) has been analyzed. See Hamza (1992) J. Phys. D: Appl. Phys. 25:1425-1431, Bhattacharyya et al. (1996) Numerical Heat Transfer, Part A 30:519-532, and Debbaut (2001) J. Non-Newtonian Fluid Mech. 98:15-31, which are herein incorporated by reference. The flow and heat transfer inside incompressible oscillatory squeezed thin films has been analyzed. See Khaled & Vafai (2002) Numerical Heat Transfer Part A 41:451-467, which is herein incorporated by reference. The effects of internal pressure pulsations have been studied on flow and heat transfer inside channels. See Hemida et al. (2002) Int. J. Heat Mass Transfer 45:1767-1780, and Joshi et al. (1985) J. Fluid Mech. 156:291-300, which are herein incorporated by reference.

[0184] Unfortunately, the prior art fails to account for the effects of both internal and external pressure pulsations on flow and heat transfer inside thin films, wherein the gap thickness will be a function of both pulsations.

[0185] Therefore, as provided herein, the upper substrate of a thin film was considered to be subjected to both external squeezing effects and the internal pressure pulsations. The influence of internal pressure pulsations on the displacement of the upper substrate was determined by the theory of linear elasticity applied to the seal supporting the substrates of an incompressible non-isothermal thin film. The laminar governing equations for flow and heat transfer were properly non-dimensionalized and reduced into simpler equations. The resulting equations were then solved numerically to determine the effects of external squeezing, internal pressure pulsations and the strength of the seal on the turbulence inside the disturbed thin films as well as on thermal characteristics of these thin films.

2A. Problem Formulation

[0186] A two dimensional thin film that has a small thickness, h, compared to its length, B, was considered. The x-axis was taken in the direction of the length of the thin film while y-axis was taken along the thickness as shown in FIG. 10. The width of the thin film, D, was assumed to be large enough such that two dimensional flow inside the thin film can be assumed. The lower substrate of the thin film was fixed (immobile and inflexible substrate) while the vertical motion of the upper substrate (mobile and inflexible substrate) was assumed to have sinusoidal behavior when the thin film gap was not charged with the working fluid. This motion due to only external disturbances is expressed according to the following Equation 15: h=h.sub.o(1-.beta. cos(.gamma..omega.t)) Eq. 15 where

[0187] .gamma. is the dimensionless frequency

[0188] .beta. is the dimensionless upper substrate motion amplitude

[0189] .omega. is a reference frequency.

The fluid was assumed to be Newtonian with constant properties.

[0190] The general two-dimensional continuity, momentum and energy equations for the laminar thin film are given as follows: .differential. u .differential. x + .differential. v .differential. y = 0 Eq . .times. 16 .rho. .function. ( .differential. u .differential. t + u .times. .differential. u .differential. x + v .times. u y ) = - .differential. p .differential. x + .mu. .function. ( .differential. 2 .times. u .differential. x 2 + .differential. 2 .times. u .differential. y 2 ) Eq . .times. 17 .rho. .function. ( .differential. v .differential. t + u .times. .differential. v .differential. x + v .times. .differential. v .differential. y ) = - .differential. p .differential. y + .mu. .function. ( .differential. 2 .times. v .differential. x 2 + .differential. 2 .times. v .differential. y 2 ) Eq . .times. 18 .rho. .times. .times. c p .function. ( .differential. T .differential. t + u .times. .differential. T .differential. x + v .times. .differential. T .differential. y ) = k .function. ( .differential. 2 .times. T .differential. x 2 + .differential. 2 .times. T .differential. y 2 ) Eq . .times. 19 where

[0191] T is the fluid temperature

[0192] .rho. is the density

[0193] p is the pressure

[0194] .mu. is the dynamic viscosity

[0195] c.sub.p is the specific heat

[0196] k is the thermal conductivity of the fluid

[0197] Equations 16-19 are non-dimensionalized using the following dimensionless variables: X = x B Eq . .times. 20 .times. a Y = y h o Eq . .times. 20 .times. b .tau. = .omega. .times. .times. t Eq . .times. 20 .times. c U = u ( .omega. .times. .times. B + V o ) Eq . .times. 20 .times. d V = v h o .times. .omega. Eq . .times. 20 .times. e .PI. = p - p e .mu. .function. ( .omega. + V o B ) .times. - 2 Eq . .times. 20 .times. f where

