Constructal placement of unequal heat sources on a plate cooled by laminar forced convection

The present study deals with the influence that the size of adiabatic spacing in an array of heat sources exerts on the heat transfer performance. This issue plays a significant role in controlling the thermal boundary layer development in order to enhance the convective heat transfer along a plate. Constructal theory was systematically applied to determine the optimal configuration of heat sources in the array. The global objective is either to minimize the 'hot spot' temperature of the plate or to maximize the rate of heat transfer. Two thermal boundary conditions for the heat sources are employed: constant heat flux condition or constant temperature. Analytical solutions were determined for several length sizes of heat sources without imposing the common simplifying assumptions that were considered in similar studies. In this work, the optimization was first carried out for a problem with no attached constraint on how to distribute the heat sources for a fixed plate length. It was shown that in the first case, the 'hot spot' temperature was reduced by 11% for two optimized-size heat sources with uniform heat flux articulated with optimum adiabatic spacing. Additionally, for two heat sources with uniform temperature, a level of maximum heat transfer enhancement of 7.7% was achieved. (C) 2012 Elsevier Masson SAS. All rights reserved.