Analysis for fin efficiency with temperature-dependent thermal conductivity of fractional order energy balance equation using HPST Method

Radiating extended surfaces are usually utilized to enhance the heat transfer between primary surface and the environment. In this paper, temperature distribution, fin efficiency, efficacy of convective straight fins with constant and temperature-dependent thermal conductivity are solved by implementing homotopy perturbation sumudu transform method (HPSTM). The proposed method is very useful and practical for solving the fractional order nonlinear diffusion equation, which is associated with variable thermal conductivity condition. A dimensionless analytical expression has been developed for fin effectiveness. The fin efficiency and the fin effectiveness have been attained as a function of thermo-geometric fin parameter. It can be noticed that the thermal conductivity parameter has a strong influence over the fin efficiency. The analytical solutions acquired by the present method illustrate the approach is easy to implement and computationally very interesting. The obtained results are compared with previously found classical order results using variational iteration method (VIM), Adomian decomposition method, and the results from Galerkin method in order to show the competence of this present method. HPSTM is a simple and effective method for rapid assessment of physical systems although the fractional order energy balance equations comprise with strong nonlinear terms. The subsequent correlation equations can benefit thermal design engineers for designing of innovative straight fins with both constant and temperature-dependent thermal conductivity.