Comparative Evaluation of the Optimal Auxiliary Function Method and Numerical Method to Explore the Heat Transfer between Two Parallel Porous Plates of Steady Nanofluids with Brownian and Thermophoretic Influences

In this study, we used the newly established optimal approach, namely, optimal auxilary function method (OAFM) along with the Adams numerical solver technique in order to investigate the heat transfer between two permeable parallel plates of steady nanofluids (HTBTP-SNFs) through Brownian and thermophoretic consequences. The new scheme model (HTBTP-SNFs) in terms of partial differential equations (PDEs) is changed to nonlinear ordinary differential equations (ODEs) by utilizing similarity transformations. The OAFM and Adams numerical methods are used to solve the resulting ODEs with boundary conditions. The OAFM along with convergence and Adams numerical method are studied in detail. The influences of the physical parameters of HTBTP-SNFs model for instance porosity parameter (m), parameter of magnetic (M), parameter of Brownian (Nb), viscosity parameter (R), Schmidt number (Sc), thermophores parameter (Nt), and Prandlt number (Pr) are discussed with the help of tabular data and graphs. The reliability and effectiveness of the technique are achieved by equating the results available in the literature.