Onset of natural convection in a rotating fluid layer with non-uniform volumetric heat sources

A study of the thermal instability in an initially quiescent liquid, placed between two horizontal plates, irradiated by a volumetric heat source, and subject to rotation about the vertical axis is carried out. The eigenvalue problem is solved using Chebyshev pseudospectral methods employing the basis recombination technique for higher order problems. The effect of the orientation of the heat source, as well as boundary conditions on the onset of natural convection is studied for different rotation rates. Rotation is seen to unconditionally increase the stationary stability in all cases. Our results indicate a linear relationship between critical Rayleigh number and Taylor number at moderate values of Taylor number, and also show that convection in rotating fluid layer is more sensitive to the exact nature of the heat source distribution in case of stable and quasi stable temperature profiles.