OPTIMIZATION OF STRAIGHT FINS WITH A STEP CHANGE IN THICKNESS AND VARIABLE THERMAL CONDUCTIVITY BY HOMOTOPY PERTURBATION METHOD

For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the thermal analysis and optimization of convective straight fins with a step change in thickness and temperature-dependent thermal conductivity have been addressed. Temperature distribution within the fin has been evaluated using homotopy perturbation method (HPM) which provides an analytical solution in the form of an infinite power series. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found by using the data from the solution. It has been observed that a SF is the better choice for transferring rate of heat in comparison with the flat fins for the same fin volume and identical thermal conditions. The derived condition of optimality gives an open choice to the designer.