[0198] T.sub.1 is the inlet temperature of the fluid

[0199] V.sub.o is a constant representing a reference dimensional velocity

[0200] As provided in the above equations, .DELTA.T is equal to T.sub.2-T.sub.1 for constant wall temperature conditions (CWT), T.sub.2 will be the temperature of both lower and upper substrates, and is equal to qh o k for uniform wall heat flux conditions (UHF). The variables X, Y, .tau., U, V, .PI. and .theta. are the dimensionless forms of x, y, t, u, v, p and T variables, respectively. The above transformations except for dimensionless temperature have been used in the art along with the perturbation parameter .epsilon. = h o B . See Langlois (1962) Quarterly of Applied Math. XX: 131-150, which is herein incorporated by reference.

[0201] Most flows inside thin films are laminar and could be creep flows especially in lubrications and biological applications. Therefore, the low Reynolds numbers flow model was adopted here. The application of this model to Equations 16-19 results in the following reduced non-dimensionalized equations: U = 1 2 .times. .differential. .PI. .differential. X .times. ( Y ) .times. ( Y - H ) Eq . .times. 21 .differential. U .differential. X + .sigma. 12 .times. .differential. V .differential. Y = 0 Eq . .times. 22 .differential. .differential. X .times. ( H 3 .times. .differential. .PI. .differential. X ) = .sigma. .times. .differential. H .differential. .tau. Eq . .times. 23 P S .function. ( .differential. .theta. .differential. .tau. + 12 .sigma. .times. U .times. .differential. .theta. .differential. X + V .times. .differential. .theta. .differential. y ) = 2 .times. .differential. 2 .times. .theta. .differential. X 2 + .differential. 2 .times. .theta. .differential. y 2 Eq . .times. 24 where

[0202] .sigma. is the squeezing number

[0203] P.sub.S is the thermal squeezing parameter

[0204] The squeezing number and the thermal squeezing parameter are defined as: .sigma. = 12 1 + V o .omega. .times. .times. B Eq . .times. 25 .times. a P S = .rho. .times. .times. c p .times. h o 2 .times. .omega. k Eq . .times. 25 .times. b

[0205] The inlet dimensionless pulsating pressure is considered to have the following relation: .PI..sub.i=.PI..sub.o(1+.alpha..sub.p sin(.gamma..sub.p.omega.t+.phi..sub.p)) Eq. 26 where

[0206] .beta..sub.p is the dimensionless amplitude in the pressure

[0207] .PI..sub.i is the inlet dimensionless pressure

[0208] .PI..sub.o is the mean dimensionless pressure

[0209] .gamma..sub.p is the dimensionless frequency of the pressure pulsations parameter

[0210] .phi..sub.p is a phase shift angle parameter

[0211] Due to both pulsations in internal pressure and external disturbances, the dimensionless film thickness H, (H=h/h.sub.o), can be represented by Equation 27 by noting the principle of superposition: H=1-.beta. cos(.gamma..omega.t)+H.sub.p Eq. 27 where H.sub.p is the dimensionless deformation of the seals resulting from pulsations in the internal pressure.

[0212] The lower substrate was assumed to be fixed (immobile and inflexible substrate) and that the upper substrate (mobile and inflexible substrate) of the thin film is rigid such that the magnitude of the deformation in the seals is similar to displacement of the upper substrate (mobile and inflexible substrate). The dimensionless deformation in the seals due to variations in the external pressure is the second term of Equation 27 on the right. The dimensionless frequency .gamma. is allowed to be different than .gamma..sub.p.

[0213] The dimensionless pressure gradient inside the thin film as a result of the solution to the Reynolds Equation 23 is: .differential. .PI. .differential. X = .sigma. H 3 .times. d H d .tau. .times. ( X - 1 2 ) - .PI. o .function. ( 1 + .beta. p .times. sin .function. ( .gamma. p .times. .tau. + .phi. p ) ) Eq . .times. 28

[0214] The reference velocity V.sub.o that was used to define the dimensionless pressure, axial dimensionless velocity and the squeezing number was taken to be related to the average velocity, u.sub.m, inside the thin film at zero .beta. and .beta..sub.p and the dimensionless thickness of the thin film that results from the application of the corresponding inlet mean pressure, H.sub.m, through the following relation: V o = u m H m 2 Eq . .times. 29

