Two dominant analytical methods for thermal analysis of convective step fin with variable thermal conductivity

Heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by convection to its surroundings is developed via differential transformation method (DTM) and variational iteration method (VIM). In this study, we compare DTM and VIM results, with those of homotopy perturbation method (HPM) and an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM and HPM. After these verifications the effects of parameters such as thickness ratio, α, dimensionless fin semi thickness,δ, length ratio, λ, thermal conductivity parameter, β, Biot number, Bi, on the temperature distribution are illustrated and explained.