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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

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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
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Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
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KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(1), 130; https://doi.org/10.3390/math8010130
Received: 18 December 2019 / Revised: 25 December 2019 / Accepted: 27 December 2019 / Published: 15 January 2020
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 λ 1 . View Full-Text
Keywords: heat consumption; laplace transform; ramp wall; MHD; corrected model; Oldroyd-B fluid heat consumption; laplace transform; ramp wall; MHD; corrected model; Oldroyd-B fluid
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Anwar, T.; Khan, I.; Kumam, P.; Watthayu, W. 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 2020, 8, 130.

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