Finite element analysis of transient thermal performance of a convective-radiative cooling fin: effects of fin tip conditions and magnetic field

The wide range of applications of cooling fins are evident in heat transfer enhancements for various thermal systems and also, for the control and prevention of thermal damages in mechanical and electronic equipment. In this work, nonlinear thermal behaviour of convective-radiative cooling fin with convective tip and subjected to magnetic field is analyzed using Galerkin finite element method. The numerical solutions are verified by the exact analytical solution of the linearized models using Laplace transforms method. Based on the numerical investigations, it is established that increase in Biot number, convective, radiative and magnetic parameters increase the rate of heat transfer from the fin and consequently improve the efficiency of the cooling fin. Also, the study shows that for a relatively short cooling fin operating for prolonged periods of time or steady state, the adiabatic/hypothetical condition (or negligible heat transfer) at the tip can be assumed without any significant loss in accuracy or equality as compared to the convective condition at the tip. However, for a long cooling fin of finite length operating in a transient state, especially for short period of time, the assumption of insulated tip produces significant different results as compared to the results of the convective tip. Therefore, for transient thermal studies of fins, the assumption that no heat transfer takes place at the fin tip should be taken with caution for a long cooling fin of finite length operating within a relatively short period of time. It is hope that the present study will enhance the understanding of transient thermal response of the solid fin under various factors and fin tip conditions.