Python approach for using homotopy perturbation method to investigate heat transfer problems

Abstract

Many researchers have used the homotopy perturbation method (HPM) method but with different strategies, and this paper aims to present a general method of HPM to make this method more straightforward to use for future studies. HPM itself has a lot of potential. By making it more general, it makes it even more useable than before and gives this paper a lot of potential applications. This paper makes the HPM more warrantyable for future works. HPM is a strong technique for investigating both linear and nonlinear differential equations. SymPy, a Python library, was also used to implement HPM and solve problems allegorically. Three issues were addressed: Convection and radiation combining to cool a lumped system, a purely convective rectangular fin, and the Laplace equation for heat transfer. The HPM has produced superior outcomes compared to numerical and analytical methods. At last, SymPy's accomplishment has been described, and for each of the three researched problems, a complete technique for implementing HPM using Python is presented. It is shown that HPM is a mathematical technique that covers the limitations of the classical perturbation approach and can be generally used in physics and engineering subjects.