Multi-objective thermal design optimization and comparative analysis of electronics cooling technologies

A multi-objective thermal design optimization and comparative study of electronics cooling technologies is presented. The cooling technologies considered are: continuous parallel micro-channel heat sinks, in-line and staggered circular pin-fin heat sinks, offset strip fin heat sinks, and single and multiple submerged impinging jet(s). Using water and HFE-7000 as coolants, Matlab’s multi-objective genetic algorithm functions were utilized to determine the optimal thermal design of each technology based on the total thermal resistance and pumping power consumption under constant pressure drop and heat source base area of 100 mm². Plots of the Pareto front indicate a trade-off between the total thermal resistance and pumping power consumption. In general, the offset strip fin heat sink outperforms the other cooling technologies.     

Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications

In this study, the cooling performance and mass of a pin-fin radial heat sink were optimized. A radial heat sink with pin fins was examined numerically to obtain a lighter heat sink while maintaining a similar cooling performance to that of a plate-fin heat sink investigated in a previous study. Both natural convection and radiation heat transfer were considered. Experiments were performed to validate the numerical model. The average temperature and mass of the heat sink for various types of fin arrays were compared to determine an appropriate reference configuration. The effects of various geometric parameters on the thermal resistance and mass of the heat sink were investigated; these indicated that the system was sensitive to the number of fin arrays, as well as the length of the long and middle fins. Multidisciplinary optimization was carried out using the three design variables to minimize the thermal resistance and mass simultaneously, and Pareto fronts were obtained with various weighting factors. A design for the optimum radial heat sink is proposed, which reduces the mass by more than 30% while maintaining a similar cooling performance to that of a plate-fin heat sink.     

OPTIMIZATION OF PIN-FIN HEAT SINKS USING ANISOTROPIC LOCAL THERMAL NONEQUILIBRIUM POROUS MODEL IN A JET IMPINGING CHANNEL

A numerical study has been carried out to optimize the thermal performance of a pin-fin heat sink. A pin-fin heat sink, which is placed horizontally in a channel, is modeled as a hydraulically and thermally anisotropic porous medium. A uniform heat flux is prescribed at the bottom of the heat sink. Cool air is supplied from the top opening of the channel and exhausts to the channel outlet. Comprehensive numerical solutions are derived from the governing Navier-Stokes and energy equations using the Brinkman-Forchheimer extended Darcy model and the local thermal nonequilibrium (LTNE) porous model for the region occupied by the heat sink. Results from this study indicate that the anisotropy in permeability and solid-phase effective thermal conductivity changes substantially with the variation of porosity. Optimum porosity for maximum heat dissipation depends on the pin-fin thickness, the pin-fin height, and the Reynolds number. A correlation for predicting the optimum porosity for a pin-fin heat sink is proposed. Generally, in the case of thin pin-fins the heat sink should be designed to have a high porosity, while in the case of thick pin-fins the heat sink should be designed to have a relatively low porosity.     

Comparison of Fluid Flow and Thermal Characteristics of Plate-Fin and Pin-Fin Heat Sinks Subject to a Parallel Flow

In this study, we compare the thermal performances of the two types of heat sinks most commonly used in the electronic equipment cooling: plate-fin and pin-fin heat sinks. In order to obtain the fluid flow and thermal characteristics of heat sinks, an experimental investigation is conducted. Based on the experimental results of the present study and the available data from the existing literature, the correlations of the friction factor and the Nusselt number are suggested for each type of heat sink. Correlations for the pin-fin heat sinks are newly developed, while correlations for the plate-fin heat sinks are selected from previous models. By using the appropriate correlations, thermal resistances of the optimized plate-fin and pin-fin heat sinks are compared under fixed pumping power conditions. Finally, a contour map, which depicts the ratio of the thermal resistances of the optimized plate-fin and pin-fin heat sinks as a function of dimensionless pumping power and dimensionless length, is presented. The contour map indicates that optimized plate-fin heat sinks possess lower thermal resistances than optimized pin-fin heat sinks when dimensionless pumping power is small and the dimensionless length of heat sinks is large. On the contrary, the optimized pin-fin heat sinks have smaller thermal resistances when dimensionless pumping power is large and the dimensionless length of heat sinks is small.     

