Variable transform-based semi-analytical methods for solving convective straight fins problem with temperature-dependent thermal conductivity

This paper presents effective algorithms to approximate solutions of nonlinear fin problem with temperature dependent thermal conductivity and heat transfer coefficient. We propose new approximate semi-analytical techniques, namely the Laplace homotopy variable transform method (LHVTM) and the differential variable transform method (DVTM), to obtain expressions for generalized convective straight fins problem. The linear dependence of thermal conductivity on temperature is considered, and fin efficiency and effectiveness are evaluated. We further analyzed the effects of the model parameters on surface heat loss, and the results are presented in tables and with graphical illustrations.