Heat Flux Dissipation Research Articles

Optimum Geometry of Plate Fins

A method and practical results are presented for finding the geometries of fixed volume plate fins for maximizing dissipated heat flux. The heat transfer theory used in optimization is based on approximate analytical solutions of conjugated heat transfer, which couple conduction in the fin and convection from the fluid. Nondimensional variables have been found that contain thermal and geometrical properties of the fins and the flow, and these variables have a fixed value at the optimum point. The values are given for rectangular, convex parabolic, triangular, and concave parabolic fin shapes for natural and forced convection including laminar and turbulent boundary layers. An essential conclusion is that it is not necessary to evaluate the convection heat transfer coefficients because convection is already included in these variables when the flow type is specified. Easy-to-use design rules are presented for finding the geometries of fixed volume fins that give the maximum heat transfer. A comparison between the heat transfer capacities of different fins is also discussed.

Copper foam based vapor chamber for high heat flux dissipation

A copper foam based vapor chamber was designed, built and tested in this paper. The vapor chamber consists of a top and bottom copper foam pieces which are sintered on the two copper plates. Several copper foam bars directly contact the tip of the condenser and evaporator wicks. The surface temperature non-uniformity was defined to characterize the temperature distribution on the condenser and evaporator surfaces. It is found that the water and ethanol based vapor chambers have the best and worst thermal performance, respectively, among the three working fluids of water, acetone and ethanol. The surface temperature non-uniformity on the bottom (evaporator) surface are 3–5 times of those on the top (condenser) surface. Generally thermal resistances of vapor chambers are decreased with increases in heating powers. Charge ratios and inclined angles are combined to influence the thermal performance of vapor chambers. The maximum heating power attains 170W, corresponding to the heat flux of 216W/cm2 without the capillary or boiling limits reached. The minimum thermal resistance is 0.09K/W. The significantly extended operation range of heat flux is due to the distinct nature of high porosity and multiscale pore sizes of copper foams.

Experimental Investigations on Thermal Performance of a Multi-Turn Closed Loop Pulsating Heat Pipe

Closed loop pulsating heat pipe (CLPHP) is a relatively new two-phase passive heat transfer device to suit present requirement of high heat flux dissipation in modern electronic components. The operating mechanism of CLPHP is not well understood and the present state of the technology cannot predict required design parameters for a given task. The aim of research work presented in this paper is to better understand thermal performance of CLPHP. A series of experimental investigation were conducted on a multi-turn CLPHP made of copper capillary tube of 2-mm inner diameter. Two kinds of working fluids viz. ethanol and acetone were employed. The influence characterization has been studied for the variation of heat input and filling ratio (FR) of the tested CLPHP. Thermal performance of the CLPHP is evaluated by heat transfer and thermal resistance. The results strongly demonstrate the effect of heat input and FR of the working fluid on thermal performance of the device.

Effect of open microchannel geometry on pool boiling enhancement

Pool boiling enhancement through surface modification has garnered the attention of many researchers for extending the limits of heat flux dissipation. Simulated copper chips were used in a pool boiling setup with water boiling at atmospheric pressure. Heat transfer performance of different microchanneled surfaces was compared to that of a plain surface. The results of the study showed that the mechanism at work for the bubble dynamics was the ability of the surface to pull liquid through the channels to induce heat transfer. Geometrical trends were observed from the study as well with the wider and deeper channels and thinner finned surfaces showing the best heat transfer results. Without reaching the critical heat flux condition, the best performing chip dissipated a heat flux of 244 W/cm 2 corresponding to a record heat transfer coefficient of 269 kW/m 2 K.

Modeling of heat and mass transfer in the liquid film of rotating heat pipes

Axially rotating heat pipes are devices used to dissipate heat flux through the latent heat of phase change of a fluid at saturation state. In these systems, centrifugal forces due to heat pipe rotation allow the liquid to flow. The present study focuses on cylindrical heat pipes due to the simplicity and cost of the manufacturing of theses devices. This paper presents a steady-state model of heat and mass transfers along the rotating heat pipe. An optimization procedure, which permits to work at a given saturation temperature and so allows to study the parameters influence for given thermophysical properties, has been developed to perform the calculations. The hypotheses of the model are also discussed and examined. Finally, a parametric study has been carried out, using water as a working fluid, to highlight the influence of parameters such as rotational speed, temperature difference between the evaporator wall and the vapour, or the mass of fluid, on the heat transfers. Finally, the operating conditions conducive to maximal performance have been described.

