Unsteady MHD natural convection flow of Casson fluid incorporating thermal radiative flux and heat injection/suction mechanism under variable wall conditions

Talha Anwar,Poom Kumam,Wiboonsak Watthayu

doi:10.1038/s41598-021-83691-2

Abstract

Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall. Thermal radiation flux and heat injection/suction terms are also incorporated in the energy equation. The electrically conducting fluid is flowing through a porous material and these phenomena are governed by partial differential equations. After employing some adequate dimensionless variables, the solutions are evaluated by dint of Laplace transform. In addition, the physical contribution of substantial parameters such as Grashof number, radiation parameter, heat injection/suction parameter, porosity parameter, Prandtl number, and magnetic parameter is appropriately elucidated with the aid of graphical and tabular illustrations. The expressions for skin friction and Nusselt number are also derived to observe wall shear stress and rate of heat transfer. A graphical comparison between solutions corresponding to ramped and constant conditions at the wall is also provided. It is observed that graphs of the solutions computed under constant conditions are always superior with respect to graphs of ramped conditions. The magnetic field decelerates the flow, whereas the radiative flux leads to an upsurge in the flow. Furthermore, the shear stress is a decreasing function of the magnetic parameter.

Highlights

Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall
For the solidification process, a magnetic field is imposed on a liquid metal, which flows through a porous material[6]
Impacts of heat blowing/suction and thermal radiation on temperature and flow of Casson fluid over stretching sheet were analyzed by M ukhopadhyay24. Pramanik[25] conducted a systematic study to evaluate the impacts of porosity and radiative heat flux on heat and mass transfer

Summary

Introduction

Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall. Investigations for unsteady MHD flows of non-Newtonian fluids in porous mediums subjected to ramped velocity and ramped temperature conditions simultaneously are very few in the literature because it is intricate to handle the resulted nonlinear complex relations analytically though, these conditions have significant practical utilities. A detailed analysis of several physical phenomena of Hall current, thermal radiation, Darcy’s law, heat consumption, and chemical reaction on mass and heat transfer with ramped wall concentration and temperature subjected to impulsive and accelerating upright plates was provided by Seth et al.[38,39,40]. Zin et al.[43] investigated the effects of thermal radiation and magnetic field on free convection Jeffrey fluid flow with ramped wall temperature. Tiwana et al.[45] recently studied the MHD time-dependent convective flow of Oldroyd-B fluid considering simultaneous ramped conditions at the boundary

Objectives

Conclusion