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It is assumed that the fluids in the two regions are incompressible, immiscible and electrically conducting, having different viscosities, electrical conductivities. With these assumptions and considering that the magnetic Reynolds number is small the basic equations of motion, current, the no-slip boundary conditions at the walls and interface conditions between the two-fluid regions have been formulated. The resulting governing linear differential equations are solved analytically, using the prescribed boundary and interface conditions to obtain the exact solutions for velocity distributions such as primary and secondary distributions in both regions. Also, their corresponding numerical results for various sets of values of the governing parameters are obtained to represent them graphically and are discussed in detail.

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Dr. Sreedhar Sobhanapuram did his Ph.D. in the Department of Applied Mathematics, Andhra University, Visakhapatnam. He is working as Assistant Professor in the Department of Applied Mathematics, Gitam Institute of Science, GITAM University, Visakhapatnam, India. He is currently working in the area of Fluid Dynamics.

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