[0215] The previous scaled reference velocity is only a function of the mean pressure, viscosity and the reference dimensions of the thin film and results in the following relation between the inlet mean dimensionless pressure to the squeezing number: .PI..sub.o=12-.sigma. Eq. 30

[0216] Accordingly, the dimensionless pressure gradient, the dimensionless pressure and the average dimensionless pressure .PI..sub.AVG inside the thin film were related to the squeezing number through the following equations: .differential. .PI. .function. ( X , .tau. ) .differential. X = .sigma. H 3 .times. d H d .tau. .times. ( X - 1 2 ) - ( 12 - .sigma. ) .times. ( 1 + .beta. p .times. sin .function. ( .gamma. p .times. .tau. + .phi. p ) ) Eq . .times. 31 .PI. .function. ( X , .tau. ) = .sigma. 2 .times. H 3 .times. d H d .tau. .times. ( X 2 - X ) - ( 12 - .sigma. ) .times. ( 1 + .beta. p .times. sin .function. ( .gamma. p .times. .tau. + .phi. p ) ) .times. ( X - 1 ) Eq . .times. 32 .PI. AVG .function. ( .tau. ) = - .sigma. 12 .times. H 3 .times. d H d .tau. + ( 12 - .sigma. ) 2 .times. ( 1 + .beta. p .times. sin .function. ( .gamma. p .times. .tau. + .phi. p ) ) Eq . .times. 33

[0217] The displacement of the upper substrate due internal pressure pulsations was related to the .PI..sub.AVG through the theory of linear elasticity by the following relation: H.sub.p=F.sub.n.PI..sub.AVG Eq. 34 where F.sub.n is equal to F n = .mu. .function. ( V o + .omega. .times. .times. B ) E .times. .times. 2 .times. d s Eq . .times. 35

[0218] The parameters E and d.sub.s in the previous equation are the modulus of elasticity of the flexible seals of the present invention and a characteristic dimension for the seal, respectively. The quantity d.sub.s is equal to the effective diameter of the seal's cross section times the ratio of the length of the seals divided by the thin film width. The effective diameter for seals having square cross section is equal to h.sub.o. The term F.sub.n will be called the fixation number of the thin film.

[0219] The fixation parameter F.sub.n represents a ratio between viscous shear force inside thin films to the elastic forces of the flexible seals. Moreover, Equation 34 is based on the assumption that transient behavior of the seal's deformation is negligible. The values of F.sub.n are about 0.001 to about 0.1 for long thin films supported by flexible seals.

[0220] The first set of dimensionless boundary conditions used were for constant wall temperatures (CWT) at both the lower and the upper substrates while the second set used assumed that the lower substrate was at uniform wall heat flux conditions (UHF) and the upper substrate is insulated. As such the dimensionless boundary conditions can be written as: .theta. .function. ( X , Y , 0 ) = 0 , .theta. .function. ( 0 , Y , .tau. ) = 0 , .theta. .function. ( X , 0 , .tau. ) = 1 .times. .times. .theta. .function. ( X , H , .tau. ) = 1 , .differential. .differential. X .times. ( 1 - .theta. .function. ( 1 , Y , .tau. ) 1 - .theta. m .function. ( 1 , .tau. ) ) = 0 .times. .times. CWT Eq . .times. 36 .theta. .function. ( X , Y , 0 ) = 0 , .theta. .function. ( 0 , Y , .tau. ) = 0 , .differential. .theta. .function. ( X , 0 , .tau. ) .differential. Y = - 1 .times. .times. .differential. .theta. .function. ( X , H , .tau. ) .differential. Y = 0 , .differential. .theta. .function. ( 1 , Y , .tau. ) .differential. X = .sigma. 12 .times. U m .times. ( 1 P S .times. H - .differential. .theta. .function. ( 1 , Y , .tau. ) .differential. .tau. ) .times. .times. UH .times. .times. F Eq . .times. 37