Application of response surface methodology in the parametric optimization of a pin-fin type heat sink

In this paper, an effective procedure of response surface methodology (RSM) has been successfully developed finding the optimal values of designing parameters of a pin-fin type heat sink (PFHS) under constrains of mass and space limitation to achieve the high thermal performance (or cooling efficiency). Various design parameters, such as height and diameter of pin-fin and width of pitch between fins are explored by experiment. The thermal resistance and pressure drop are considered as the multiple thermal performance characteristics. Experiments are performed by a standard RSM design called a central composite design (CCD). The results identify the significant influence factors to minimize thermal resistance and pressure drop. The obtained optimal designing parameters have been predicted and verified by conducting confirmation experiments.     

Effect of cooling channel geometry on re-cooled cycle performance for hydrogen fueled scramjet

Developing fuel with higher heat sink is widely carried out to meet the cooling requirement for an airbreathing hypersonic vehicle. However, a Re-Cooled Cycle has been newly proposed for a regeneratively cooled scramjet to reduce the fuel flow for cooling. Fuel heat sink (cooling capacity) is repeatedly used to indirectly increase the fuel heat sink. Parametric sensitivity analysis of Re-Cooled Cycle of a hypersonic aircraft is explored. An analytical fin-type model for incompressible flow in smooth-wall rectangular ducts in terms of hydrodynamic, thermal, power balance and Mach number constraints is proposed. Based on this model, the difference of the cooling channel structure design between Re-Cooled Cycle and regenerative cooling is discussed, and a new optimization index is introduced for Re-Cooled Cycle. The sensitivity of the cycle performance to cooling channel geometry is investigated, and the optimal performance of a Re-Cooled Cycle is obtained by satisfying constraints. The differences of the effect of channel design variables between Re-Cooled Cycle and regenerative cooling are also discussed.     

Parametric study on the combined thermal and hydraulic performance of single phase micro pin-fin heat sinks part I: Square and circle geometries

This paper is the first part of a three paper series studying the overall performance of a micro pin-fin heat sink with single phase liquid flow and different pin-fin geometries operating under and similar conditions. Two different heat sinks, one with square shaped pin-fins and the other with circular pin-fins are selected for study in this paper. The paper focuses on studying the effect of thermal resistance and pressure drop of micro heat sinks when subjected to various factors such as pitch distance in axial and transverse directions, aspect ratio of the pin-fin, hydraulic diameters of the pin-fin, and the liquid flow rate through the device. A figure of merit (FOM) involving both the thermal resistance and pressure drop across the heat sink is introduced in the paper and the performance is evaluated on the basis of this FOM. The heat sinks are subjected to uniform heat flux at the bottom of the heat sink and the characteristic study is based on constant Reynolds number of liquid flow at the entrance of the channel. Water is used as the fluid in this study. The study is conducted over the Reynolds number range of 50–500. The characteristic study is carried out with the help of simulations developed using commercially available computational fluid dynamics software CoventorWare?. The characteristic study carried out in this paper is divided into four cases. In the first case the axial pitch distance is varied between 350 μm and 650 μm by keeping the aspect ratio of the pin-fin structure constant at 0.5. For the second case the transverse pitch distance is varied between 150 μm and 300 μm and the aspect ratio is kept the same as in the first case. Third case studies the effect of varying the aspect ratio (between 0.33 and 1) of the pin-fin structures by keeping both pitches constant. Case four studies the variation in the performance of the heat sink with the change in the hydraulic diameter of the pin-fins. The study conducted in this paper reveals the importance of considering the pressure drop along with the thermal resistance in evaluating the overall performance of the micro pin-fin heat sink. At low Reynolds number (below 300) the heat sinks with circular pin-fins shows better performance compared with heat sinks with square pin-fins and vice versa at high Reynolds number (above 300). FOM varies considerably with the change in the parameters like axial pitch distance, transverse pitch distance, aspect ratio and hydraulic diameter of the pin-fins.     

