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An investigation of the combined influence of rarefaction and Darcy effects on the flow of oscillatory MHD viscous, incompressible, chemically reacting, and electrically conducting fluid in a vertical channel is carried out. The fluid is assumed to be gray and absorbing and emitting radiation but to be a nonscattering medium. The flow is assumed to be laminar and hydrodynamically and thermally fully developed. The Navier--Stokes, energy, and concentration equations, which are accompanied by appropriate velocity-slip and temperature-jump boundary conditions, are analytically solved. It is found that rarefaction effects significantly influence the flow and thermal fields such that mass flow and heat transfer rates are increased as compared to the continuum regime.

Rarefaction and Darcy effects on the hydromagnetic flow of radiating and reacting fluid in a vertical channel