Reverse flow in magnetoconvection of two immiscible fluids in a vertical channel

This paper concerns the study of the influence of an external magnetic field on the reverse flow occurring in the steady mixed convection of two Newtonian immiscible fluids filling a vertical channel under the Oberbeck-Boussinesq approximation. The two isothermal boundaries are kept either at different or at equal temperatures. The velocity, the temperature, and the induced magnetic field are obtained analytically. The results are presented graphically and discussed for various values of the parameters involved in the problem (in particular, the Hartmann number and the buoyancy coefficient) and are compared with those for a single Newtonian fluid. The occurrence of the reverse flow is explained and carefully studied.