Development of a theoretical model for predicting the thermal performance characteristics of a vertical pin-fin array heat sink under combined forced and natural convection with impinging flow

A comprehensive theoretical and experimental study was carried out on the thermal performance of a pin-fin heat sink. A theoretical model was formulated that has the capability of predicting the influence of various geometrical, thermal, and flow parameters on the effective thermal resistance of the heat sink. An experimental technique was developed for measuring the thermal performance of the heat sink, and the overall convective heat transfer coefficient for the fin bundle. Experiments were carried out, and correlations obtained, for a wide range of parameters for pure natural convection and for combined forced and natural convection. The predictive capability of the theoretical model was verified by comparison with experimental data including the influence of various fin parameters and the existence of an optimum fin spacing.     

Prediction algorithm of thermal resistance for impingement cooling of heat sinks for LSI packages with pin-fin arrays

This paper is a semi-empirical report on an algorithm for the prediction of thermal resistance for impingement cooling of pin-fin heat sinks for LSI packages when the inlet orifice is relatively large and is located over the center of the sink. We present a physical model suitable for these types of heat sinks, based on flow visualization results. The model divides the flow region into five parts: I) the top surfaces of the fins where they are directly under the inlet orifice, II) the portions of the vertical surfaces of the pin-fin cylinders, where those surfaces are directly below the inlet port, III) the surface of the base to which the fins are attached, excluding the areas occupied by the feet of the fins themselves, IV) the portions of the vertical surfaces of the fin-cylinders excluding those portions of the surfaces that are directly below the inlet port (complementary to region II), V) the portions of the top surfaces of the pins, excluding those portions directly below the inlet port (complementary to region I). We predicted thermal resistance values for heat sinks with pin-fin arrays, for a variety of orifice diameters, gaps, pin-fin diameters, and heights, and number of fins. These values agreed with experimental data within ±30%. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(7): 434–448, 1996     

受限空气射流冲击矩形柱鳍热沉换热实验研究

采用实验方法研究了受限空气冲击射流与矩形柱鳍热沉相结合的散热方式应用于芯片冷却的换热规律,采用最小二乘法对实验数据进行了拟合,并最终获得平均努塞尔数关于雷诺数、喷口高度-孔径比及普朗特数的实验准则方程。在此基础上将这种散热方式与其他空冷方式进行了换热能力的比较,结果表明此种散热方式的换热能力大大超过其他空冷方式。最后,对实验系统误差进行了分析,根据误差传递理论求得的平均努塞尔数的实验相对误差不超过6%。     

NUMERICAL SHAPE OPTIMIZATION FOR HIGH PERFORMANCE OF A HEAT SINK WITH PIN-FINS

The design optimization of a 7 × 7 pin-fin heat sink is performed numerically. To achieve higher thermal performance of the heat sink, the thermal resistance at the junction of the chip and the heat sink and the overall pressure drop in the heat sink have to be minimized simultaneously. The fin height (h), fin width (w), and fan-to-heat sink distance (c) are chosen as the design variables, and the pressure drop (ΔP) and thermal resistance (θ _ja ) are adopted as the objective functions. To obtain the optimum design values, we used the finite-volume method for calculating the objective functions, the Broydon-Fletcher-Goldfarb-Shanno method for solving the unconstrained nonlinear optimization problem, and the weighting method for predicting the multiobjective problem. The results show that the optimum design variables for the weighting coefficient of 0.5 are as follows: w = 4.653 mm, h = 59.215 mm, and c = 2.669 mm. The objective functions corresponding to the optimal design are calculated as ΔP = 6.82 Pa and θ _ja  = 0.56 K/W. The Pareto solutions are also presented for various weighting coefficients, and they offer very useful data for designing a pin-fin heat sink.     

