APPARATUS FOR COOLING OF ELECTRONIC DEVICES UTILIZING MICROFLUIDIC COMPONENTS

Abstract

System and method for cooling of an integrated circuit utilizing Micro-Electro Mechanical Systems (MEMS) components. A flexible thin film has an upper flexible substrate, a lower inflexible substrate and flexible seals. One face of the lower substrate is in contact with at least one hot medium and the other face is in contact with a coolant fluid. One face of the upper substrate is in contact with the coolant fluid and the other face is in contact with the surrounding ambient. Two continuous flexible seals are attached to the faces of the upper lower substrates to form at least one closed enclosure comprising a thermally conducting gas. The thermally conducting gas is in direct contact with the lower substrate. The upper substrate deflects continuously and maximally in the direction along the coolant fluid flow direction when the flexible seals deflect when the thermally conducting gas undergoes volumetric thermal expansion.

Description

FIELD OF THE INVENTION

Embodiments are generally related to thin film channels. Embodiments also relate to the field of microfluidic devices and cooling of electronic devices. Embodiments additionally relate to system and method for cooling of an integrated circuit utilizing Micro-Electro Mechanical Systems (MEMS) components.

BACKGROUND OF THE INVENTION

Various engineering applications utilize fluidic thin films as cooling devices. Examples include heat pipes and microchannel heat sinks.

Such devices are widely utilized in electronic cooling applications where rapid developments in the electronics industry necessitates a continuing need for increasing cooling capacity. Several solutions have been proposed to increase the cooling capacity of fluidic thin films. For example, some solutions have demonstrated that two-phase flow in a minichannel is capable of removing maximum heat fluxes generated by electronic packages however the system may become unstable near certain operating conditions. Further, it has been found that the use of porous medium in cooling of electronic devices can enhance heat transfer. However, a porous medium can create a substantial increase in the pressure drop inside the thin film.

Recently, flexible fluidic thin films have been introduced for enhancing the cooling capability of fluidic thin films. Flexible thin films utilize soft seals to separate between their plates instead of having rigid thin film construction. It has also been demonstrated that more cooling is achievable when flexible fluidic thin films are utilized. The expansion of the flexible thin film including flexible microchannel heat sink is directly related to the average internal pressure inside the microchannel. Additional increases in the pressure drop across a flexible microchannel not only increases the average velocity, but also expands the microchannel causing an apparent increase in the coolant flow rate which, in turn, increases the cooling capacity of the thin film.

It has also been demonstrated that the cooling effect of flexible thin films can be further enhanced if the supporting soft seals contain closed cavities filled with a gas, which is in contact with the heated substrate boundary of the thin film. Such special kind of sealing assembly is referred as “flexible complex seals”. The resulting fluidic thin film device is expandable according to an increase in the working internal pressure or an increase in the heated substrate temperature.

Flexible thin films have been analyzed and considered in the context of special designs that result in a uniform displacement of the thin film mobile substrate. In contrast, the displacement of a mobile substrate in other flexible thin film designs can be non-uniform especially if the mobile substrate itself is flexible.

Therefore, it is believed that a need exists for improved thermally expandable flexible fluidic thin films that can be utilized in Micro-Electro Mechanical Systems (MEMS) and electronic cooling applications such as those involving integrated circuits, servers, and so forth. Also such films should produce significant increase in cooling as the heating load increases especially when operated at lower Peclet numbers.

SUMMARY OF THE INVENTION

The following summary is provided to facilitate an understanding of some of the innovative features unique to the disclosed embodiment and is not intended to be a full description. A full appreciation of the various aspects of the embodiments disclosed herein can be gained by taking the entire specification, claims, drawings, and abstract as a whole.

It is, therefore, one aspect of the disclosed embodiments to provide for thin film channels in the context of cooling electronic devices, such as, for example, integrated circuits, computers, servers, and the like.

It is another aspect of the disclosed embodiments to provide for microfluidic devices and the cooling of electronic devices.

It is yet another aspect of the disclosed embodiments to provide for a system and method for cooling electronic devices utilizing Micro-Electro Mechanical Systems (MEMS) components.