Estimation of a source term in a quasi steady two-dimensional heat transfer problem: application to an electron beam welding

In previous work, we have analyzed the feasibility of the estimation for a source term S(x, y, z) in a transversal section. The present study is concerned with a two-dimensional inverse phase change problem. The goal is the estimation of the dissipated heat flux in the liquid zone (reconstruction of a source term in the energy equation) from experimentally measured temperatures in the solid zone. This work has an application in the electron beam welding of steels of thickness about 8 cm. The direct thermometallurgical problem is treated in a quasi steady two-dimensional longitudinal section (x, y). The beam displacement is normally in the y direction. But in the quasi steady simulation, the beam is steady in the study section. The sample is divided in the axial direction z in few sections. At each section, a source term is defined with a part of the beam and creates a vaporized zone and a fused zone. The goal of this work is the rebuilding of the complete source term with the estimations at each section. In this paper, we analyze the feasibility of the estimation. For this work, we use only the simulated measurements without noise.

On-chip thermal management of hotspots using a perspiration nanopatch

A cooling mechanism based on evaporation from thin liquid films is utilized for thermal management of hotspots combining efficient heat and mass transfer techniques. Dissipation of large heat fluxes from small form-factor areas is made possible by minimizing the thermal resistance across the evaporating liquid film. This is achieved by maintaining a very thin film (∼15 µm) of coolant by capillary confinement using a nano-porous membrane (∼10 µm). At the same time, evaporation is promoted by using jet impingement of dry air on the membrane. Based on these underlying ideas, a MEMS device called a ‘perspiration nanopatch’ is presented. The design and fabrication process of this micro-fluidic device is described along with experimental performance characterization under different operating conditions. Dissipation of heat fluxes in excess of 600 W cm−2 is demonstrated with heat transfer coefficients approaching 0.1 MW m−2 K−1 for surface temperatures well below the saturation temperature of the working fluid.

Computational Analysis and Optimization of Wire - Sandwiched Micro Heat Pipes

Micro heat pipes are a promising option for the thermal management of microelectronic systems with high heat flux dissipation rates. A computational analysis is performed on wire-sandwiched micro heat pipes, a relatively new design of micro heat pipes, which utilizes an array of wires sandwiched between metallic plates to produce the flow channels. A transient one-dimensional model incorporating the longitudinal variations in the flow cross sections of the liquid and vapor media has been utilized, while developing the governing equations for the analysis. A fully implicit finite difference scheme is utilized to obtain solutions for the velocity, pressure and temperature distributions in the vapor and the liquid phases. The performance of the heat pipe has been obtained, with the effective thermal conductivity as the indicator, and extensive optimization studies have been performed with respect to the geometric parameters namely the length of the heat pipe sections, the diameter and pitch of the wires in t...

Experimental Investigation of the Thermal Performance of Graphite Foam for Evaporator Enhancement in Both Pool Boiling and an FC-72 Thermosyphon

High-conductivity graphite foam is investigated for use as a surface enhancement for improved thermal performance in both pool boiling and an FC-72 thermosyphon. The influences of heat load and fluid level on the overall system thermal performance including surface superheat, effective heat transfer coefficient, and thermal resistance are examined. The thermal resistance of the foam heat sink is found to be extremely low at a minimum of 0.024 K/W, well below that of many other methods. The featured low thermal resistance is the primary benefit of this system. The thermal resistance is found to rise with increasing heat flux, but still remains advantageously low and exhibits excellent potential for high heat flux dissipation with low surface superheat, making it suitable for thermal management of advanced electronics.

