Rayleigh-Benard convection in micropolar fluids with internal heat generation

Rayleigh-Bénard convection is the heat transfer process which due to buoyancy forces that occurred in a plane horizontal layer of micropolar fluids heated from below. The effect of feedback control and magnetic field on the onset of Rayleigh-Bénard convection in a horizontal micropolar fluids layer in the presence of heat generation has been studied. The fluid layer with various boundary conditions at the lower and upper boundaries, and perfectly heat conduction are investigated theoretically based on the linear stability analysis. The various boundary conditions are assumed to be rigid-rigid, rigid-free and free-free. The resulting eigenvalue problems are solved analytically using the Galerkin method. The critical Rayleigh numbers are obtained and the influences of various parameters have been analyzed. It is found that the rigid-rigid surface is the most stable system, and the effect of feedback control as well as the magnetic field always stabilized the system is shown.

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