The aforementioned aspects and other objectives and advantages can now be achieved as described herein. A flexible thin film includes an upper flexible substrate, a lower inflexible substrate and flexible seals. One face of the lower substrate is in contact with at least one hot medium and the other face is in contact with a coolant fluid. The “hot medium” can be, for example, an electronic device. One face of the upper substrate is in contact with the coolant fluid and the other face is in contact with the surrounding ambient. Two continuous flexible seals are attached to the faces of the upper substrate and the lower substrate to form at least one closed enclosure comprising a thermally conducting gas. The thermally conducting gas is in direct contact with the lower substrate. The upper substrate deflects continuously and maximally in the direction along the coolant fluid flow direction when the flexible seals deflect and the thermally conducting gas undergoes volumetric thermal expansion.

Heat transfer inside thermally expandable fluidic and flexible thin films is analyzed. The upper flexible substrate of the thin film is allowed to expand as functions of both the pressure inside the thin film and the local heated substrate temperature via utilizing flexible complex seals. The expansion of the thin film is considered to be in the transverse direction of the fluid flow direction. The expansion in the thin film heights is generally related to both the local internal pressure and the local heated substrate temperature. The governing equations for flow and heat transfer can be properly non-dimensionalized and reduced into simpler forms. The resulting equations can be then computationally solved and various pertinent results obtained. The controlling parameters can be obtained and their role regarding the thermal behavior of thermally expandable fluidic flexible thin films can be established.

DESCRIPTION OF THE DRAWINGS

The accompanying figures, in which like reference numerals refer to identical or functionally-similar elements throughout the separate views and which are incorporated in and form a part of the specification, further illustrate the disclosed embodiments and, together with the detailed description of the invention, serve to explain the principles of the disclosed embodiments.

FIG. 1A illustrates a side view of a thermally expandable flexible thin film with mobile flexible upper substrate, in accordance with the disclosed embodiments;

FIG. 1B illustrates a sectional view of a thermally expandable flexible thin film with mobile flexible upper substrate of FIG. 1A, in accordance with the disclosed embodiments;

FIG. 2 illustrates a graph depicting the variation of the dimensionless thin film height H with the thermal expansion parameter FT1, in accordance with the disclosed embodiments;

FIG. 3 illustrates a graph depicting the variation of the dimensionless mean bulk temperature θ_m and dimensionless lower substrate temperature θ_B with the thermal expansion parameter F_T1, in accordance with the disclosed embodiments;

FIG. 4 illustrates a graph depicting the variation of the dimensionless thin film height H with Peε, in accordance with the disclosed embodiments;

FIG. 5 illustrates a graph depicting the variation of the dimensionless mean bulk temperature θ_m and dimensionless lower substrate temperature θ_B with Peε, in accordance with the disclosed embodiments;

FIG. 6 illustrates a graph depicting the variation of the lower substrate temperature at the exit θ_B(F_T1,X=1) relative to that when F_T1=0 with Peε and F_T, in accordance with the disclosed embodiments; and

FIG. 7 illustrates a graph depicting the, variation of the average Nusselt number Nu_ATC(F_T1,X=1) relative to that when F_T1=0 with Peε and F_T1, in accordance with the disclosed embodiments.

DETAILED DESCRIPTION OF THE INVENTION

The particular values and configurations discussed in these non-limiting examples can be varied and are cited merely to illustrate at least one embodiment and are not intended to limit the scope thereof.