Thermal performance study of integrated cold plate with power module

A novel cold plate for cooling of the electronic components with high heat flux and high heat dissipation requirements is proposed. The cold-plate structure of the S-type with guide plates is introduced to avoid the heat hot concentration and increase the heat transfer area. The experimental results show that the maximum chip temperature of the novel cold plate is approximately 40% lower than those of the conventional cold plate. Thermal performance optimizations are conducted, indicating that it is extremely effective to install the heat source on two sides of the cold plate. Compared with the single-side heat source, the maximum chip temperature is increased only 20%. However, the heat dissipation is doubled in the limited space for the double-sides arrangement heat source. Moreover, the integrated density of the power module is greatly enhanced by using the cold plate. Transient state temperature variation indicates that the cold plate have quick thermal response in start-up process. It is beneficial to the heat dissipation of integrated module for high power density.

Compressible convection in the deep atmospheres of giant planets

Fast rotating giant planets such as Jupiter and Saturn possess alternate prograde and retrograde zonal winds which are stable over long periods of time. We consider a compressible model of convection in a spherical shell with rapid rotation, using the anelastic approximation, to explore the parameter range for which such zonal flows can be produced. We consider models with a large variation in density across the layer. Our models are based only on the molecular H/He region above the metallic hydrogen transition at about 2 Mbar, and we do not include the hydromagnetic effects which may be important if the electrical conductivity is significant. We find that the convective velocities are significantly higher in the low density regions of the shell, but the zonal flow is almost independent of the z-coordinate parallel to the rotation axis. We analyse how this behaviour is consistent with the Proudman–Taylor theorem. We find that deep prograde zonal flow near the equator is a very robust feature of our models. Prograde and retrograde jets alternating in latitude can occur inside the tangent cylinder in compressible as well as Boussinesq models, particularly at lower Prandtl numbers. However, the zonal jets inside the tangent cylinder are suppressed if a no-slip condition is imposed at the inner boundary. This suggests that deep high latitude jets may be suppressed if there is significant magnetic dissipation. Our compressible calculations include the viscous dissipation in the entropy equation, and we find this is comparable to, and in some cases exceeds, the total heat flux emerging from the surface. For numerical reasons, these simulations cannot reach the extremely low Ekman number found in giant planets, and they necessarily also have a much larger heat flux than planets. We therefore discuss how our results might scale down to give solutions with lower dissipation and lower heat flux.

Critical Heat Flux During Flow Boiling in Microchannels: A Parametric Study

The application of flow boiling in microchannels in copper cooling elements for very high heat flux dissipation from microprocessor chips is one of the promising technologies to replace air cooling and water cooling of these units, particularly in mainframes and servers. Recently, the authors have proposed a new theoretical model to predict the critical heat flux (CHF) in microchannels, and it is used here to perform a parametric study to investigate the effects of fluid, saturation temperature, mass flux, inlet subcooling, microchannel diameter, and heated length on CHF for this application. The parametric study shows that CHF is increased by: (i) decreasing channel length, (ii) lowering saturation temperature, (iii) increasing mass flux, (iv) increasing inlet subcooling, and (v) increasing microchannel diameter. The best coolant is water, but water is not feasible for the present application because of its very low saturation pressure at 30–40°C. Of the other four fluids simulated, their order of merit from best to worst is as follows: R-245fa, R-134a, R-236fa, and FC-72. FC-72, however, has a low saturation pressure (in fact, it would operate under vacuum at the saturation temperatures of 30–40°C envisioned here) and is not a candidate fluid for the flow boiling coolant here. Furthermore, the authors have also recently proposed a diabatic flow map for microchannels based on their database for R-134a and R-245fa in 0.5- and 0.8-mm channels. The new CHF model has been incorporated into their map here to predict the transition from annular flow to dry-out, which is a critical design limitation for microprocessor coolers. Importantly, this map then provides the feasible operating range of such coolers with flow boiling as the cooling process, in terms of mass flux and maximum vapor quality at the outlet to avoid CHF.

