On the Natural Convection Heat Transfer from an Inclined Surface with Porous Fins

Abstract

This paper presents a simplified model to estimate the heat loss from an inclined porous-finned surface subjected to a constant heat flux under natural convection environment. The effect of attaching several infinitely long uniformly distributed porous fins at the hot surface is investigated and documented. A closed-form solution for the temperature at the base of a porous fin attached to an inclined surface is presented. The definitions of porous fin efficiency and effectiveness are introduced and estimated for several operating conditions and surface inclinations angles. It is found for a single fin that the temperature at the fin base and the fin efficiency is mainly controlled by a single parameter, $S_{\text{H}}^{*} = \frac{{D_{\text{a}} {\text{Ra}}^{*} \sin (\tau )}}{{K_{\text{r}}^{2} }}$. And when the value of S_H* increases the surface temperature at the fin base and the fin efficiency decreases. Thus, for the same operating conditions, as the inclination angle increases the fin base temperature decreases, i.e., better heat transfer. Moreover, for a specific tilt angle, as the heat flux increases the fin efficiency decreases. Also, it is found that the fin effectiveness is mainly controlled by S_H*, conductivity ratio, K_r and bare surface heat transfer coefficient. Moreover, an expression of the surface heat transfer effectiveness of a surface finned with multi fins is introduced.