The following Table 1 provides various symbols and meanings, which can be utilized in the context of the disclosed embodiments:

TABLE 1
Nomenclature
B     thin film length [m]
D     half thin film width [m]
Do    reference half thin film width [m]
cp    specific heat of the fluid [J/kg K]
FT1   thermal expansion parameter for flexible complex seal
FT2   thermal expansion parameter for side biomaterial side
      supports
H     dimensionless thin film height
H1    dimensionless inlet thin film height
h     thin film height [m]
ho    reference thin film height [m]
hc    convective heat transfer coefficient [W/m2 K]
k     thermal conductivity of the fluid [W/m K]
Nu    Nusselt number
P     pressure [Pa]
Pi    inlet pressure [Pa]
Pe    exit pressure [Pa]
Pe    Peclet number
P     fluid pressure [Pa]
q     heat flux at the lower substrate [W/m2]
S1,2  stiffness parameter for flexible complex seal or bimaterial plate
T, Ti temperature in fluid and the inlet temperature [K]
U, u  dimensionless and dimensional axial velocities
uo    reference axial velocity [m/s]
V, v  dimensionless and dimensional normal velocities
W, w  dimensionless and dimensional spanwise velocities
X, x  dimensionless and dimensional axial coordinates
Y, y  dimensionless and dimensional normal coordinates
Z, z  dimensionless and dimensional spanwise coordinates
Greek Symbols
ε     aspect ratio
μ     dynamic viscosity of the fluid
θ, θm dimensionless temperature and dimensionless mean bulk
      temperature
θB    dimensionless temperature at the lower substrate
ρ     density of the fluid [kg/m3]
η     variable transformation for the dimensionless Y-coordinate

A two dimensional thin film having a small height h compared to its length B can be considered. The x-axis can be taken in the direction of the length of the thin film while y-axis is taken along the height of the thin film as shown in FIGS. 1A and 1B. The z-axis can be taken along the half thin film width, D, where it is large enough such that two-dimensional flow within the thin film can be assumed. The thin film height and width can be allowed to vary with the axial distance. The flow is assumed to be laminar and the convective terms are neglected compared to diffusion terms in the momentum equation (hydrodynamically fully developed flow is assumed). Under these conditions, the velocity field, Reynolds equation and the energy equation can be obtained as follows:

$\begin{array}{cc}X=\frac{x}{B};Y=\frac{y}{h_o};Z=\frac{z}{D_o}& \mathrm{Eqs}.6\left(a,b,c\right)\\ U=\frac{u}{u_o};V=\frac{v}{u_o\left(h_o/B\right)};W=\frac{w}{u_o\left(D_o/B\right)}& \mathrm{Eqs}.6\left(d,e,f\right)\\ \theta =\frac{T-T_1}{{\mathrm{qh}}_o/k};\stackrel{\_}{P}=\frac{P-P_e}{P_i-P_e}& \mathrm{Eqs}.6\left(g,h\right)\\ H=\frac{h}{h_o};\stackrel{\_}{D}=\frac{D}{D_o}& \mathrm{Eqs}.6\left(i,k\right)\end{array}$

where the variables T, u, v, w, ρ, P, μ, c_p and k represent, respectively, the fluid temperature, axial velocity, normal velocity, velocity component in the z-direction, fluid's density, pressure, fluid's dynamic viscosity, fluid's specific heat and the fluid's thermal conductivity.

The dimensionless variables are as follows:

$\begin{array}{cc}X=\frac{x}{B};Y=\frac{y}{h_o};Z=\frac{z}{D_o}& \mathrm{Eqs}.6\left(a,b,c\right)\\ U=\frac{u}{u_o};V=\frac{v}{u_o\left(h_o\text{/}B\right)};W=\frac{w}{u_o\left(D_o\text{/}B\right)}& \mathrm{Eqs}.6\left(d,e,f\right)\\ \theta =\frac{T-T_1}{qh_o\text{/}k};\stackrel{\_}{P}=\frac{P-P_e}{P_i-P_e}& \mathrm{Eqs}.6\left(g,h\right)\\ H=\frac{h}{h_o};\stackrel{\_}{D}=\frac{D}{D_o}& \mathrm{Eqs}.6\left(i,k\right)\end{array}$

where q, u_o, T₁, h_o and D_o are the heat flux at the lower substrate, reference velocity, inlet temperature, a reference thin film height and a reference half thin film width, respectively. The reference thin film height h_o and width D_o are taken to be the thin film height and width at the inlet when both the flow and the heat flux in the thin film are zero. The Reynolds and energy equations can be written as

