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This study is interested in the effect of an axial magnetic field imposed on incompressible flow of electrically conductive fluid between two horizontal coaxial cylinders. The imposed magnetic field is assumed uniform and constant. The effect of heat generation due to viscous dissipation is also taken into account. The inner and outer cylinders are maintained at different uniform temperatures and concentrations. The movement of the fluid is due to rotation of the cylinder with a constant speed. An exact solution of the governing equations for momentum and energy are obtained in the form of Bessel functions. A finite difference implicit scheme was used in the numerical solution to solve the governing equations of convection flow and mass transfer. The velocity, concentration and temperature distributions were obtained with and without the magnetic field. The results show that for different values ​​of the Hartmann number, the velocity and concentration between the two cylinders decreases as the Hartmann number increases. On the other hand, the Hartmann number does not affect the temperature. Also, it is found that by increasing the Hartmann number, the Nusselt and Sherwood numbers decreases.       Key words: Rotating cylinders,  viscous dissipation, heat transfer, mass transfer,  magnetic field, Bessel function, finite difference.

Effect of an axial magnetic field on the heat and mass transfer in rotating annulus