Constructal design of nonuniform heat generating area based on triangular elements: A case of entropy generation minimization

Abstract

This paper reports a constructal investigation of heat transfer in a nonuniform heat generating triangular area, and numerically studies the entropy generation performance over the area inserted with constant and discrete variable cross-sectional high conductive channels (HCCs), respectively. The effects of the nonuniform heat generating (NUHG) coefficient and width coefficient on the overall thermal performance are also analyzed with several conditions of heat distributions. This model has two constraints: the area ratio of HCCs to the whole heat generating area and the global heat generation (the heat is nonuniformly distributed over the area). The structure of the HCCs is free to morph in order to present a better thermal performance. The numerical results show that for an elemental triangle, the optimal structure tends to elongate as the NUHG coefficient increases. It is also indicated that the dimensionless entropy generation rate for the first-order construct constituting of six elements is decreased by 20.0% in comparison with the counterpart constituting of four elements, which means that increasing the number of incorporated elements makes it favorable to improve the overall thermal performance. Additionally, the quartic minimized dimensionless entropy generation rate of the first-order construct with discrete cross-sectional HCCs performs 14.2% better than the counterpart with constant highly conductive routes. In this context, the thermal performance can be improved reasonably by intruding the variable cross-sectional architecture into the heat generating area. In general, the effects of the nonuniform heat generating coefficient p, width coefficient m and the number of triangular elements n on the overall thermal performance are studied. The pivotal innovation of this paper is introducing entropy generation minimization theory into the constructal design of triangular assemblies with both nonuniform heat generation and discrete variable cross-sectional HCCs, which can contribute to the design of practical electronic devices to a promising heat transfer performance.