$\begin{array}{cc}{\left(\frac{D_o}{B}\right)}^2\frac{\partial }{\partial X}\left({\left[H\left(X\right)\right]}^3\frac{\partial \stackrel{\_}{P}}{\partial X}\right)+\frac{\partial }{\partial Z}\left({\left[H\left(X\right)\right]}^3\frac{\partial \stackrel{\_}{P}}{\partial Z}\right)=0& \mathrm{Eq}.7\\ U\frac{\partial \theta }{\partial X}+V\frac{\partial \theta }{\partial Y}+W\frac{\partial \theta }{\partial Z}=\frac{1}{\mathrm{Pe}\varepsilon }\frac{{\partial }^2\theta }{\partial Y^2}& \mathrm{Eq}.8\end{array}$

where the Peclet number (Pe) and the aspect ratio (ε) are defined as

$\begin{array}{cc}\mathrm{Pe}=\frac{\rho c_pu_oh_o}{k};\varepsilon =\frac{h_o}{B}& \mathrm{Eqs}.9\left(a,b\right)\end{array}$

Referring to FIGS. 1A and 1B, a flexible thin film 100 includes an upper substrate 102 and a lower substrate 104. The lower substrate 104 comprises an inflexible substrate and the upper substrate 102 comprises a flexible substrate. The one face of the lower substrate 104 is generally in contact with at least one “hot medium” and the other face is in contact with a coolant fluid 110. The one face of the upper substrate 102 is in contact with the coolant fluid 110 and the other face is in contact with the surrounding ambient. The faces of the upper and lower substrates 102 and 104 are in contact with the coolant fluid 110 and oppose each other. Two flexible seals 106 and 108 can be attached to the faces of the upper substrate 102 and the lower substrate 104 opposing the coolant fluid 110 to form one or more closed enclosures containing a thermally conducting gas.

FIG. 1B is a sectional view of a thermally expandable flexible thin film with mobile flexible upper substrate 102 taken along A-A of FIG. 1A, in accordance with the disclosed embodiments. The thermally conducting gas is in direct contact with the lower substrate 104. The flexible seals 106 and 108 move relative to the lower substrate 104 fin the normal direction when the thermally conducting gas undergoes volumetric thermal expansion. The upper substrate 102 deflects continuously and maximally in the direction along the coolant fluid 110 flow direction when the flexible seals 106 and 108 deflect when the thermally conducting gas undergoes volumetric thermal expansion. The thermally conducting gas has high volumetric thermal expansion coefficient.

The flexible seals 106 and 108 allow a local expansion in the thin film 100 heights due to both changes in internal pressure and the lower (heated) substrate 104 temperature. Similar effects are expected when the upper substrate 102 is a bimaterial plate separated from the lower substrate 104 via soft seals. The thin film 100 height varies linearly with local pressure and local lower substrate 104 temperature according to the following relations:

$\begin{array}{cc}H\left(X\right)=\frac{h\left(x\right)}{h_o}=1+\frac{\stackrel{\_}{P}\left(X\right)}{S_1}+F_{T1}{\theta }_B\left(X\right)& \mathrm{Eq}.10\end{array}$

where F_T1 is the thermal expansion parameter, which is equal to:

$\begin{array}{cc}{F}_{T1}=\beta \frac{qh_o}{k}& \mathrm{Eq}.11\end{array}$

The coefficient β is thermal expansion coefficient of the flexible complex seals 106 and 108. The parameter F_T1 increases as the heating load q, the thermal expansion coefficient β and the reference thin film height increase while it decreases as the fluid thermal conductivity k decreases. The stiffness parameter s_i is generally related to the elastic properties of the flexible complex seals 106 and 108. When the thin film width is uniform (D=D₀), the velocity field (Equations 1, 2 and 3) reduces to the following:

