Application of He?s homotopy and perturbation method to solve heat transfer equations: A python approach

In this research article, an attempt has been made to solve the linear/nonlinear and steady/unsteady heat transfer equations using the Homotopy and Perturbation method (HPM). Moreover, the implementation of HPM has been done by using SymPy, a library in python, to solve problems symbolically. Total three problems were dealt viz. steady-state conduction with heat generation, lumped capacitance analysis with a variable specific heat of the material, and heat transfer in uniform rectangular fin with radiation from the surface. In all the cases, the HPM has given excellent results compared to the analytical and numerical. Finally, the execution of SymPy has been explained, and a detailed procedure to implement HPM through python has been presented for all three cases.

Automated summary

This research article attempts to solve the linear/nonlinear and steady/unsteady heat transfer equations using the Homotopy and Perturbation method (HPM) and symbolically in SymPy. Three problems were solved, and HPM demonstrated excellent results compared to analytical and numerical methods. Furthermore, the execution of SymPy and a detailed procedure for implementing HPM in Python were explained.