Homotopy perturbation sumudu transform method for solving convective radial fins with temperature-dependent thermal conductivity of fractional order energy balance equation

In order to enhance the heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilised. In this present analysis, temperature distribution and effectiveness of convective radial fins with constant and temperature-dependent thermal conductivity are solved by applying homotopy perturbation sumudu transform method (HPSTM). The concept of homotopy perturbation sumudu transform method is briefly introduced, and then it is employed to derive solution of fractional order nonlinear governing equation. The fractional derivative is considered in the Caputo sense. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He's polynomials. The nonlinear terms can be easily handled by the use of He's polynomials. The fin effectiveness has been obtained as a function of thermo-geometric fin parameter. The analytical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive. In order to show the efficiency of this proposed method, the results are compared with previously obtained classical order results using Variational Iteration Method (VIM) (Coskun and Atay, 2007) [1]. It has revealed that homotopy perturbation sumudu transform method is a very simple and effective approach for a rapid assessment of physical systems even if the energy balance equations of fractional order include terms with strong nonlinearities. The resulting correlation equations can assist thermal design engineers for designing of radial fins with both constant and temperature-dependent thermal conductivity.