Gas-Assisted Thin-Film Evaporation from Confined Spaces for Dissipation of High Heat Fluxes

A new cooling scheme utilizing evaporation from an ultrathin, spatially confined liquid film is described and analyzed for thermal management of hot spots with local heat fluxes in excess of 600 W/cm2. This is achieved by a stable monolayer of liquid maintained on the surface and using fully dry sweeping gas (e.g., air) blown at high velocity (50–100 m/s) above this liquid monolayer. We also demonstrate how dielectric coolants like FC72 can outperform water as an evaporative coolant for this scheme. This work presents the conceptual system design, the results of performance analysis supporting the feasibility of the proposed cooling scheme, and experimental results that demonstrate the idea as well as validate the computational results. The analysis allows one to elucidate the salient physical features of evaporative cooling from spatially confined thin films subjected to a sweeping gas and to identify the key parameters resulting enhanced performance. The simplified model provides results in a form suitable for designing a full-scale cooling device (perspiration nanopatch) that exploits the unique advantages of the proposed cooling scheme.

Experimental investigation of micro heat pipes of different cross-sections having same hydraulic diameter

Effects of micro heat pipe (MHP) cross-sections and orientations on its thermal performance are experimentally investigated in this study. Tests are conducted using five different cross-sections (circular, semicircular, elliptical, semi-elliptical and rectangular) of micro heat pipes having same hydraulic diameter of 3 mm placed at three different inclination angles (0°, 45°, 90°), where water is used as the working fluid. Evaporator section of the MHP is heated by an electric heater and the condenser section is cooled by circulation of water in an annular space between condenser section and the water jacket. Temperatures at different locations of the MHP are measured using five calibrated K type thermocouples. Heat supply is varied using a voltage regulator which is measured by a precision ammeter and a voltmeter. It is found that thermal performance tends to deteriorate as the MHP is flattened. Thus among all cross-sections of MHP, circular one exhibits the best thermal performance in terms of heat flux dissipation followed by semi-elliptical, semi-circular, elliptical and rectangular cross-sections. Moreover, its heat transfer capability also decreases with decreasing of its inclination angle. Finally, a correlation is developed which covers all the experimental data within +7%.

Effect of Local Hot Spots on the Maximum Dissipation Rates During Flow Boiling in a Microchannel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> One of the most promising technologies to replace air-cooling of micro-processor chips is flow boiling in microchannels. The very high heat flux dissipation from micro-processor chips is highly non-uniform due to the presence of multiple localized hot spots usually related to the localization of bridges and gate oxide shorts. Previous studies focused on the performance of microchannels under uniform heating conditions. Recently, Revellin and Thome <citerefgrp> <citeref refid="ref1"/></citerefgrp> have proposed a new theoretical model to predict the critical heat flux (CHF) in microchannels. This model has been modified here to take into account a non-uniform axial heat flux along a microchannel. The model is used here to perform a local hot spot study to investigate the effects of fluid, saturation temperature, mass flux, microchannel diameter, heated length, size, location and number of hot spots as well as the distance between two consecutive hot spots. Based on the present simulations, to best dissipate a hot spot's heat flux, microchannel heat sinks should follow the following recommendations for a channel of fixed length: determine the optimum channel diameter for the fluid (typically either very small or large is best), utilize as high of mass flux as feasible, and design with as low of saturation temperature as possible. Furthermore, the local hot spot size should be as small as possible, the number of local hot spots as few as possible and the distance between two hot spots as large as possible. Utilizing the present numerical method for individual microchannels arranged in parallel in a multi-microchannel cooling element, it is possible to simulate the entire power dissipation profile of a microprocessor die for local limits of CHF. </para>

Thermal Design Methodology for Low Flow Rate Single-Phase and Two-Phase Micro-Channel Heat Sinks

This study provides a systematic thermal design methodology for both single-phase and two-phase micro-channel heat sinks under a fixed liquid coolant flow rate. The parameters relevant to heat sink design are grouped into geometrical parameters, operating parameters, and thermal/fluid parameters. The objective of the proposed thermal design methodology is to determine micro-channel dimensions leading to the most desirable heat sink performance corresponding to a given dissipative heat flux and liquid coolant flow rate. An acceptable design region is first identified which encompasses all possible micro-channel dimensions corresponding to the prescribed dissipative heat flux and liquid coolant flow rate. Heat sink performance maps are then constructed within the acceptable design region. Finally, micro-channel dimensions yielding most desirable heat sink performance can be selected using the performance maps.

