Abstract
In this article, we present a comprehensive analysis of the flow and heat transfer characteristics of a fully developed incompressible, electrically conducting, and radiatively active fluid flow in micro-channel in the presence of transverse magnetic field. The Navier–Stokes and energy governing equations for magnetohydrodynamic flow, including thermal radiation and rarefaction effects, are considered to examine the wall properties (friction and heat transfer) and the flow properties (temperature and velocity). Two rarefaction effects of velocity slip and temperature jump at the wall are modeled as the product of characteristic slip/jump length and the first derivatives of velocity and temperature, respectively. Since the natural convection of magnetohydrodynamic flow in channel is resulted from the competition between deriving forces by pressure gradient, temperature gradient, and magnetic field, its flow and heat transfer characteristics should be understood systematically. First, we obtain the system parameters representing thermal radiation, buoyancy, magnetic field, temperature difference, velocity slip length, and temperature jump length through the non-dimensionalization process, and then their influences are rigorously evaluated by solving the governing equations numerically using Runge–Kutta algorithm with shooting method.
Highlights
Considering all the above, the purpose of this study is to investigate the natural convection of MHD flow in micro-channel with thermal radiation and rarefaction effects of velocity slip and temperature jump
We thoroughly investigated the laminar natural convection of highly radiatively active MHD flow in vertical micro-channel including the rarefaction effects represented as velocity slip and temperature jump
As Gr=Re becomes large the velocity profile is changed from parabola to the sinusoidal shape due to buoyancy: the fluid in hot side moves faster than in the cold side; 4
Summary
Natural convection of magnetohydrodynamic (MHD) flow in vertical channels has been extensively studied for the last three decades.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] Osterle and Young[1] first discussed the effect of viscous dissipation and applied magnetic field for the fully developed natural convection for a fluid between two heated walls. The effect of Joule heating and viscous dissipation in the flow is thoroughly investigated by Barletta and colleagues.[13,14] Singh et al.[15] identified the unsteady characteristics of the flow Another kind of the integral transform solution for low-magnetic MHD flow and heat transfer in the entrance region of a channel was proposed by Lima and Rego.[16]
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