Mixed convection in cylindrical annulus with rotating outer cylinder and constant magnetic field with an effect in the radial direction

In the present study, mixed convection of a fluid in the fully developed region in a horizontalconcentric cylindrical annulus with different uniform wall temperatures, is numerically investigated inboth steady and unsteady states in the presence of radial mhd force, as well as in consideration of heatgeneration due to viscous dissipation. also, cylinder length is assumed to be infinite. moreover, radiationheat 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 cylinderat slow constant angular velocity, with its axis at the center of the annulus. investigations are madefor various combinations of non-dimensional group numbers; reynolds number (re), rayleigh number(ra), hartmann number (ha), eckert number (eck) and annulus gap width ratio (0). these dimensionlessparameters used in the present study will be investigated over a wide range to present the basic flowpatterns and isotherms in a concentric cylindrical annulus. a finite volume scheme, consisting of thetri-diagonal matrix algorithm (tdma), is used to solve governing equations, which are continuity, two-dimensional momentum and energy, by the simple algorithm. the numerical results reveal that the flowand heat transfer are suppressed more effectively by imposing an external magnetic field. furthermore, itis found that the external magnetic field causes the fluid velocity and temperature to be suppressed moreeffectively. moreover, it will be shown that viscous dissipation terms have significant effects in situationswith high values of eckert and prandtl number and low values of reynolds number.