Constructal Optimizations of Liquid-Cooled Channels with Triangle or Square Sections in a Cylindrical Heating Body

Abstract

Two new integrated models with heat source–heat sink are established, in which isothermal liquid cooling channels with triangle or square sections are, respectively, embedded in a cylindrical heating body with uniform heat production. Based on constructal theory, under the conditions of a fixed cylinder cross-sectional area and the proportion of channels, taking the dimensionless maximum temperature and the dimensionless entransy equivalent thermal resistance (EETR) as the optimization goals, the influences of distribution of liquid cooling channels on the heat dissipation capacity of integrated models are studied with the number and the center distance of liquid cooling channels as design variables, and the optimal constructs with different proportions of channels are obtained. The results show that when the proportion of channels, cross-sectional area and the number of liquid cooling channels are given, there is an optimal center distance to make the overall heat dissipation performance of the integrated model reach its best, but the optimal center distances for the two indicators are different. The dimensionless maximum temperature and the dimensionless EETR decrease when the proportion of channels increases, but the optimal dimensionless center distances are almost the same for different proportions of channels. The dimensionless maximum temperature with the triangular cross-section is lower than that with the square cross-section under the conditions of constant cross-sectional area and dimensionless center distance, which is the same as the case for the dimensionless EETR. The results can furnish the theoretical guidelines for the thermal design of cylindrical devices needing efficient cooling.