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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

Numerical analysis of natural convection of magnetohydrodynamic flow in vertical micro-channel with rarefaction effects and radiative heat transfer