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The problem of unsteady laminar, two-dimensional hydromagnetic natural convection heat transfer in a concentric horizontal cylindrical annulus filled with a fluid-saturated porous medium in the presence of a transverse magnetic field and fluid heal generation effects is studied numerically. It is assumed that the inner and outer walls of the cylindrical annulus are maintained at uniform and constant temperatures Ti and To respectively. The model consists of the heat equation and the equations of motion under the Darcy law. The derived problem with the stream function-temperature formulation is solved numerically using the alternating direction implicit method. This investigation concerns the effect of magnetic field inclination angle, Hartmann number and heat generation on the heat transfer and the flow pattern. The obtained numerical results are presented graphically in terms of streamlines and isotherms. It was found that the heat transfer mechanisms and the flow characteristics depend strongly on the magnetic field inclination angle, Hartmann number and heat generation..

The effect of quasi-periodic gravitational modulation on the natural convection in a horizontal porous annulus is studied in this paper. The model we consider includes the heat and the hydrodynamics equations under Darcy law. The derived model with the stream function is solved numerically using the alternate direction implicit method. Results show that the convective instability and the flow regime are influenced by frequencies ratio of the quasi-periodic gravitational modulation.