$\begin{array}{cc}U\left(X,\eta ,Z\right)=\frac{u\left(X,\eta ,Z\right)}{u_o}-6\frac{\stackrel{\_}{P}}{X}H^2\left(\eta -{\eta }^2\right);u_o=\frac{\left(P_i-P_e\right)h_o^2}{12\mu B}& \mathrm{Eq}.12\\ V\left(X,\eta ,Z\right)={\left[H\left(X\right)\right]}^2\left(\frac{\stackrel{\_}{P}}{X}\right)\left(\frac{H}{X}\right)\left({\eta }^3-{\eta }^2\right)& \mathrm{Eq}.13\\ W\left(X,\eta ,Z\right)=0& \mathrm{Eq}.14\end{array}$

where

$\xi =X,\eta =\frac{{\mathrm{Yh}}_o}{h\left(x\right)}.$

As such, Equation 8 can be written as:

$\begin{array}{cc}-6\frac{\stackrel{\_}{P}}{X}H^4\left(\eta -{\eta }^2\right)\frac{\partial \theta }{\partial \xi }=\frac{1}{\mathrm{Pe}\varepsilon }\frac{{\partial }^2\theta }{\partial {\eta }^2}& \mathrm{Eq}.15\end{array}$

where

$\frac{\stackrel{\_}{P}}{X}$

is evaluated from the following reduced form of the Reynolds equation:

$\begin{array}{cc}\frac{\partial }{\partial X}\left({\left[H\left(X\right)\right]}^3\frac{\partial \stackrel{\_}{P}}{\partial X}\right)=0& \mathrm{Eq}.16\end{array}$

The uniform wall heat flux is assumed at the lower substrate while the upper substrate is considered to be insulated. This models the case where the fluidic thin film with a thin conductive lower substrate is placed on the top of a heated surface while its upper substrate is configured from a less conductive flexible material (e.g. plastics). The boundary conditions are

$\begin{array}{cc}\theta \left(X,0\right)=0,\frac{\partial \theta }{\partial \eta }{|}_{X,\eta =0}=-H\left(X\right),\frac{\partial \theta }{\partial \eta }{|}_{X,\eta =11}=-{\varepsilon }^2H\left(X\right)\left(H\left(X\right)-1\right)\frac{\partial \theta }{\partial \eta }{|}_{X,\eta =11}\cong 0& \mathrm{Eq}.17\end{array}$

The Nusselt number is defined as

$\begin{array}{cc}\mathrm{Nu}\left(X\right)\equiv \frac{h_ch_o}{k}=\frac{1}{{\theta }_B\left(X\right)-{\theta }_m\left(X\right)}=\frac{1}{\theta \left(X,0\right)-{\theta }_m\left(X\right)}& \mathrm{Eq}.18\end{array}$

where h_c, θ_m, and θ_B are the local convection coefficient, dimensionless mean bulk temperature and dimensionless lower substrate temperature, respectively, and are defined as follows:

$\begin{array}{cc}{\theta }_m\left(X\right)=\frac{1}{U_m\left(X\right)H}{\int }_0^HU\left(X,Y\right)\theta \left(X,Y\right)YU_m\left(X\right)=\frac{1}{H}{\int }_0^HU\left(X,Y\right)Y& \mathrm{Eq}.19\end{array}$

where U_m(X) is the average velocity inside the thin film at the dimensionless axial distance X.

Equations 15 and 16 are discretized using three points central differencing in the transverse direction (η-direction) while two points differencing was utilized in the axial direction (X-direction). The finite difference equations for Equations 16 and 15 are the following, respectively:

$\begin{array}{cc}{\stackrel{\_}{P}}_{i-1}-\left[1+{\left(\frac{H_{i+1/2}}{H_{i-1/2}}\right)}^3\right]{\stackrel{\_}{P}}_i+{\left(\frac{H_{i+1/2}}{H_{i-1/2}}\right)}^3{\stackrel{\_}{P}}_{i+1}=0& \mathrm{Eq}.20\\ -6\left(\frac{{\stackrel{\_}{P}}_i-{\stackrel{\_}{P}}_{i-1}}{\mathrm{\Delta \xi }}\right)H_i^4\left({\eta }_j-{\eta }_j^2\right)\left(\frac{{\theta }_{i,j}-{\theta }_{i-1,j}}{\Delta \xi }\right)=\frac{1}{\mathrm{Pe}\varepsilon }\left(\frac{{\theta }_{i,j+1}-2{\theta }_{i,j}+{\theta }_{i,j-1}}{\Delta {\eta }^2}\right)& \mathrm{Eq}.21\end{array}$

