Three dimensional MHD free convection flow and heat transfer through a vertical channel

An analysis is made on the three dimensional MHD flow of a viscous incompressible fluid through a vertical channel in the presence of a uniform injection on the right plate and the left plate is subject to a periodic suction. The velocity and temperature fields are derived using the perturbation technique. It is observed that the primary velocity increases near the left plate and decreases near the right plate with an increase in the Reynolds number while it decreases with an increase in the magnetic parameter. It is seen that with an increase in the Prandtl number the primary velocity decreases whereas it increases with an increase in the Grashof number. It is seen that the magnitude of the secondary velocity increases in the range […] and thereafter decreases with an increase in the Reynolds number. It is also seen that the shear stress due to primary flow increases with an increase in either the Grashof number or Reynolds number but decreases with an increase in the Prandtl number. It is seen that the shear stress […] at the plate […] decreases with an increase in the magnetic parameter. Also, the magnitude of the shear stress due to cross flow increases with an increase in the Reynolds number. It is seen that the temperature at any point decreases with an increase in either the Prandtl number or Reynolds number. The rate of heat transfer in terms of the Nusselt number is also studied. Dimensional variables are indicated by dropping the asterisk and are defined in Eq.(2.8).