Optimization of geometry and flow rate distribution for double-layer microchannel heat sink Lin Lin a , Yang-Yang Chen a , Xin-Xin Zhang a , Xiao-Dong Wang b, c, * a School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China b State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China c Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China article info Article history: Received 28 July 2013 Received in revised form 16 December 2013 Accepted 16 December 2013 Available online 23 January 2014 Keywords: Double-layer microchannel heat sink Optimization Simplified conjugate-gradient method Global thermal resistance Cooling abstract A three-dimensional solidefluid conjugated model is coupled with a simplified conjugate-gradient method to optimize the flow and heat transfer in a water-cooled, silicon-based double-layer micro- channel heat sink (MCHS). Six design variables: channel number, bottom channel height, vertical rib width, thicknesses of two horizontal ribs, and coolant velocity in the bottom channel are optimized simultaneously to search for a minimum of global thermal resistance. The optimal design variables are obtained at fixed pumping powers, coolant volumetric flow rates, and pressure drops through the MCHS, respectively. The dependences of design variables on the increased pumping power, volumetric flow rate, and pressure drop are discussed. Although the combined optimization is proven effective only for the double-layer MCHS with a specific dimension, it is expected that the proposed design strategy provide a valuable guide for the practical double-layer MCHS design. Ó 2013 Elsevier Masson SAS. All rights reserved. 1. Introduction Over the last two decades, with the advances in MEMS tech- nology, micro-systems become more and more compact and small, which results in an ever-increasing heat generation rate from mi- croelectronic devices. The microchannel heat sink (MCHS) origi- nally proposed by Tuckerman and Pease [1] is found to have many advantages such as higher heat dissipation, smaller size and vol- ume per heat load, lower coolant requirement and lower opera- tional cost over the convectional cooling techniques, and has received extensive studies [2e17]. Especially, Ng’s group for the first time introduced the concept of electric double layer to explain the microscale deviation between flows in microscale channels and large-scale channels [12e14]. In original MCHS configuration, there is only one layer of parallel microchannels separated by solid ribs. Due to the limitation of pumping power, only a small coolant flow rate can be adopted. When the coolant passes through the channels and takes heat away from the heat dissipating microelectronic device attached below, its temperature gradually increases and the cooling capacity gradually deteriorates. Thus, a relatively higher temperature rise along the microchannel is inevitably formed. This undesirable temperature gradient may produce a large thermal stress in microelectronic device due to mismatch of thermal expansion coefficients between different materials. In addition, the large temperature gradient may also produce instability and thermal breakdown of microelectronic device. In order to reduce the undesirable temperature gradient, Vafai and Zhu [18] originally proposed a new design concept based on stacking two layers of microchannel heat sink structures, one atop the other, with coolant flow in the opposite direction in each of the microchannel layers. Followed by Vafai and Zhu’s work, many investigations [19e28] studied the cooling performance of double- layer MCHSs. These investigations confirmed that the double-layer structure significantly improved the temperature uniformity at the bottom wall compared with the single-layer one, and therefore the pressure drop required for the double-layer design can be much smaller than that of the single-layer design when small tempera- ture rise is required for microelectronic devices. Optimal geometric structure for the double-layer MCHS was also investigated by optimization algorithms [29,30]. Chong et al. [29] adopted a ther- mal resistance model linked with a multivariable constrained direct search optimization algorithm to optimize the performance of single- and double-layer MCHSs at fixed pressure drops. Their re- sults showed that both single- and double-layer MCHSs operating * Corresponding author. State Key Laboratory of Alternate Electrical Power Sys- tem with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China. Tel./fax: þ86 10 6232 1277. E-mail address: wangxd99@gmail.com (X.-D. Wang). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2013.12.009 International Journal of Thermal Sciences 78 (2014) 158e168