Double-diffusive Hadley–Prats flow in a horizontal porous layer with a concentration based internal heat source

Double-diffusive Hadley–Prats flow with a concentration based heat source is investigated through linear and non-linear stability analyses. The resultant eigenvalue problems for both theories are solved numerically using Shooting and fourth order Runga–Kutta methods, with the critical thermal Rayleigh number being evaluated with respect to various flow governing parameters such as the magnitudes of the heat source and mass flow. It is observed, in the linear case, that an increase in the horizontal thermal Rayleigh number is stabilising for both positive and negative values of the solutal Rayleigh number. In the non-linear case, a destabilising effect is identified at higher mass flow rates. An increase in both the heat source and mass flow results in destabilisation.