Steady state thermal analysis of a porous fin with radially outwards fluid flow

Abstract

Fins are used ubiquitously in engineering devices and systems for enhancement of heat transfer and energy storage. While traditional fins are made of non-porous materials, porous fins with natural convection porous flow orthogonal to the fin direction have also been studied. In contrast to these, there is a lack of work on porous fins in which the fluid flow may be along the direction of the fin. In such a fin, porosity may increase advective heat removal due to increased flow rate but may also impede conductive heat removal due to reduction in effective thermal conductivity. Due to these competing trade-offs, there is a need for comprehensive analysis of thermal performance of such a porous fin. This work derives a solution for the steady-state temperature distribution in a porous fin with advection along the fin direction. It is shown that temperature distribution in such a porous fin is governed by a convection-diffusion-reaction equation. A solution for the temperature distribution is derived in the form of modified Bessel functions of non-zero order. Two distinct fin performance parameters are defined and derived in order to characterize porous fin performance. It is found that thermal properties of the fin as well as ambient convective conditions strongly impact the relationship between fin porosity and fin performance. While in some cases, it is found that an optimum porosity exists that maximizes heat removal, in other cases, the use of a porous fin is found to be not desirable at all. The analysis presented here helps fully understand these trade-offs, and provides useful guidelines for porous fin design for maximum heat removal.