Cooling a Solid Disc with Uniform Heat Generation Using Inserts of High Thermal Conductivity within the Constructal Design Platform

Abstract

In the present study, the problem of cooling a solid disc by way of placing inserts with high thermal conductivity was examined analytically and numerically within the platform of Constructal Theory. The work was accomplished using a fixed amount of a highly conductive material distributed in the form of incomplete inserts from the center (sink). Using Constructal Theory, the magnitudes of the heat resistances in the radial and the branching configurations were calculated analytically. Additionally, to validate the analytical solution, a numerical solution with the Finite Element Method was employed. The one-to-one comparison between the two distinct results reveals a good agreement. In the present case, the length of the inserts was different from the disc radius viz. a new degree of freedom was considered and the solution was remarkably different from the case involving a complete insert. The heat resistance was minimized with respect to the aspect ratio in order to determine the optimal number of inserts as well as the disc radius. It was demonstrated that within in a certain range of parameters, the heat conduction performance of incomplete inserts in the solid disc surpasses the heat conduction performance of standard complete inserts.