General solutions for optimum dimensions of convective longitudinal fins with base wall thermal resistances

This paper deals with optimum design of convective longitudinal fins with consideration of wall thermal resistances at the other side of the fin, i.e., the analysis includes the thermal resistance by convection from the flowing fluid to the inner wall of the finned pipe, conduction of the pipe wall and thermal contact resistance between the primary and the extended surfaces. The longitudinal fins of an arbitrary profile are considered. The governing equations are solved analytically and the optimum conditions are thus obtained. To facilitate the thermal designers, the numerical results are presented both in graphical forms and working formulae.