[0221] The last condition of Equation 36 is based on the assumption that the flow at the exit of the thin film is thermally fully developed. Moreover, the last thermal condition of Equation 37 was derived based on an integral energy balance at the exit of the thin film realizing that the axial conduction is negligible at the exit. The calculated thermal parameters considered were the Nusselt numbers at the lower and upper substrates, and the dimensionless heat transfer from the upper and lower substrates, .THETA., for CWT conditions, which are defined according to the following equations: .times. Nu U .function. ( X , .tau. ) .ident. h c .times. h o k = 1 1 - .theta. m .function. ( X , .tau. ) .times. .differential. .theta. .function. ( X , H , .tau. ) .differential. Y .times. .times. CWT .times. .times. Nu L .function. ( X , .tau. ) .ident. h c .times. h o k = - 1 1 - .theta. m .function. ( X , .tau. ) .times. .differential. .theta. .function. ( X , 0 , .tau. ) .differential. Y .times. .times. .times. .THETA. .function. ( X , .tau. ) = ( .differential. .theta. .function. ( X , H , .tau. ) .differential. Y - .differential. .theta. .function. ( X , 0 , .tau. ) .differential. Y ) Eq . .times. 38 UH .times. .times. F .times. .times. Nu 1 .function. ( X , .tau. ) .ident. h c .times. h o k = 1 .theta. .function. ( X , 0 , .tau. ) - .theta. m .function. ( X , .tau. ) Eq . .times. 39 where .theta.m and Um are the dimensionless mean bulk temperature and the dimensionless average velocity at a given section and are defined as follows: .theta. m .function. ( X , .tau. ) = 1 U m .function. ( X , .tau. ) .times. H 0 .times. .intg. 0 H .times. U .function. ( X , Y , .tau. ) .times. .theta. .function. ( X , Y , .tau. ) .times. d Y .times. .times. U m .function. ( X , .tau. ) = 1 H .times. .intg. 0 H .times. U .function. ( X , Y , .tau. ) .times. d Y Eqs . .times. 40 .times. a , 40 .times. b

[0222] Due to symmetric flow and thermal conditions for CWT, Nusselt numbers at lower and upper substrates were expected to be equal.

2B. Numerical Methods

[0223] The dimensionless thickness of the thin film was determined by solving Equations 27, 33 and 34 simultaneously. Accordingly, the velocity field, U and V, was determined from Equations 21 and 22. The reduced energy equation, Equation 24, was then solved using the Alternative Direction Implicit techniques (ADI) known in the art by transferring the problem to one with constant boundaries using the following transformations: .tau.*=.tau., .xi.=X and .eta. = Y H . Iterative solution was employed for the .xi.-sweep of the energy equation for CWT conditions so that both the energy equation and the exit thermal condition, last condition of Equation 36, are satisfied. The values of 0.008, 0.03, 0.002 were chosen for .DELTA..xi., .DELTA..eta. and .DELTA..tau.*. 2C. Effects of Pressure Pulsations on the Dimensionless Film Thickness

[0224] FIG. 11 and FIG. 12 describe the importance of the fixation number F.sub.n on the dimensionless film thickness H and the dimensionless normal velocity at the upper substrate V(X,H,.tau.), respectively. As F.sub.n increases, H and absolute values of V(X,H,.tau.) increase. Soft (flexible seals) fixations have large F.sub.n values. Increases in the viscosity and flow velocities or a decrease in the thin film thickness, perturbation parameter and the seal's modulus of elasticity increase the value of F.sub.n as provided by Equation 35.

[0225] The effects of pressure pulsations on H are clearly seen for large values of F.sub.n as shown in FIG. 11 and FIG. 12. At these values, the frequency of the local maximum or minimum of H is similar to the frequency of the pressure pulsations as seen from FIG. 11. Further, the degree of turbulence at the upper substrate is increased when F.sub.n increases as shown in FIG. 12. The degree of turbulence at the upper substrate refers to the degree of fluctuations at the upper substrate and the number of local maximum and minimum in V(X,H,.tau.). This is also obvious when the values of .gamma..sub.p increase as shown in FIG. 13. The increase in turbulence level at the upper substrate may produce back flows inside the thin film at large values of .gamma..sub.p, which will have an effect on the function of a thin film such as those used as chambers in detection and sensing devices.

[0226] For .sigma.=12 where the time average of the average gage pressure inside the thin film is zero, the variation in H decreases as F.sub.n increases. This effect can be seen from Equation 33 and Equation 34 and will cause reductions in the flow and in the cooling process. However, the mean value of .PI..sub.AVG is always greater than zero for other values of .sigma. which causes an increase in the mean value of H as F.sub.n increases resulting in an increase in the mean value of the flow rate inside the thin film.

