Horizontal pressure gradient and Soret effects on the onset of thermosolutal porous convection

The intricacies of a constant horizontal pressure gradient on the onset of Soret-driven thermosolutal porous convection have been investigated. The resulting generalized eigenvalue problem is solved numerically using the Galerkin method and also the condition for the onset is obtained in a closed-form using a single-term Galerkin method with trigonometric trial function. The results obtained from both methods are found to be in good agreement. The effect of increasing horizontal pressure gradient, Lewis number, Soret parameter, and the Vadasz number is to hasten, while the increase in the solute Darcy–Rayleigh number is to delay the onset of oscillatory convection. The presence of the horizontal pressure gradient is found to decrease the threshold value of solute Darcy–Rayleigh number beyond which the instability sets in as oscillatory. Moreover, the horizontal pressure gradient imparts a conflicting behavior on the critical wave number and critical frequency of oscillations. The numerical results attained under the limiting cases are shown to be in excellent agreement with the published ones.