Constructal conjugate cooling channels with internal heat generation

This paper presents a geometric optimisation of conjugate cooling channels in forced convection with internal heat generation. Two configurations were studied; circular channels and square channels. The configurations were optimised in such a way that the peak temperatures were minimised subject to the constraint of fixed total global volume. The fluid was forced through the cooling channels by the pressure difference across the channels. The structure has one degree of freedom as design variable: channel hydraulic diameter and once the optimal channel hydraulic diameter is found, optimal elemental volume and channel-to-channel spacing result. A gradient-based optimisation algorithm is applied in order to search for the best and optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. This optimiser adequately handles the numerical objective function obtained from CFD simulations. The results obtained show the behaviour of the applied pressure difference on the optimised geometry. There are unique optimal design variables for a given pressure difference. The numerical results obtained are in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes.     

Constructal optimisation of conjugate triangular cooling channels with internal heat generation

This paper presents the development of the three-dimensional flow architecture of conjugate cooling channels in forced convection with internal heat generation within a solid. Two types of cross-section channel geometries were used. The first involved equilateral triangles with three equal legs in length and all three internal angles of 60°. The second was isosceles right triangles with two legs of equal length and internal angles of 90°, 45° and 45°. Both the equilateral triangle and isosceles right triangle are special case of triangle that can easily and uniformly be packed and arranged to form a larger constructs. The configurations were optimised in such a way that the peak temperature of the heat generating solid was minimised subject to the constraint of a fixed global volume of the solid material. The cooling fluid was driven through the channels by the pressure difference across the channel. The degrees of freedom of the channels were aspect ratio, hydraulic diameter and channel to channel spacing ratio. The shape of the channel was allowed to morph to determine the best configuration that gives the lowest thermal resistance. A gradient-based optimisation algorithm was applied in order to search for the best optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. The effects of porosities, applied pressure and heat generation rate on the optimal aspect ratio and channel to channel spacing are reported. It was found that there are unique optimal design variables for a given pressure difference. The numerical results that were obtained were in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes. Results obtained show that the effects of applied dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.     

Analysis of three-dimensional heat transfer in micro-channel heat sinks

In this study, the three-dimensional fluid flow and heat transfer in a rectangular micro-channel heat sink are analyzed numerically using water as the cooling fluid. The heat sink consists of a 1-cm² silicon wafer. The micro-channels have a width of 57 μm and a depth of 180 μm, and are separated by a 43 μm wall. A numerical code based on the finite difference method and the SIMPLE algorithm is developed to solve the governing equations. The code is carefully validated by comparing the predictions with analytical solutions and available experimental data. For the micro-channel heat sink investigated, it is found that the temperature rise along the flow direction in the solid and fluid regions can be approximated as linear. The highest temperature is encountered at the heated base surface of the heat sink immediately above the channel outlet. The heat flux and Nusselt number have much higher values near the channel inlet and vary around the channel periphery, approaching zero in the corners. Flow Reynolds number affects the length of the flow developing region. For a relatively high Reynolds number of 1400, fully developed flow may not be achieved inside the heat sink. Increasing the thermal conductivity of the solid substrate reduces the temperature at the heated base surface of the heat sink, especially near the channel outlet. Although the classical fin analysis method provides a simplified means to modeling heat transfer in micro-channel heat sinks, some key assumptions introduced in the fin method deviate significantly from the real situation, which may compromise the accuracy of this method.     

Critical heat flux for subcooled flow boiling in micro-channel heat sinks

Critical heat flux (CHF) was measured and examined with high-speed video for subcooled flow boiling in micro-channel heat sinks using HFE 7100 as working fluid. High subcooling was achieved by pre-cooling the working fluid using a secondary low-temperature refrigeration system. The high subcooling greatly reduced both bubble departure diameter and void fraction, and precluded flow pattern transitions beyond the bubbly regime. CHF was triggered by vapor blanket formation along the micro-channel walls despite the presence of abundant core liquid, which is consistent with the mechanism of Departure from Nucleate Boiling (DNB). CHF increased with increasing mass velocity and/or subcooling and decreasing hydraulic diameter for a given total mass flow rate. A pre-mature type of CHF was caused by vapor backflow into the heat sink’s inlet plenum at low mass velocities and small inlet subcoolings, and was associated with significant fluctuations in inlet and outlet pressure, as well as wall temperature. A systematic technique is developed to modify existing CHF correlations to more accurately account for features unique to micro-channel heat sinks, including rectangular cross-section, three-sided heating, and flow interaction between micro-channels. This technique is shown to be successful at correlating micro-channel heat sink data corresponding to different hydraulic diameters, mass velocities and inlet temperatures.     