[0227] FIG. 14 shows the effects of the squeezing number .sigma. on H. Small values of .sigma. indicates that the thin film is having relatively large inlet flow velocities and therefore large pressure gradients and large values of .PI..sub.o. Accordingly, H increases as .sigma. decreases as seen in FIG. 14. Further, the degree of turbulence at the upper substrate increases as .sigma. decreases. This is shown in FIG. 15. The changes in the pressure phase shift results in similar changes in the dimensionless thin film thickness phase shift as shown in FIG. 16.

2D. Effects of Pressure Pulsations on Heat Transfer Characteristics of the Thin Film

[0228] FIG. 17 and FIG. 18 illustrate the effects of F.sub.n and P.sub.S on the dimensionless mean bulk temperature .theta..sub.m and the average lower substrate temperature .theta..sub.W, average of .theta.(X,0,.tau.), for constant wall temperature CWT and uniform heat flux UHF conditions, respectively. As F.sub.n increases when softer flexible seals are used, the induced pressure forces inside the thin film due to internal pressure pulsations will increase the displacement of the upper substrate (mobile and inflexible substrate) as shown before. This enables the thin film to receive larger flow rates since the insulating assemblies in these figures have similar values for the dimensionless pressure at the inlet. Thus, there is more cooling to the substrates results as F.sub.n increases resulting in a decrease in the .theta..sub.m and average .theta..sub.W values and their corresponding fluctuations for CWT and UHF conditions, respectively. The effect of the thermal squeezing parameter P.sub.S on the cooling process is also shown in FIG. 17 and FIG. 18. The cooling at the substrates is enhanced as P.sub.S increases.

[0229] FIG. 19 and FIG. 20 show the effects of F.sub.n on the Nusselt number at the lower substrate Nu.sub.L for CWT and UHF conditions, respectively. The irregularity in Nu.sub.L decrease as F.sub.n decreases because the upper substrate will not be affected by the turbulence in the flow if the flexible seals have relatively large modulus of elasticity. In other words, the induced flow due to the upper substrate motion is reduced as F.sub.n decreases resulting in less disturbances to the flow inside the thin film. This can be seen in FIG. 21 for UHF conditions where Nu.sub.L reaches a constant value at low values of F.sub.n after a certain distance from the inlet. The values of Nu.sub.L and the corresponding fluctuations are noticed to decrease as F.sub.n increases.

[0230] FIG. 22 and FIG. 23 illustrate the effects of dimensionless frequency of the inlet pressure pulsations .gamma..sub.p on the average dimensionless heat transferred from the substrates .THETA. and the average .theta..sub.W for CWT and UHF conditions, respectively. The figures show that the mean value of .THETA. and .theta..sub.W are unaffected by .gamma..sub.p and that the frequency of the average values of .THETA. and .theta..sub.W increase as .gamma..sub.p increases. FIG. 24 describes the effects of .gamma..sub.p on the fluctuation in the average .THETA. and .theta..sub.W, half the difference between the maximum and the minimum values of the average .THETA. and .theta..sub.W. The effects of .gamma..sub.p on the fluctuation in the average .THETA., .delta..THETA., and the fluctuation in the average .theta..sub.W, .delta..theta..sub.W, are more pronounced at lower values of .gamma..sub.p as shown in FIG. 24.

[0231] Flow and heat transfer inside externally oscillatory squeezed thin films supported by flexible seals in the presence of inlet internal pressure pulsations were analyzed. The governing laminar continuity, momentum and energy equations were properly non-dimensionalized and reduced to simpler forms for small Reynolds numbers. The reduced equations were solved by the alternative direction implicit (ADI) method. The turbulence level at the upper substrate increases by increases in both the fixation number and the frequency of the internal pressure pulsations. However, an increase in the squeezing number decreases the turbulence level at the upper substrate. The fluid temperatures and the corresponding fluctuations were found to decrease when the fixation number and the thermal squeezing parameter were increased for both CWT and UHF conditions. Finally, fluctuations in the heat transfer and the fluid temperatures were more pronounced at lower frequency of internal pressure pulsations.

