Finite difference schemes for MHD mixed convective Darcy–forchheimer flow of Non-Newtonian fluid over oscillatory sheet: A computational study

Abstract

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order scheme is deliberated. The stability of the proposed scheme is set for scalar partial differential equation, whereas its convergence is specified for a system of parabolic equations. The scheme is applied to linear scalar partial differential equation and non-linear systems of time-dependent partial differential equations. The non-linear system comprises a set of governing equations for the heat and mass transfer of magnetohydrodynamics (MHD) mixed convective Casson nanofluid flow across the oscillatory sheet with the Darcy–Forchheimer model, joule heating, viscous dissipation, and chemical reaction. It is noted that the concentration profile is escalated by mounting the thermophoresis parameter. Also, the proposed scheme converges faster than the existing Crank-Nicolson scheme. The findings that were provided in this study have the potential to serve as a helpful guide for investigations into fluid flow in closed-off industrial settings in the future.

COMSOL Multiphysics simulation of hydromagnetic flow in horizontal channels with diverse media: Insights into momentum and heat diffusion limitations

“…Hazarika and Ahmed 33 used a finite difference numerical tool of the fourth order Runge-Kutta shooting method in 2022 to investigate the behavior of Cu-water nanofluids on the dual solutions for time-independent, 2D nanofluid flow along a semi-infinite porous stretching horizontal wall in a porous material for the variation of wall suction/injection and nanoparticle volume fraction. Further, the investigations focused on Darcy-Forchheimer magnetized flow models for Newtonian and non-Newtonian fluids with different geometric surfaces and suitable configurations, which were analyzed by the authors [34][35][36][37][38][39][40][41][42][43][44][45][46] and they adopted various numerical schemes to solve the conservation equations.…”