Constructal multi-scale design of compact micro-tube heat sinks and heat exchangers

A constructal multi-scale design approach is examined for micro-tube heat sinks and heat exchangers. Heat transfer per unit volume is increased by considering the use of additional micro-tubes placed in the intersticial regions of a circular tube array. Three constructs are considered in the proposed analysis. As the system complexity increases, the heat transfer rate increases, and exceeds the theoretical value for a volume of similar size, composed of parallel plates. Approximate solutions for the diameter of the principal construct are obtained for each case using Bejan's intersection of asymptotes method. Exact analytical methods are applied to determine the relative increase in heat dissipation per unit volume as compared with systems containing parallel plates.     

Constructal design of forced convection cooled microchannel heat sinks and heat exchangers

Heat transfer from arrays of circular and non-circular ducts subject to finite volume and constant pressure drop constraints is examined. It is shown that the optimal duct dimension is independent of the array structure and hence represents an optimal construction element. Solutions are presented for the optimal duct dimensions and maximum heat transfer per unit volume for the parallel plate channel, rectangular channel, elliptic duct, circular duct, polygonal ducts, and triangular ducts. Approximate analytical results show that the optimal shape is the isosceles right triangle and square duct due to their ability to provide the most efficient packing in a fixed volume. Whereas a more exact analysis reveals that the parallel plate channel array is in fact the superior system. An approximate relationship is developed which is very nearly a universal solution for any duct shape in terms of the Bejan number and duct aspect ratio. Finally, validation of the relationships is provided using exact results from the open literature.     

Constructal design of underground heat sources or sinks for the annual cycle

Here we show that the heat transfer between a pipe assembly and the soil during the annual temperature cycle of a heat pump depends on the configuration of the flow system. We rely on constructal design to find the flow architecture (spacings, shapes) such that the heat transfer between the assembly and the ground is increased. The flow configuration changes freely, and its design is evolutionary. The better shapes change gradually from slender to square as the volume fraction occupied by the flow assembly increases. The heat transfer performance increases as the depth of the structure decreases, but the depth has a negligible effect on the shape of the structure. The results also show that the heat transfer performance increases as the configuration of the ground volume and the buried structure evolves to the most slender shape possible.     

Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks

Experiments were performed to measure the incipient boiling heat flux in a heat sink containing 21 rectangular (231 μm wide and 713 μm deep) micro-channels. Tests were performed using deionized water with inlet liquid velocities of 0.13-1.44 m/s, inlet temperatures of 30, 60 and 90 °C, and an outlet pressure of 1.2 bar. Using a microscope, boiling incipience was identified when the first bubbles were detected growing at, and departing from the micro-channel wall near the outlet. A comprehensive model was developed to predict the incipient boiling heat flux, accounting for the complexities of bubble formation along the flat and corner regions of a rectangular flow channel, as well as the likelihood of bubbles growing sufficiently large to engulf the entire flow area of a micro-channel. The model is based on a bubble departure criterion, which combines both mechanical considerations (force balance on a bubble) and thermal considerations (superheating entire bubble interface). The model shows good agreement with the experimental results.     

Analysis of microchannel heat sinks for electronics cooling

This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio (α_s) and effective thermal conductivity ratio (k?) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number (Nu) increases as α_s is increased and decreases with increasing k?. However, the results also reveal that there exists significant difference between the two approaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either α_s or k? is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity (ε) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.     

A comparative analysis of innovative microchannel heat sinks for electronic cooling

In this work, a comparative analysis of innovative microchannel heat sinks such as two-layered and multi-layered microchannel heat sinks (MCHS), or thin films within flexible complex seals and cooling augmentation using microchannels with rotatable separating plates, is presented. A compilation of the numbers of layers, main characteristics, setups, advantages and disadvantages, thermal resistance, pumping power in double-layer (DL-MCHS) and multi-layer MCHS (ML-MCHS) is presented. In addition, the thermal resistance is analyzed in order to present a comparison between the single-layer MCHS (SL-MCHS) and multi-layer microchannels. The results of comparison indicates that double-layer and multi-layer MCHS have lower thermal resistance and require smaller pumping power and they resolve the high streamwise temperature rise problem of SL-MCHS.     

