The Application of Homotopy Perturbation Method in Newtonian Fluids

Abstract

The Homotopy Perturbation Method (HPM) has advanced as an efficient semi-analytical technique for solving nonlinear differential equation arising in fluid mechanics. In this study, the application of HPM to Newtonian fluid flow problems is investigated in order to obtain accurate approximate solutions with reduced computational effort. The governing momentum equations of a Newtonian fluid flow, with a focus on deriving and analyzing engineering parameters like skin friction, Nusselt number, and Sherwood number was formulated under appropriate boundary conditions. The nonlinear partial differential equations describing the momentum, Navier-stokes equation and concentration equation were transformed into a homotopy framework by embedding an auxiliary a parameter. The solution is constructed in form of a rapidly convergent series without the need for small perturbation parameters or linearization. The analytical results obtaining using (HPM) are discussed and, where possible, compared with exact or numerical solutions to validate the accuracy and convergence of the method. The impact of the material parameters from the basic hydrodynamic equations were noticed and the findings demonstrate that the Homotopy Perturbation Method provides a reliable, Straightforward, and computationally efficient approach for analyzing Newtonian fluid flow phenomena and can be readily extended to more complex transport and heat transfer problems in engineering and applied sciences, making it a valuable tool for solving a wide range of nonlinear fluid mechanics models.