IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 4, APRIL 2013
Design Optimization of Manifold Microchannel Heat Sink Through Evolutionary Algorithm Coupled With Surrogate Model Afzal Husain and Kwang-Yong Kim
Abstract— A liquid flow manifold microchannel heat sink is optimized with the help of 3-D numerical analysis, a surrogate method, and a multiobjective evolutionary algorithm. The performance of the manifold microchannel heat sink is optimized for the overall thermal resistance and the pumping power required for driving the coolant. The design variables related to the width of the microchannel, depth of the microchannel, width of fins, length of the nozzles, and height of the nozzles, which contribute to objective functions, are identified and optimized for minimum thermal resistance and pumping power. A Latin hypercube sampling method is used to exploit the design space. The numerical solutions obtained at these design points are utilized to construct a surrogate model, i.e., response surface approximation. The Navier–Stokes and energy equations for laminar flow and conjugate heat transfer are solved using a finitevolume solver. A hybrid multi objective evolutionary algorithm coupled with a surrogate model is applied to find out global Pareto-optimal designs (PODs). Trade-off analysis is performed in view of the conflicting nature of the two objectives, which yields PODs with low thermal resistance at various pumping powers. The ratio of the microchannel width to the microchannel height and that of the nozzle height to the microchannel height are found to be more Pareto-optimal sensitive (sensitive along the Pareto-optimal front) than others. In contrast, the ratio of the fin width to the microchannel height and that of the nozzle length to the microchannel width are found to be less Pareto-optimal sensitive than other design variables. The PODs showed lower thermal resistance and pumping power than the reference designs at various mass flow rates. Index Terms— Electronics cooling, evolutionary algorithm, manifolds, microchannels, multiobjective optimization, numerical simulation.
anz E cv f(x)
N OMENCLATURE Area of nozzle. Generalized root mean square error based on leave-one-out cross-validation. Vector of objective functions.
Manuscript received May 30, 2011; revised March 30, 2012; accepted January 21, 2013. Date of publication February 22, 2013; date of current version March 28, 2013. This work was supported in part by a Multiphenomena CFD Engineering Research Center Grant Funded by the National Research Foundation of Korea and by a Inha University Research Grant. Recommended for publication by Associate Editor P. Sathyamurthy upon evaluation of reviewers’ comments. A. Husain was with the Department of Mechanical Engineering, Inha University, Incheon 402-751, Korea. He is now with the Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat PC-123, Oman (e-mail:
[email protected]). K.-Y. Kim is with the Department of Mechanical Engineering, Inha University, Incheon 402-751, Korea (e-mail:
[email protected]). Digital Object Identifier 10.1109/TCPMT.2013.2245943
fˆ(x) g(x) h hc hs h nz h(x) k lc L chip lnz m Nm nc n nz Ndv Ngen Npop p P q Rth R2 2 Radj T u v nz V˙ Wchip Wm,c Wm,w wc ww x x, y, z
Response of surrogate model. Vector of inequality functions. Specific enthalpy. Microchannel depth. Thickness of the substrate base. Height of the nozzle. Vector of equality functions. Thermal conductivity. Length of the unit cell of microstructure. Length of the chip. Length of the nozzle. Number of design points in the design space. Number of manifold systems. Number of microchannels. Number of inlet nozzles. Number of design variables. Number of generations. Population size. Pressure. Pumping power. Heat flux. Thermal resistance. Coefficient of multiple determinations. Adjusted value of R 2 . Temperature. Liquid velocity in the microchannel. Velocity of fluid through the nozzle. Flow rate through the heat sink. Width of the chip. Width of the manifold channel. Width of the manifold wall. Width of the microchannel. Fin width. Vector of design variables. Orthogonal coordinate system. G REEK S YMBOLS
α, β α∗, β∗ γ, η γ ∗, η∗ μ
Design variables, wc / h c and ww / h c . Normalized design variables ranging from 0 to 1. Design variables, lnz /wc and h nz / h c . Normalized design variables ranging from 0 to 1. Change/difference in value. Dynamic viscosity.
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IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 4, APRIL 2013
ρ τi j ξ
Density. Stress tensor. Estimated parameters.
f i max o s
S UBSCRIPTS Fluid. Inlet. Maximum value. Outlet. Substrate. I. I NTRODUCTION
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HE ever-growing demands for high heat-flux dissipation from various devices such as electronics chips, microchemical reactors, microfuel cells, laser diodes, and power electronics etc., pose a challenge to heat-transfer researchers and constitute a limitation for packaging industries regarding multichips and multidimensional integration of electronic circuits. The miniaturization of electronic components and the increased density of electronic circuits have led to a significant increase in heat generation in an integrated circuit. For the next generation, electronics cooling through forced air convection will not be sufficient for ultralarge scale integration of electronics. These electronics require cooling solutions for high heat flux as well as minimal temperature nonuniformity. Therefore, improvements in heat transfer techniques and new design concepts have received greater attention at the microlevel. Recent research and developments have shown the possibility of integrating liquid cooling systems with high-density electronic circuits. Tuckerman and Pease [1] first realized the potential of this technology and laid a foundation for experimentation with silicon-based microchannel heat sinks (MCHSs). Since then silicon-based MCHS has been long studied for its thermal characterization [2]–[8] and optimization [9]–[14]. The growing limitations in terms of the temperature nonuniformity of the heat source and high heat-flux removal from the chip surface have encouraged researchers to investigate manifold MCHSs (MMCHSs). The MMCHS was first investigated by Harpole and Eninger [15] as being an effective way of reducing the temperature variations within the heat source and the pressure drop. Later on, Copeland [16] and Copeland et al. [17] carried out analytical and experimental studies, respectively, demonstrating the performance of an MMCHS. In various experiments concerning MMCHSs, Copeland et al. [17] reported that the thermal resistance was inversely proportional to the volumetric flow rate on a log-log scale. Escher et al. [18] carried out an experimental investigation of an ultrathin MMCHS. They suggested fabrication and packaging procedures to manufacture a prototype by means of standard microprocessing. They found that for lower pumping power, the optimum shifted toward wider channels, and a reduction in the hydrodynamic resistance shifted the design optimum toward higher manifold systems. Kim et al. [19] studied the effect of geometrical parameters of an air-flow MMCHS. They found that the ratio of the manifold channel width to the microchannel depth was an important parameter in the optimal design of the MMCHS.
Ryu et al. [20] carried out numerical analysis of a 3-D MMCHS for a unit cell. They investigated the sensitivity of design variables and performed optimization by coupling a numerical model with a search algorithm. Escher et al. [21] carried out 3-D numerical analysis for ultrathin MMCHSs. They developed a semiempirical model to optimize the MMCHS and determine the sensitivity of the geometric parameters. They showed that an optimized 2 × 2 cm2 chip offers a total thermal resistance of 0.087 cm2 K/W for flow rates of
