Constructal design of T-shaped assemblies of fins cooling a cylindrical solid body

Abstract

This paper considers the numerical optimization of a T-shaped assembly of fins cooling a cylindrical solid body. The objective is to minimize the maximum excess of temperature between the solid cylindrical body and the ambient. Internal heat generation is distributed uniformly throughout the solid body. The assemblies of fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The outer surfaces of the cylindrical body are adiabatic. The total volume of the body and the total volume of the fins are fixed, but the lengths of the fins can vary. The initial simulations demonstrated that the optimal performance is achieved when the tributaries shape becomes slender and the stem thicker so that the system has more freedom to morph. However, when the number of assembly exceeds 2, the best configuration is the one that presents slender stems and shorter tributaries. The reason of this sudden change in behavior is that the tributaries length is limited by the presence of the neighbor assembly of fins: the system becomes “locked” and has no more freedom to morph. Finally, a digression on how the number of T-shaped fin assembly affects the configuration patterns concludes the paper.