3. Control of Exit Flow and Thermal Conditions Using Two-Layered Thin Films Supported by Flexible Complex Seals

[0232] Although thin films are characterized by having laminar flows with relatively low Reynolds numbers leading to stable hydrodynamic performance, the thickness of the thin films is small enough such that small disturbances at one of the boundaries may cause a significant squeezing effect at the boundary. See e.g. Langlois (1962) Quarterly of Applied Math. XX:131-150 (flow inside isothermal oscillatory squeezed films with fluid density varying with the pressure), Khaled & Vafai (2002) Numerical Heat Transfer, Part A 41:451-467 and Khaled & Vafai (2003) Int. J. Heat and Mass Transfer 46:631-641 (flow and heat transfer inside incompressible thin films having a prescribed oscillatory squeezing at one of their boundaries), and Khaled & Vafai (2002) Int. J. Heat and Mass Transfer 45:5107-5115 (internal pressure through the elastic behavior of the supporting seal), which are herein incorporated by reference.

[0233] Recently, the situation where the squeezing effect at the free substrate is initiated by thermal effects was studied. See Khaled & Vafai (2003) ASME J. Heat Transfer 125:916-925, which is herein incorporated by reference. As provided herein, flexible seals with closed cavities of stagnant fluids having a relatively large volumetric thermal expansion coefficient, flexible complex seal, were studied. Flexible complex seals in a single layer thin film can cause flooding of the coolant when the thermal load of the thin film is increased over its projected capacity. As a result, an enhancement in the cooling process is attained especially if ultrafine suspensions are present in the coolant, a fluid that exhibits high heat transfer performance. Ultrafine suspensions in the fluid such as copper or aluminum particles with diameters of order nanometer are found to enhance the effective thermal conductivity of the fluid. See Eastman et al. (2001) Applied Physics Letters 78: 718-720, which is herein incorporated by reference.

[0234] As provided herein, the flow and heat transfer inside an oscillatory disturbed two-layered thin film channel supported by flexible complex seals in the presence of suspended ultrafine particles was studied. Oscillatory generic disturbances were imposed on the two-layered thin film channels supported by flexible complex seals in the presence of suspended ultrafine particles, which correspond to disturbances in the upper substrate temperature and in the inlet pressure of the secondary fluid layer. The governing continuity, momentum and energy equations for both layers were non-dimensionalized and categorized for small Reynolds numbers and negligible axial conduction. The deformation of the supporting seals was linearly related to both the pressure difference across the two layers and the upper substrate's temperature based on the theory of the linear elasticity and the principle of the volumetric thermal expansion of the stagnant fluid filling the closed cavities of the flexible complex seals.

[0235] As provided herein, the flow rate and heat transfer in the main thin film channel can be increased by an increase in the softness of the seals, the thermal squeezing parameter, the thermal dispersion effect and the total thickness of two-layered thin film. However, the flow rate and heat transfer in the main thin film channel decrease as the dimensionless thermal expansion coefficient of the seals and the squeezing number of the primary fluid layer increase. Both the increase in thermal dispersion and the thermal squeezing parameter for the secondary fluid layer were found to increase the stability of the intermediate or the mobile and inflexible substrate. Furthermore, the two-layered thin film channel was found to be more stable when the secondary fluid flow was free of pulsations or it had relatively a large pulsating frequency. Finally, the proposed two-layered thin film supported by flexible complex seals, unlike other controlling systems, does not require additional mechanical control or external cooling devices, i.e. is self-regulating for the flow rate and temperature of a primary fluid layer.

