Effects of uniform and non-uniform salinity profiles on the onset of double diffusive Rayleigh-Benard convection in a composite system bounded by rigid-rigid boundaries with Soret effects and constant heat sources

Abstract The onset of double diffusive Rayleigh-Benard (DD-RB) convection in a composite system comprising an incompressible fluid saturated densely packed porous layer over which lies a layer of the same fluid with Soret effect and constant heat sources is investigated. The lower rigid surface of the porous layer and the upper free surface of the fluid layer are insulating to heat and mass. The resulting eigen value problem is solved using regular perturbation technique with wave number as a perturbation parameter. The expression for the critical Rayleigh number is obtained for Linear (LSP), Parabolic (PSP), Inverted parabolic (IPSP), Salted from below (SFB) and step function (SF) salinity profiles. The effects of variation of different dimensionless parameters on the onset of DD-RB convection is discussed.