Nonlinear polarization and dissipative correspondence between low-frequency fluid and gyrofluid equations

The correspondence between gyrofluid and low-frequency fluid equations is examined. The lowest-order conservative effects in E×B advection, parallel dynamics, and curvature match trivially. The principal concerns are polarization fluxes, and dissipative parallel viscosity and parallel heat fluxes. The emergence of the polarization heat flux in the fluid model and its contribution to the energy theorem is reviewed. It is shown that gyroviscosity and the polarization fluxes are matched by the finite gyroradius corrections to advection in the long-wavelength limit, provided that the differences between gyrocenter and particle representations are taken into account. The dissipative parallel viscosity is matched by the residual thermal anisotropy in the gyrofluid model in the collision-dominated limit. The dissipative parallel heat flux is matched by the gyrofluid parallel heat flux variables in the collision-dominated limit. Hence, the gyrofluid equations are a complete superset of the low-frequency fluid equations.

Force-fed evaporation and condensation utilizing advanced micro-structured surfaces and micro-channels

This paper presents results of an experimental study on phase change cooling of high flux electronics utilizing an innovative phase-change technique involving force-fed evaporation and condensation. The technique utilizes high-performance micro-structured surfaces consisting of alternating fins and channels, coupled with a force-fed mechanism in the evaporator and condenser. The force-fed mechanism provides a highly vigorous micro-channel convective heat transfer environment with the net effect of substantially higher heat transfer coefficients without the high-pressure drop penalties that are normally associated with such flows. Our recent results demonstrate dissipation heat flux levels well above 300W/cm2 with corresponding heat transfer coefficients of close to 90,000–100,000W/m2K, using HFE-7100 as the working fluid. For the condensation mode, the force-fed method produces heat fluxes up to 58W/cm2 with a heat transfer coefficient of 32,000W/m2K using HFE-7100.

Turbulent Heat Flux and Temperature Variance Dissipation Rate in Natural Convection in Lead-Bismuth

Results of a direct numerical simulation (DNS) for Rayleigh-Bénard convection for the Rayleigh number Ra = 105 in a fluid with the Prandtl number Pr = 0.025, which corresponds to liquid lead-bismuth, are used to analyze the turbulent heat flux and the temperature variance dissipation rate. The results indicate that application of a thermal or a mixed timescale may considerably improve gradient diffusion and algebraic heat flux models at these Rayleigh and Prandtl numbers. Therefore, a good approximation of the temperature variance dissipation rate is required. The standard temperature variance dissipation rate model is investigated using the DNS results. The analysis of the standard model shows the importance of wall functions and qualitatively good predictions by the model for this type of flow. Quantitatively, the model overpredicts the temperature variance dissipation rate evaluated from the results of DNS by ˜25%. The two-point correlation method is used to derive new models for the temperature variance dissipation rate. Comparison with DNS results shows qualitatively and quantitatively good predictions by the new models. These new models lead therefore to an increased accuracy of the turbulent heat flux models for this type of flow.

An equation for thermal dispersion flux transport and its mathematical modelling for heat and fluid flow in a porous medium

It is shown for the first time that the gradient diffusion hypothesis often adopted for thermal dispersion heat flux in heat transfer within porous media can be derived from a transport equation for the thermal dispersion heat flux based on the Navier–Stokes and energy equations. The transport equation valid for both thermal equilibrium and non-equilibrium cases is mathematically modelled so that all unknown spatial correlation terms, associated with redistribution and dissipation of the dispersion heat flux, are expressed in terms of determinable variables. The unknown coefficients are determined analytically by considering of macroscopically unidirectional flow through a tube as treated by Taylor. Taylor's expression for the dispersion has been generated from the transport equation. Both laminar and turbulent flow cases are investigated to obtain two distinct limiting expressions for low- and high-Péclet-number regimes. The results obtained for the Taylor diffusion problem are translated to the case of heat and fluid flow in a packed bed, to obtain the corresponding expressions for the axial dispersion coefficient in a packed bed. The resulting expression for the high-Péclet-number case agrees well with the empirical formula, validating of the present transport analysis.