In the present study, mixed convection of a fluid in the fully developed region in horizontal concentric cylindrical annulus with different uniform wall temperatures is numerically investigated in both of steady and unsteady states in the presence of radial MHD force as well as consideration of heat generation due to viscous dissipation. Also, cylinders length is assumed to be infinite. Moreover, radiation heat transfer from the hot surface is assumed to be negligible. Buoyancy effects are also considered along with Boussinesq approximation. The forced flow is induced by the cold rotating outer cylinder in slowly constant angular velocity with its axis at the center of annulus. Investigations are made for various combinations of non-dimensional group numbers, Reynolds number ( ), Rayleigh number ( ), Hartmann number ( ), Eckert number ( ), and annulus gap width ratio ( ). These dimensionless parameters used in the present study, will be investigated over a wide range to present the basic flow patterns and isotherms in concentric cylindrical annulus. Finite volume scheme consisting of tri-diagonal matrix algorithm (TDMA) is used to solve governing equations which are continuity, two-dimensional momentum and energy by SIMPLE algorithm. The numerical results reveal that the flow and heat transfer are suppressed more effectively by imposing an external magnetic field. Furthermore, it is found that the external magnetic field causes the fluid velocity and temperature to be suppressed more effectively. Moreover, it will be shown that viscous dissipation terms have significant effects in situations with high values of Eckert and Prandtl numbers and low values of Reynolds numbers.

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