“Volume-Point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular element

Abstract

By taking equivalent thermal resistance, which reflects the average heat conduction effect and is defined based on entransy dissipation, as optimization objective, the “volume to point” constructal problem of how to discharge the heat generated in a fixed volume to a heat sink on the border through relatively high conductive link is re-analyzed and re-optimized in this paper. The constructal shape of the control volume with the best average heat conduction effect is deduced. For the elemental area and the first order construct assembly, when the thermal current density in the high conductive link is linear with the length, the optimized shapes of assemble based on the minimization of entransy dissipation are the same as those based on minimization of maximum temperature difference, and the mean temperature difference is 2/3 of the maximum temperature difference. For the second and higher order construct assemblies, the thermal current densities in the high conductive link are not linear with the length, and the optimized shapes of assemble based on the minimization of entransy dissipation are different from those based on minimization of maximum temperature difference. For the same parameters, the constructs based on minimization of entransy dissipation and the constructs based on minimization of maximum temperature difference are compared, and the results show that the constructs based on entransy dissipation can decrease the mean temperature difference better than the constructs based on minimization of maximum temperature difference. But with the increase of the number of the order, the mean temperature difference does not always decrease, and there exist some fluctuations. Because the idea of entransy describes the heat transfer ability more suitably, all of the heat conduction constructal problems may be re-optimized based on it.