[0236] The following Table 6 provides the various symbols and meanings used in this section: TABLE-US-00006 TABLE 6 B thin film length C.sub.F correction factor for the volumetric thermal expansion coefficient c.sub.p specific heat of the fluid D width of the thin film E* softness index of seals supporting the intermediate or mobile and inflexible substrate G width of closed cavity containing stagnant fluid H.sub.t dimensionless total thickness of the two-layered thin film F.sub.T dimensionless coefficient of the thermal expansion for the complex seal H, h, h.sub.o dimensionless, dimensional and reference thin film thickness h.sub.c convective heat transfer coefficient K* effective stiffness of the sealing k thermal conductivity of the fluid k.sub.o reference thermal conductivity of the fluid Nu lower substrate's Nusselt number P.sub.S thermal squeezing parameter p fluid pressure q.sub.o reference heat flux at the lower substrate for UHF T, T.sub.o temperature in fluid and the inlet temperature t time V.sub.o reference axial velocity U, U.sub.m dimensionless axial and average axial velocities u dimensional axial velocity V, v dimensionless and dimensional normal velocities X, x dimensionless and dimensional axial coordinates Y, y dimensionless and dimensional normal coordinates .alpha. thermal diffusivity of the fluid .beta..sub.q dimensionless amplitude of the thermal load .beta..sub.p dimensionless amplitude of the pressure .beta..sub.T coefficient of volumetric thermal expansion .epsilon. perturbation parameter .phi..sub.p phase shift angle .gamma. dimensionless frequency of the thermal load .gamma..sub.p dimensionless frequency of the internal pressure .mu. dynamic viscosity of the fluid .theta., .theta..sub.m dimensionless temperature and dimensionless mean bulk temperature .rho. density of the fluid .tau., .tau.* dimensionless time .sigma. squeezing number .omega. reciprocal of a reference time (reference squeezing frequency) .eta. variable transformation for the dimensionless Y-coordinate .lamda. dimensionless dispersion parameter .PI. dimensionless pressure .PI..sub.n dimensionless inlet pressure .LAMBDA. reference lateral to normal velocity ratio Subscripts i i.sup.th layer l lower substrate P due to pressure T due to thermal expansion u upper substrate

[0237] The present invention provides flexible complex seals. The flexible complex seals may be used in two-layered thin films are utilized in order to regulate the flow rate of the primary fluid layer such that excessive heating in the second layer results in a reduction in the primary fluid flow rate. The flexible complex seals of the present invention may be used in internal combustion applications where the fuel flow rate should be reduced as an engine gets overheated. The flexible complex seals of the present invention may be used to minimize bimaterial effects of many biosensors that are sensitive to heat and flow conditions. See Fritz et al. (2000) Science 288:316-318, which is herein incorporated by reference.

3A. Problem Formulation and Analysis

[0238] FIG. 25 shows a two-layered thin film supported by flexible complex seals. The lower layer contains the primary fluid flow passage where the lower substrate is fixed (immobile and inflexible substrate) and the upper substrate is insulated and free to move in the vertical direction (mobile and inflexible substrate). The primary fluid flow is that of a fluid sample, such as the fuel flow or fuel-air mixture prior to combustion or flow of a biofluid in a fluidic cell. The upper layer of the thin film contains a secondary fluid flow parallel or counter to the primary fluid flow direction. This flow can have similar properties as the primary fluid flow. This insulating assembly is suitable for fluidic cell applications since inlet pressure pulsations will be equal across the intermediate substrate, thereby eliminating disturbances at the intermediate substrate. The secondary fluid flow, however, can have different properties than the primary fluid flow. For example, when the secondary fluid flow is initiated from external processes such as flow of combustion residuals or the engine coolant flow.

[0239] The heat flux of the upper substrate can be independent of the primary fluid flow or can be the result of external processes utilizing the primary fluid flow as in combustion processes. The latter can be used for controlling the primary fluid flow conditions while the former may model the increase in the ambient temperature in a fluidic cell application, thereby preventing an increase in the average fluid temperature in an ordinary fluidic cell avoiding a malfunctioning of a device such as a biosensor.

[0240] The sealing assembly of the upper layer contains flexible complex seals, closed cavities filled with a stagnant fluid having a relatively large volumetric thermal expansion coefficient. The upper layer also contains flexible seals in order to allow the intermediate substrate to move in the normal direction. Any excessive heating at the upper substrate results in an increase in the upper substrate's temperature such that the stagnant fluid becomes warmer and expands. This expansion along with the increase in inlet pressure in the upper layer, if present, cause the intermediate substrate to move downward. Thus, a compression in the film thickness of the lower layer is attained resulting in reduction in mass flow rate within the primary fluid flow compartment. This insulating assembly may be used to control combustion rates since part of the excessive heating and increased pressure due to deteriorated combustion conditions can be utilized to prescribe the heat flux at the upper substrate. Thus, the flow rate of the fuel in the primary fluid layer can be reduced and combustion is controlled.

