Rarefaction and Darcy effects on the hydromagnetic ow of radiating and reacting uid in a vertical channel

An investigation of the combined in uence of rarefaction and Darcy e ects on the ow of oscillatory MHD viscous, incompressible, chemically reacting, and electrically conducting uid in a vertical channel is carried out. The uid is assumed to be gray and absorbing and emitting radiation but to be a nonscattering medium. The ow 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 e ects signi cantly in uence the ow and thermal elds such that mass ow and heat transfer rates are increased as compared to the continuum regime.