where i and j are the location of the discretized point in the X and η directions respectively. The resulting tri-diagonal systems of algebraic equations, Equations 20 and 21 can be then solved utilizing, for example, the well-established Thomas algorithm. The same procedure is repeated for the consecutive i values of P_i and θ_i,j until j reaches the value M (M=101) at which X=1.0.

A thin film with h_o=200 μm and B=3 mm results in Peε=1.0 when u_o=0.075 m/s (water as coolant) and it results in Peε=50 when u_o=0.04 m/s (oil as coolant). It should be noted that a 100% increase in the heated substrate temperature relative to the inlet fluid temperature, (T_w−T₁)/T₁=1.0, results in an expansion of the thin film height of the orders of 1.0<H(X=1.0)<2.0. The value of H(X=1.0)=2.0 occurs when both lateral expansions and elastic forces in the flexible complex seal are negligible as well as when an ideal gas is contained in the closed cavities of these seals.

FIG. 2 illustrates a graph 200 depicting the variation of the dimensionless thin film height H with dimensionless axial distance X and the thermal expansion parameter FT1. It is noticed that the thin film height increases as FT1 increases and that the maximum gradient of H occurs near the thin film inlet. This increases normal stresses due to bending in this region.

FIG. 3 illustrates a graph 300 depicting the variation of the dimensionless mean bulk temperature θ_m and dimensionless lower substrate temperature θ_B with the thermal expansion parameter FT1, in accordance with the disclosed embodiments. The increase in FT1 (when Peε=1.0 and S₁=5.0) enhances cooling inside the thin film where the mean bulk temperature θ_m at the exit is reduced by 70% by increasing FT1 from FT1=0.0 to FT1=1.0. The lower substrate temperature θ_B at the exit is reduced by 25% when FT1 is changed from FT1=0.0 to FT1=1.0. The reduction in θ_B is apparent when FT1<1.0 for the parameters shown in FIG. 3.

The expansion in the local thin film height and the lower substrate temperatures decrease as the Peclet number Pe or the aspect ratio ε increase as shown in the graphs 400 and 500 of FIGS. 4 and 5 respectively. The decrease in H, θ_m and θ_B as Peε increases is apparent when Peε<10.

FIG. 6 illustrates a graph 600 depicting the variation of the lower substrate temperature at the exit θ_B(F_T1,X=1) relative to that when F_T1=0 with Peε and F_T, in accordance with the disclosed embodiments. The flexible thin film can provide maximum enhancement in the cooling effect of 45% and above (compared to the performance ordinary flexible fluidic thin films) as the heating load increases when Peε is decreased below Peε=0.5. This indicates that thermally expandable flexible fluidic thin films are recommended to be used in Micro-Electro Mechanical Systems (MEMS) and electronic cooling applications. It is worth noting that increasing the thermal expansion parameter beyond certain values will decrease the coolant velocity near the heated substrate which can result in a reduction in the cooling enhancement as can be seen from FIG. 6.

This fact can also be seen from FIG. 7, where the average Nusselt number decreases to a minimum and then it increases as FT1 increases. FIG. 7 illustrates a graph 700 illustrating the, variation of the average Nusselt number Nu_AVG(F_T1,X=1) relative to that when F_T1=0 with Peε and F_T1, in accordance with the disclosed embodiments. For full and stable utilization of thermally expandable flexible fluidic thin films, the thermal expansion parameter is recommended to be lower than the following critical value:

F_T1<(F_T1)_critical=0.642Peε+2.363   Eq. 33

The following correlations are for (Nu)_AVG and (θ_m)_AVG for thin films supported by flexible complex seals with flexible upper substrate for the specified range of parameters, 1.0<S₁<10, 1.0<Peε<50 and 0<F_T1<1.0:

