Constructal tree-shaped designs for self-cooling

Abstract

In this paper, we show how a plate which is subjected to a heating load can be kept under an allowable temperature. Vascular channels in which coolant fluid flows have been embedded in the plate. Two types of vascular channel designs were compared: radial and tree-shaped. The effects of channel design on the thermal performance for different volume fractions (the fluid volume over the solid volume) are documented. Changing the design from radial to tree-shaped designs decreases the order of pressure drop. Hence increase in the order of the convection coefficient is achieved. However, treeshaped designs do not bath the entire domain. Therefore, we have inserted additional branches at the uncooled regions. Then, we have compared the peak temperatures of radial, traditional tree-shaped and improved tree-shaped designs. The effect of design on the maximum temperature shows that there should be an optimum design for a distinct set of boundary conditions, and this design should be varied as the boundary conditions change. This result is in accord with the constructal law, i.e. the shape should be varied in order to minimize resistances to the flows.