Finite difference schemes for MHD mixed convective Darcy–forchheimer flow of Non-Newtonian fluid over oscillatory sheet: A computational study - Nawaz, Yasir; Arif, Muhammad Shoaib; Abodayeh, Kamaleldin; Mansoor, Muavia (Frontiers in Physics, 2023)
This contribution proposes two third-order numerical schemes for solving time-dependent linear and nonlinear partial differential equations (PDEs). For spatial discretization, a compact fourth-order scheme is deliberated. The stability of the proposed scheme is set for scalar PDE, whereas its convergence is specified for a system of parabolic equations. The scheme is applied to linear scalar PDE and nonlinear systems of time-dependent PDEs. The nonlinear 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.