A tree-shaped high thermal conductivity channel in a stacked chip with minimizing maximum temperature difference and entropy generation rate

Combining constructal theory with entropy-generation-minimization theory, a model of a stacked chip with tree-shaped high-thermal-conductivity channels (TSHTCC) is established, and its performance are optimized with minimizing non-dimensional maximum temperature-difference (MTD) and non-dimensional entropy-generation-rate (EGR), respectively. Effects of length ratio of first order channel to elemental channel, length and width of first order channel, heat-generation-rate per volume, temperature of heat sink and thermal-conductivity of TSHTCC on its MTD and EGR are analyzed. The results show that optimal construct of TSHTCC obtained with minimum EGR objective stretches slightly towards the center than that with minimum MTD objective. When thickness is 28 μm and width of second order channel is 1500 μm, non-dimensional MTD reaches its minimum at value of 0.824, and is reduced by 17.6 % compared to initial design. When thickness is 29 μm and width of second order channel is 1500 μm, non-dimensional EGR reaches its minimum at value of 0.759, and is reduced by 24.1 % compared to initial design. Non-dimensional MTD and non-dimensional EGR are reduced by 67.9 % and 83.5 %, respectively, compared to those of a model without TSHTCC. Therefore, heat dissipation performances of stacked chip are increased.