Constructal entransy dissipation rate minimization of a rectangular body with nonuniform heat generation

Abstract

Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate (EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel (HCC) are derived. For the rectangular first order assembly (RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.