Numerical simulation of Darcy–Brinkman oscillatory flow of dissipative fluid: Utilization of finite difference method

Abstract

This study investigates viscous flow behavior in a Darcy–Brinkman porous medium, considering the effects of porous dissipation and frictional heating. The fluid is flowing over a flat plate, oscillating in its plane. The velocity and temperature profiles are simulated using a mathematical model that includes linear convection and considers the effects of porous and viscous dissipation. After performing mathematical transformations, the governing equations are modified into coupled and nonlinear dimensionless PDEs. The forward time centered space method numerically solves the modeled dimensionless equations. The acquired results are explicitly validated against the findings of the literature in a situation where limits are considered. The numerical results are presented graphically, providing a comprehensive analysis of the variables impacting fluid characteristics, including temperature and velocity. Interestingly, this work shows that a rise in the porosity parameter causes temperature profiles to rise and velocity to decrease. Moreover, a drop in velocity is linked to a rise in the Prandtl number. Furthermore, the influence of surface friction is diminished by including the porosity parameter. Moreover, a rise in the heat transmission rate at the surface can be observed.

Keywords:

• Darcy Brinkman porous medium
• FTCS
• heat transfer
• linear convection
• oscillatory flow
• porous dissipation
• viscous dissipation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by Provincial Department of Education Philosophy and Social Science. Research Project (No.: 22Q216) 2021 School-Level Scientific Research Project (No. XJ2021003401).