Comparison of Analytical and Numerical Methods to Solve Boundary-Layer Natural Convection Problem for Various Prandtl Number Fluids

Abstract

Semianalytical approaches such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM), as well as the Numerical Method, are investigated in this study to solve the boundary-layer natural convection problem for various Prandlt number fluids on a horizontal flat plate. Nonlinear partial differential expressions can be incorporated into the ordinary differential framework by applying appropriate transformations. The purpose of this study is to show how analytical solutions to heat transfer problems are more versatile and broadly applicable. The results of the analytical solutions are compared with numerical solutions, revealing a high level of approximation accuracy. The numerical findings clearly imply that the analytical techniques can produce accurate numerical solutions for nonlinear differential equations. We analyze the temperature distribution, velocity, and flow field under various conditions. The study found that temperature patterns, velocity distribution, and flow dynamics are all improved by raising the Prandtl numbers. As a result, the thickness of the boundary layer is significantly reduced, leading to an enhanced heat transfer rate at the moving surface. This reduction in boundary-layer thickness contributes to a more efficient convection process. The study further highlights that the HPM and the VIM both offer highly accurate approximations for solving nonlinear differential equations related to boundary-layer flow and heat transfer. Among these methods, HPM was found to provide a higher level of precision compared with VIM.