Impacts of Thermal Radiation and Heat Consumption/Generation on Unsteady MHD Convection Flow of an Oldroyd-B Fluid with Ramped Velocity and Temperature in a Generalized Darcy Medium

Mathematics

Ilyas Khan¹  Poom Kumam²  Wiboonsak Watthayu²  Talha Anwar² 

[1] Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia;Department of Mathematics, Faculty of science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand;

关键词: heat consumption;    laplace transform;    ramp wall;    mhd;    corrected model;    oldroyd-b fluid;   

DOI  :  10.3390/math8010130

来源: DOAJ

【 摘 要 】

This article analyzes the time-dependent magnetohydrodynamic flow of Oldroyed-B fluid in the presence of heat consumption/generation and thermal radiation. The flow is restricted to a vertical infinite plate saturated in porous material along with ramp wall velocity and ramp wall temperature conditions. This flow also incorporates the generalized Darcy’s law. In this paper, accurate equation of velocity field is presented first and then solutions of mass and energy equation are derived in Laplace domain. Real-time domain solutions are obtained by tackling the complexity of Laplace domain expressions through numerical Laplace inversion. Skin friction coefficient and Nusselt number are also calculated. A comparison for ramp wall temperature condition and isothermal temperature condition is also drawn to investigate the difference. A graphical study is conducted to analyze the influence of parameters on fluid flow and heat transfer. It is found that radiation parameter and heat generation elevate the energy profile, while flow is accelerated by increasing the retardation time and porosity parameter and an opposite behavior is noted for increasing relaxation time and magnetic parameter. Furthermore, heat transfer rate is higher for increasing Prandtl number and velocity on plate decreases with increase in relaxation time ${\lambda }_1$ .

【 授权许可】

Unknown