Constructal optimization for “disc-point” heat conduction with nonuniform heat generating

Abstract

This paper builds up “disc-point” heat conduction models considering the nonuniform heat generating (NUHG) characteristic. Constructal optimizations are respectively carried out for the radial-pattern disc and tree-shaped discs with constant and variable cross-sectional high conductivity channels (HCCs) by minimizing the maximum temperature difference (MTD). For various NUHG conditions, the optimal constructs of the two kinds of discs are obtained, and the impacts of NUHG coefficient and width coefficient on the optimal results are analyzed in detail. The results indicate that for the tree-shaped disc with constant cross-sectional HCCs, the stems of the HCCs grow thicker and longer, while the branches become thinner and shorter when more heat is generated near the heat sink, and the high conductivity material should be distributed preferably where the heat sink is located to enhance the heat transfer performance (HTP). Meanwhile, the optimal tree-shaped disc tends to degrade into a radial-pattern disc when the number of the stems is less than 18. For the tree-shaped disc with variable cross-sectional HCCs, the twice minimized dimensionless MTD with the width coefficient of 1.7 is reduced by 4.3% in contrast with the width coefficient of 1, which demonstrates that applying the variable cross-sectional HCCs architecture can further improve its HTP. The constructal results obtained in this paper can contribute to the design of practical electronics.