Three-dimensional thermal analysis of heat sinks with circular cooling micro-channels

The pressure drop and thermal characteristics of heat sinks with circular micro-channels are investigated using the continuum model consisting of the conventional Navier-Stokes equations and the energy conservation equation. Developing flow (both hydrodynamically and thermally) is assumed in the fluid region and three-dimensional conjugate heat transfer is assumed in the solid region. Thermal results based on this approach are shown to be in good agreement with existing experimental data. Effects of various geometrical parameters, material properties, and Reynolds number on the thermal performance of the sink were investigated. A comparison between circular and rectangular channels at the same Reynolds number and hydraulic diameter showed that sinks with rectangular channels have lower thermal resistance, while sinks with circular channels dissipate more heat per unit pumping power.     

Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow

Based on constructal theory, five different cases with multistage bifurcations are designed as well as one case without bifurcations, and the corresponding laminar fluid flow and thermal performance have been investigated numerically. All laminar fluid flow and heat transfer results are obtained using computation fluid dynamics, and a uniform wall heat flux thermal boundary condition is applied all heated surfaces. The inlet velocity ranges from 0.66 m/s to 1.6 m/s with the corresponding Reynolds number ranging from 230 to 560. The pressure, velocity, temperature distributions and averaged Nusselt number are presented. The overall thermal resistances versus inlet Reynolds number or pumping power are evaluated and compared for the six microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with multistage bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sink with a long bifurcation length in the first stage (Case 1A) is superior. The usage of multistage bifurcated plates in microchannel heat sink can reduce the overall thermal resistance and make the temperature of the heated surface more uniform (Case 3). It is suggested that proper design of the multistage bifurcations could be employed to improve the overall thermal performance of microchannel heat sinks and the maximum number of stages of bifurcations is recommended to be two. The study complements and extends previous works.     

Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks

Published studies concerning transport phenomena in micro-channel heat sinks can be divided into those concerning saturated boiling versus those focused on subcooled boiling, with the vast majority related to the former. What has been lacking is a single generalized method to tackle both boiling regimes. The primary objective of the present paper is to construct a consolidated method to predicting transport behavior of micro-channel heat sinks incurring all possible heat transfer regimes. First, a new correlation is developed for subcooled flow boiling pressure drop that accounts for inlet subcooling, micro-channel aspect ratio, and length-to-diameter ratio. This correlation shows excellent predictive capability against subcooled HFE 7100 pressure drop data corresponding to four different micro-channel geometries. Next, a consolidated method is developed for pressure drop that is capable of tackling inlet single-phase liquid, subcooled boiling, saturated boiling, and single-phase vapor regimes as well as inlet contraction and outlet expansion. A similar consolidated method is developed to predict the heat transfer coefficient that is capable of tackling all possible combinations of heat transfer regimes. The new consolidated method is shown to be highly effective at reproducing both data and trends for HFE 7100, water and R134a.     

Study of impingement cooling of heat sinks for LSI packages with longitudinal fins

This paper describes an experimental and a semi-empirical study on the impingement cooling characteristics of heat sinks with longitudinal fins of a type suitable for LSI packages. The experiments were performed with a variety of different fins. To enhance impingement cooling, one long rectangular inlet orifice (slit) over the center of the heat sink was found to offer the best structure. The optimum orifice width is about 1/6 of the base width of the heat sink. The thermal resistance at a fixed volumetric flow rate and orifice width varies little with size of the gap between the fin tops and inlet orifice, but gaps near 2 mm slightly lower the resistance. Correlations are proposed between the thermal resistance of the heat sink and the geometry of the longitudinal fins. The accuracy of the predicted thermal resistances was found to be within ±25% of the experimental data. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(8): 537–553, 1996     

