Thermal analysis of the convective-radiative fin with a step change in thickness and temperature dependent thermal conductivity

This paper provides heat transfer analysis in a straight fin with a step change in thickness and variable thermal conductivity, which is losing heat by simultaneous convection and radiation. The calculations are carried out by using the differential transformation method (DTM) that can be applied to various types of differential equations. The results obtained employing DTM are compared with an accurate numerical solution to verify the accuracy of the proposed method. Several graphs are provided to illustrate how the temperature distribution is affected by the (i) thickness parameter, (ii) dimensionless fin semi thickness, (iii) length ratio, (iv) thermal conductivity parameter, (vi) Biot's number, and (vii) radiation-conduction parameter. This collection of graphs provides a comprehensive picture of the thermal performance of the system under steady state conditions.