[0241] In fluidic cells, excessive heating at the upper substrate causes compression to the primary fluid layer's thickness. Thus, average velocity in the primary fluid layer increases, when operated at constant flow rates, enhancing the convective heat transfer coefficient. This causes the average fluid temperature to approach the lower substrate temperature, thereby reducing the bimaterial effects. When it is operated at a constant pressure or at a constant velocity, the compression of the primary fluid layer due to excessive heating at the upper substrate reduces the flow rate. Thus, the fluid temperatures approach the lower substrate temperature at a shorter distance. As such, bimaterial effects are also reduced. The flexible seals can be placed between guiders as shown in FIG. 25B. The use of guiders for the flexible seals, including flexible complex seals, of the present invention minimize side expansion and maximize the transverse thin film thickness expansion.

[0242] As provided herein, upper and lower thin films that have small thicknesses h.sub.1 and h.sub.2, respectively, compared to their length B and their width D.sub.1 and D.sub.2, respectively, were analyzed. The x-axis for each layer is taken along the axial direction of the thin film while y-axis for each layer is taken along its thickness as shown in FIG. 25B. Further, the film thickness was assumed to be independent of the axial direction. For example, as in symmetric thin films having a fluid injected from the center as shown in FIG. 25A.

[0243] Both lower and upper substrates were assumed to be fixed (immobile and inflexible substrates) while the intermediate substrate was free to move only in the normal direction due to the use of flexible complex seals (mobile and inflexible substrate). The generic motion of the intermediate substrate due to both variations of the stagnant fluid temperature in the secondary fluid flow passage and the induced internal pressure pulsations within both primary fluid and secondary fluid flow passages is expressed according to the following Equation 41: H 1 = h 1 h o = ( 1 + H T + H p ) Eq . .times. 41 where

[0244] h.sub.o is a reference thickness for the primary fluid passage

[0245] H.sub.1 is the dimensionless motion of the intermediate substrate

[0246] H.sub.T is the dimensionless motion of the intermediate substrate due to the volumetric thermal expansion of the stagnant fluid

[0247] H.sub.p is the dimensionless motion of the intermediate substrate due to the deformation in seals as a result of the internal pressure.

[0248] The fluid was assumed to be Newtonian having constant average properties except for the thermal conductivity. The general two-dimensional continuity, momentum and energy equations for a laminar thin film are given as follows: .differential. u i .differential. x i + .differential. v i .differential. y i = 0 Eq . .times. 42 .rho. i .function. ( .differential. u i .differential. t + u i .times. .differential. u i .differential. x i + v i .times. .differential. u i .differential. y i ) = - .differential. p i .differential. x i + .mu. i .function. ( .differential. 2 .times. u i .differential. x i 2 + .differential. 2 .times. u i .differential. y i 2 ) Eq . .times. 43 .rho. i .function. ( .differential. v i .differential. t + u i .times. .differential. v i .differential. x i + v i .times. .differential. v i .differential. y i ) = - .differential. p i .differential. y i + .mu. i .function. ( .differential. 2 .times. v i .differential. x i 2 + .differential. 2 .times. v i .differential. y i 2 ) Eq . .times. 44 ( .rho. .times. .times. c p ) i .times. ( .differential. T i .differential. t + u i .times. .differential. T i .differential. x i + v i .times. .differential. T i .differential. y i ) = .differential. .differential. x i .times. ( k i .times. .differential. T i .differential. x i ) + .differential. .differential. y i .times. ( k i .times. .differential. T i .differential. y i ) Eq . .times. 45 where

[0249] T is the fluid temperature

[0250] u is the dimensional axial velocity

[0251] v is the dimensional normal velocity

[0252] .rho. is the average fluid density

[0253] p is pressure

[0254] .mu. is the average fluid dynamic viscosity

[0255] cp is the average specific heat of the fluid

[0256] k is the thermal conductivity of the fluid

[0257] When the fluid contains suspended ultrafine particles, these properties will be for the resulting dilute mixture so long as the diameter of the particles is very small compared to h.sub.o. The index "i" is "1" when analyzing the primary fluid layer while it is "2" when analyzing the secondary fluid layer. Equations 42-45 are non-dimensionalized using the following dimensionless variables: X i = x i B Eq . .times. 46 .times. a Y i = y i h o Eq . .times. 46 .times. b .tau. = .omega. .times. .times. t Eq . .times. 46 .times. c U i = u i ( .omega. .times. .times. B + V oi ) Eq . .times. 46 .times. d V i = v i h o .times. .omega. Eq . .time