Measurement of performance of plate-fin heat sinks with cross flow cooling

This work assesses the performance of plate-fin heat sinks in a cross flow. The effects of the Reynolds number of the cooling air, the fin height and the fin width on the thermal resistance and the pressure drop of heat sinks are considered. Experimental results indicate that increasing the Reynolds number can reduce the thermal resistance of the heat sink. However, the reduction of the thermal resistance tends to become smaller as the Reynolds number increases. Additionally, enhancement of heat transfer by the heat sink is limited when the Reynolds number reaches a particular value. Therefore, a preferred Reynolds number can be chosen to reduce the pumping power. For a given fin width, the thermal performance of the heat sink with the highest fins exceeds that of the others, because the former has the largest heat transfer area. For a given fin height, the optimal fin width in terms of thermal performance increases with Reynolds number. As the fins become wider, the flow passages in the heat sink become constricted. As the fins become narrower, the heat transfer area of the heat sink declines. Both conditions reduce the heat transfer of the heat sink. Furthermore, different fin widths are required at different Reynolds numbers to minimize the thermal resistance.     

Constructal tree-shaped two-phase flow for cooling a surface

This paper documents the strong relation that exists between the changing architecture of a complex flow system and the maximization of global performance under constraints. The system is a surface with uniform heating per unit area, which is cooled by a network with evaporating two-phase flow. Illustrations are based on the design of the cooling network for a skating rink. The flow structure is optimized as a sequence of building blocks, which starts with the smallest (elemental volume of fixed size), and continues with assemblies of stepwise larger sizes (first construct, second construct, etc.). The optimized flow network is tree shaped. Three features of the elemental volume are optimized: the cross-sectional shape, the elemental tube diameter, and the shape of the elemental area viewed from above. The tree that emerges at larger scales is optimized for minimal amount of header material and fixed pressure drop. The optimal number of constituents in each new (larger) construct decreases as the size and complexity of the construct increase. Constructs of various levels of complexity compete: the paper shows how to select the optimal flow structure subject to fixed size (cooled surface), pressure drop and amount of header material.     

Two-phase flow in high-heat-flux micro-channel heat sink for refrigeration cooling applications: Part II—heat transfer characteristics

This paper is the second of a two-part study concerning two-phase flow and heat transfer characteristics of R134a in a micro-channel heat sink incorporated as an evaporator in a refrigeration cycle. Boiling heat transfer coefficients were measured by controlling heat flux (q″ = 15.9 − 93.8 W/cm²) and vapor quality (x_e = 0.26 − 0.87) over a broad range of mass velocity. While prior studies point to either nucleate boiling or annular film evaporation (convective flow boiling) as dominant heat transfer mechanisms in small channels, the present study shows heat transfer is associated with different mechanisms for low, medium and high qualities. Nucleate boiling occurs only at low qualities (x_e < 0.05) corresponding to very low heat fluxes, and high fluxes produce medium quality (0.05 < x_e < 0.55) or high quality (x_e > 0.55) flows dominated by annular film evaporation. Because of the large differences in heat transfer mechanism between the three quality regions, better predictions are possible by dividing the quality range into smaller ranges corresponding to these flow transitions. A new heat transfer coefficient correlation is recommended which shows excellent predictions for both R134a and water.     

Conjugate heat transfer characterization in cooling channels

Cooling technology of gas turbine blades,primarily ensured via internal forced convection,is aimed towards withdrawing thermal energy from the airfoil.To promote heat exchange,the walls of internal cooling passages are lined with repeated geometrical flow disturbance elements and surface non-uniformities.Raising the heat transfer at the expense of increased pressure loss;the goal is to obtain the highest possible cooling effectiveness at the lowest possible pressure drop penalty.The cooling channel heat transfer problem involves convection in the fluid domain and conduction in the solid.This coupled behavior is known as conjugate heat transfer.This experimental study models the effects of conduction coupling on convective heat transfer by applying iso-heat-flux boundary condition at the external side of a scaled serpentine passage.Investigations involve local temperature measurements performed by Infrared Thermography over flat and ribbed slab configurations.Nusselt number distributions along the wetted surface are obtained by means of heat flux distributions,computed from an energy balance within the metal domain.For the flat plate experiments,the effect of conjugate boundary condition on heat transfer is estimated to be in the order of 3%.In the ribbed channel case,the normalized Nusselt number distributions are compared with the basic flow features.Contrasting the findings with other conjugate and convective iso-heat-flux literature,a high degree of overall correlation is evident.