Constructal Design applied to geometric optimization of a material with high thermal conductivity

Abstract

This work uses the Constructal Design method in the numerical study of geometric configuration of a T-shaped material of high thermal conductivity which minimizes the resistance of heat flux, since the areas occupied by the materials of high and low conductivity are kept constant. To solve numerically the heat diffusion equation it is used the finite element method (FEM), more specifically the PDETOOL of MATLAB. The objective is to minimize the thermal resistance of the heat generating system, with low thermal conductivity, by inserting a T-shaped pathway, whose material has high thermal conductivity and constant volume, being the dimensions of single and bifurcated branches free to vary. The optimal geometry of this material was that which led to lower thermal resistance. The results showed that the optimal geometry leads to a decrease of the minimum dimensionless maximum temperature in about 33% in comparison with a non-optimized geometry. Finally, this study showed that the optimum geometry is the one that best distributes imperfections, i.e., the hot spots (points of maximum temperature), which is in agreement with the Constructal principle of optimal distribution of imperfection.