Modeling and optimization of designing parameters for a parallel-plain fin heat sink with confined impinging jet using the response surface methodology

The parallel-plain fin (PPF) array structure is widely applied in convective heat sinks in order to create extended surface for the enhancement of heat transfer. In the present study, for investigating the influences of designing parameters of PPF heat sink with an axial-flow cooling fan on the thermal performance, a systematic experimental design based on the response surface methodology (RSM) is used. The thermal resistance and pressure drop are adopted as the thermal performance characteristics. Various designing parameters, such as height and thickness of fin, width of passage between fins, and distance between the cooling fan and the tip of fins, are explored by experiment. Those parameters affect the structure arrangement, geometry of fins and the status of impinging jet from an axial-flow cooling fan installed over the heat sink. A standard RSM design called a central composite design is selected as experimental plan for the four parameters mentioned above. An effective procedure of response surface methodology (RSM) has been proposed for modeling and optimizing the thermal performance characteristics of PPF heat sink with the design constrains. The most significant influential factors for minimizing thermal resistance and pressure drop have been identified from the analysis of variance. The confirmation experimental results indicate that the proposed model is reasonably accurate and can be used for describing the thermal resistance and pressure drop with the limits of the factors studied. The optimum designing parameters of PPF heat sink with an axial-flow cooling fan under constrains of mass and space limitation, which are based on the quadratic model of RSM and the sequential approximation optimization method, are found to be fin height of 60 mm, fin thickness of 1.07 mm, passage width between fins of 3.32 mm, and distance between the cooling fan and the tip of fins of 2.03 mm.     

Fluid flow and heat transfer characteristics of cross-cut heat sinks

In this study, effects of cross-cuts on the thermal performance of heat sinks under the parallel flow condition are experimentally studied. To find effects of the length, position, and number of cross-cuts, heat sinks with one or several cross-cuts ranging from 0.5 mm to 10 mm were fabricated. The pressure drop and the thermal resistance of the heat sinks are obtained in the range of 0.01 W<P_p < 1 W. Experimental results show that among the many cross-cut design parameters, the cross-cut length has the most significant influence on the thermal performance of heat sinks. The results also show that heat sinks with a cross-cut are superior to heat sinks containing several cross-cuts in the thermal performance. Based on experimental results, the friction factor and Nusselt number correlations for heat sinks with a cross-cut are suggested. Using the proposed correlations, thermal performances of cross-cut heat sinks are compared to those of optimized plate-fin and square pin-fin heat sinks under the constant pumping power condition. This comparison yields a contour map that suggests an optimum type of heat sink under the constraint of the fixed pumping power and fixed heat sink volume. The contour map shows that an optimized cross-cut heat sink outperforms optimized plate-fin and square pin-fin heat sinks when 0.04 < log L1 < 1.     

Scroll heat sink: A novel heat sink with the moving fins inserted between the cooling fins

In this paper, a new type of a fan-integrated heat sink named a scroll heat sink is proposed and demonstrated. The most striking feature of the scroll heat sink is that heat dissipation and fluid pumping occurs simultaneously in the whole cooling space without requiring any additional space for a fan module. In the scroll heat sink, the moving fins, which rotate with two eccentric shafts, are inserted between the fixed (cooling) fins. By a relative motion between the moving fins and the cooling fins, a coolant is drawn into the space between them, takes heat away from the cooling fins, and the heated coolant is discharged out of the heat sink. In the present study, an experimental investigation is performed in order to demonstrate the concept of the scroll heat sink. Average coolant velocities and thermal resistances of the scroll heat sink are measured for various rotating speeds of the moving fins from 200 rpm to 500 rpm. Experimental results show that measured flow rates of the coolant are almost linearly proportional to the rotating speed of the moving fins. A theoretical model is also developed to estimate the required pumping power and the thermal resistance, and validated using experimental results. The theoretical model shows that optimized scroll heat sinks have lower thermal resistances than optimized plate-fin heat sinks under the fixed pumping power condition.     

