https://seniordesign.engr.uidaho.edu/2006_2007/am2/experimental%20_and_numerical_study_of_pressure_drop_and_heat_transfer_in_a_single-phase_micro-channel_heat_sink.pdf

Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink

THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

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The Kinetic Theory of Gases

The equations governing the fluid dynamics and combined conduction/convection heat transfer in a heat sink are presented in dimensionless form for both laminar and turbulent flow. A scheme presented for solving these equations permits the determination of heat sink dimensions that display the lowest thermal resistance between the hottest portion of the heat sink and the incoming fluid. Results from the present method are applied to heat sinks reported by previous investigators to study effects of their restrictions regarding the nature of the flow (laminar or turbulent), the ratio of fin thickness to channel width, or the aspect ratio of the fluid channel. Results indicate that when the pressure drop through the channels is small, laminar solutions yield lower thermal resistance than turbulent solutions. Conversely, when the pressure drop is large, the optimal thermal resistance is found in the turbulent region. With the relaxation of these constraints, configurations and dimensions found using the present procedure produce significant improvement in thermal resistance over those presented by all three previous studies. >

Heat sink optimization with application to microchannels

Design optimization of electric vehicle battery cooling plates for thermal performance

Apparatus and methods according to the present invention preferably utilize electroosmotic pumps that are capable of generating high pressure and flow without moving mechanical parts and the associated generation of unacceptable electrical and acoustic noise, as well as the associated reduction in reliability. These electroosmotic pumps are preferably fabricated with materials and structures that improve performance, efficiency, and reduce weight and manufacturing cost relative to presently available micropumps. These electroosmotic pumps also preferably allow for recapture of evolved gases and deposited materials, which may provide for long-term closed-loop operation. Apparatus and methods according to the present invention also allow active regulation of the temperature of the device through electrical control of the flow through the pump and can utilize multiple cooling loops to allow independent regulation of the special and temporal characteristics of the device temperature profiles. Novel microchannel structures are also described.

Electroosmotic microchannel cooling system

For fully developed flow in closed finned channels used to augment heat transfer, there exists an optimal geometrical design of the size and number of cooling channels. In this paper, the problem is generalized with a statement of dimensionless thermal resistance in terms of 9 the number of channels 9 a fin to channel thickness ratio 8 the length to width {planar dimensions) ratio of the heat source, and 9 a specified fin efficiency or fin length 9 a fluid to fin thermal conductivity ratio 9 the Prandtl Number of the coolant 8 a dimensionless pressure term, which incorporates the maximum allowable pressure drop through the cooling channels or alternatively, 9 a dimensionless work rate term, which incorporates the maximum allowable cool­ ant pumping power required, An optimization scheme is described and used for comparison with two previously published cases wherein both designs were restricted to a fixed fin to channel thickness ratio and laminar flow; one by Goldberg (1984) using air and copper and a second one only by Tuckerman and Pease (1981) for water-cooled Silicon wafers. Results from the present optimization scheme show that upon reexamination of the first study by Goldberg, significant reduction of thermal resistance can be obtained by using fin/channel dimensions other than unity. A similar reduction is found in the second instance (Tuckerman and Pease) with the relaxation of the laminar limitation.

Optimal Thermal Design of Forced Convection Heat Sinks-Analytical

D.B. Tuckerman and R.F.W. Pease (1981) showed that microchannels with water flow could be used to cool VLSI systems. Their work required the flow to be laminar, and the channel system, or fin array, was optimized analytically. Recently, it has been shown that, for some geometries and fluid pressure drops, a lower thermal resistance can be found if the channels are designed to allow turbulent flow. The current work uses the optimization scheme developed by R.W. Knight et al. (1991 and in this issue) to design three air-cooled aluminum finned arrays, which were built and tested experimentally. The thermal performances of the fin array designs, one containing 5 fins, one with 11 fins, and one with the predicted optimum of 8 fins, are compared. All arrays had turbulent flow and pressure drop across them, and all fins were the same length and width. The best thermal performance was obtained with the design predicted to be optimal. The scheme can be applied to a variety of heat sink design applications, including water-cooled microchannels. >

Roy W. Knight

Papers

Optimal Thermal Design of Forced Convection Heat Sinks-Analytical

Optimal thermal design of air cooled forced convection finned heat sinks-experimental verification

Investigation into the application of low melting temperature alloys as wet thermal interface materials

Characterization of transferred vertically aligned carbon nanotubes arrays as thermal interface materials

Thermal performance of low melting temperature alloys at the interface between dissimilar materials