$\begin{array}{cc}{\mathrm{Nu}}_{\mathrm{AVG}}=\frac{0.0455{\left(\mathrm{Pe}\varepsilon \right)}^{0.6793}F_{T1}^{0.8345}+1.5285{\left(\mathrm{Pe}\varepsilon \right)}^{0.2877}S_1^{0.3225}}{{\left(0.5169S_1^{0.620}+1.255\times {10}^{-3}F_{T1}^{1.8691}\right)}^{0.5503}};R^2=0.996& \mathrm{Eq}.34\\ {\left({\theta }_m\right)}_{\mathrm{AVG}}=\frac{1.3709{\left(\mathrm{Pe}\varepsilon \right)}^{-0.7717}F_{T1}^{1.6939}+1.1520{\left(\mathrm{Pe}\varepsilon \right)}^{-0.9898}S_1^{-0.4380}}{{\left(2.1144S_1^{-0.3449}+1.8401F_{T1}^{1.3294}\right)}^{2.4686}};R^2=0.992& \mathrm{Eq}.35\end{array}$

CONCLUSIONS

Heat transfer within flexible fluidic thin films that are expandable due to pressure and heat can be analyzed as indicated herein. The upper substrate of the thin film can be assumed to be flexible and mobile. The expansion in the thin film heights is generally linearly related to the local fluid pressure and local lower substrate (e.g., heated). The governing Reynolds, momentum and energy equations can be properly non-dimensionalized and cast in proper forms. Such equations can be then solved numerically utilizing an implicit computational method.

Parameters such as, for example, a stiffness parameter, a Peclet number, a thermal expansion parameter, an aspect ratio and the ratio of the width to the thin film length can be utilized as the main controlling parameters. The thin films produce significant increase in cooling capacity as the heating load increases especially those operated with lower Peclet numbers. Finally, thermally expandable flexible fluidic thin films are recommended to be utilized in small sized thin films as for Micro-Electro Mechanical Systems (MEMS) and electronic cooling applications.

To the extent necessary to understand or complete the disclosure herein, all publications, patents, and patent applications mentioned herein are expressly incorporated by reference therein to the same extent as though each are individually so incorporated.

Having thus described exemplary embodiments of the present invention, it should be noted by those skilled in the art that the within disclosures are exemplary only and that various other alternatives, adaptations, and modifications may be made within the scope of the present invention. Accordingly, the present invention is not limited to the specific embodiments as illustrated herein, but is only limited by the following claims.

Claims

1. An apparatus comprising:

a first substrate and a second substrate, said first substrate comprising an inflexible substrate having a face in contact with at least one hot medium and having said other face in contact with a coolant fluid;

said second substrate comprising a flexible substrate having a face in contact with said coolant fluid and having said other face in contact with said surrounding ambient;

the faces of the first and second substrates in contact with the coolant fluid are opposing each other;

at least two continuous flexible seals attached to said faces of said first substrate and said second substrate opposing said coolant fluid to form at least one closed enclosure comprising a thermally conducting gas;

said thermally conducting gas in direct contact with said first substrate;

said flexible seal movable relative to said first substrate in said normal direction when said thermally conducting gas undergoes volumetric thermal expansion;

a first at least one opening on said first substrate and a second at least one opening on said first substrate;

said coolant fluid flowing between said first at least one opening and said second at least one opening through said volume between said substrates excluding said volumes of said at least two continuous flexible seals and said thermally conducting gas.

2. The apparatus of claim 1, wherein said second substrate deflects continuously and maximally in a direction along a direction of said flow of said coolant fluid when said at least two continuous flexible seals deflect when said thermally conducting gas undergoes volumetric thermal expansion.

3. The apparatus as set forth in claim 1, wherein said second substrate does not deflect or deflects minimally in a direction normal to a direction of said flow of said coolant fluid when said at least two continuous flexible seals deflect and when said thermally conducting gas undergoes volumetric thermal expansion.

4. The apparatus as set forth in claim 1, wherein said thermally conducting gas comprises a high volumetric thermal expansion coefficient.