Comparison of thermal performances of plate-fin and pin-fin heat sinks subject to an impinging flow

In this paper, we compare thermal performances of two types of heat sinks commonly used in the electronic equipment industry: plate-fin and pin-fin heat sinks. In particular, heat sinks subject to an impinging flow are considered. For comparison of the heat sinks, experimental investigations are performed for various flow rates and channel widths. From experimental data, we suggest a model based on the volume averaging approach for predicting the pressure drop and the thermal resistance. By using the model, thermal resistances of the optimized plate-fin and pin-fin heat sinks are compared. Finally, a contour map, which depicts the ratio of the thermal resistances of the optimized plate-fin and pin-fin heat sinks as a function of dimensionless pumping power and dimensionless length, is presented. The contour map indicates that optimized pin-fin heat sinks possess lower thermal resistances than optimized plate-fin heat sinks when dimensionless pumping power is small and the dimensionless length of heat sinks is large. On the contrary, the optimized plate-fin heat sinks have smaller thermal resistances when dimensionless pumping power is large and the dimensionless length of heat sinks is small.     

Effect of tip clearance on the cooling performance of a microchannel heat sink

In this paper, the effect of tip clearance on the cooling performance of the microchannel heat sink is presented under the fixed pumping power condition. The thermal resistance of a microchannel heat sink is defined for evaluating its cooling performance. The effect of tip clearance is numerically investigated by increasing tip clearance from zero under the fixed pumping power condition. From the numerical results, the optimized tip clearance is determined, for which the thermal resistance has a minimum value. Finally, we show that the presence of tip clearance can improve the cooling performance of a microchannel heat sink when tip clearance is smaller than a channel width.     

Optimization design of microchannel heat sink geometry for high power laser mirror

Microchannel heat sink for high power laser mirror with water cooling was analyzed as a function of microchannel geometry and operation parameters. A comparative analysis of the thermal deformation on the mirror surface without cooling and that with cooling revealed that the maximal thermal deformation on the mirror surface could decrease from about 0.115 μm to around 0.040 μm under the laser power of 200 W/cm² by using microchannel heat sink designed. In order to enhance the performance of microchannel heat sink, the effects of channel width, channel depth, fin width, mirror thickness and cooling region were investigated. The results indicated that the heat transfer performance of the microchannel heat sink could be further improved by narrow and deep channel, narrow fin, thin mirror and large cooling region.     

Heat transfer and pressure loss characteristics of very compact heat sinks

High-performance compact heat sinks have been developed for the effective cooling of high-density LSI packaging. Heat transfer and pressure loss characteristics of the heat sinks in both air-cross-flow and air-jet cooling have been experimentally studied. The present heat sinks were of plate-fin and pin-fin arrays with a fin pitch of 0.7 mm. The plate-fin heat sinks had higher cooling performance than the pin-fin heat sinks in the range of large airflow rates both in air-cross-flow and air-jet cooling. The thermal conductance in cross-flow cooling was 20 or 40% larger than that in jet cooling. The correlation of Colburn j-factor/Fanning friction factor versus the Reynolds number for the present heat sinks was found to be very close to that of a conventional large-size heat exchanger. © Scripta Technica, Heat Trans Asian Res, 28(8): 687-705, 1999     

Parametric study of heat-transfer design on the thermoelectric generator system

This study developed an integral thermoelectric generator system with high-performance heat transfer and thermoelectric conversion functions, using the metal pin-fin array coupling with the forced convection heat transfer technique to be the heat absorber and heat sink. A one-dimensional steady heat conduction model with internal Joule heat generation and Seebeck effect was proposed to predict the power generation performance of the present thermoelectric system including the heat absorber and heat sink at various operation conditions. Critical heat-transfer parameters on the design of the integral thermoelectric generator system were derived and discussed. Finally, a series of systematical experiments were performed to simulate an integral thermoelectric generator system operating at the exhaust pipe. The experimental results also demonstrated the validity of the proposed theoretical model.     

数据中心服务器水冷散热器的数值模拟与实验验证

水冷散热器在数据中心服务器CPU芯片冷却技术中发挥着重要的作用。如何获得高性能的散热效率成为了该领域关注的重点。针对一种翅柱式水冷散热器,用数值模拟的方法,通过改变翅柱的结构参数来优化散热器的散热性能以及流动特性。在相同的翅柱间距下,改变翅柱的直径和高度,在不同的入口流量下,研究其温度,努塞尔数,压降,摩擦系数,分析比较其综合系数对散热性能的影响,并对结果进行了实验验证。结果表明翅柱高度3.9mm,直径为0.9mm的散热器其综合系数最大