Comparison of Exact Solutions for Heat Transfer in Extended Surfaces of Different Geometries

Abstract

We consider a steady state problem for heat transfer in fins of various geometries, namely, rectangular, radial, and spherical. The nonlinear steady state problem is linearizable provided that the thermal conductivity is the differential consequence of the term involving the heat transfer coefficient. As such, one is able to construct exact solutions. On the other hand, we employ the Lie point symmetry methods when the problem is not linearizable. Some interesting results are obtained and analyzed. The effects of the parameters such as thermogeometric fin parameter and the exponent on temperature are studied. Furthermore, fin efficiency and heat flux along the fin length of a spherical geometry are also studied.