Application of He's homotopy and perturbation method to solve heat transfer equations: A python approach. (August 2022)

• Record Type: Journal Article
• Authors: Dumka, Pankaj; Pawar, Parth Singh; Sauda, Abhay; Shukla, Gaurav; Mishra, Dhananjay R.
• Is Part Of: Advances in engineering software. Volume 170(2022)
• Publication Date: 2022-08
• Subjects: Heat transfer -- Homotopy and perturbation method (HPM) -- Nonlinear differential equations -- Python -- SymPy; ADM Adomian Decomposition Method -- VIM Variational Therapy Method -- HPM Homotopy Perturbation Method -- WRMs Weighted Residual Methods -- LSM Least Square Methods; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2022.103160
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: Homotopy and Perturbation method has been used to solve heat transfer equations. Both linear and nonlinear differential equations are solved. Python programming has been used to solve the problem. Developed python code has been presented. The results of computer program are in very good agreement with the analytical results. Abstract: 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.