Instability of Jeffrey Fluid Throughflow in a Porous Layer Induced by Heat Source and Soret Effect

In this study, we investigated the instability of thermosolutal convection of Jeffrey fluid in a porous layer with internal heating and the Soret effect. The layer is bounded by two fixed permeable parallel plates which are assumed to be isothermal and isosolutal. An existing initial flow in the vertical direction is passing the layer at a constant speed. The flow fields are adequately presented by PDEs and transformed into dimensionless forms. A small perturbation to the basic flow profiles with linear stability analysis results the problem in an eigenvalue problem. The Runge–Kutta method is used to derive the numerical value of the critical thermal Rayleigh number. The convective instability for asymptotic cases for $Le=1$ and $Pe=0$ are also examined as special cases. The analysis reveals that for a nonpositive Soret parameter the flow is stable for all Lewis numbers and independent of the heat source. But in the case of a positive Soret parameter in the absence of a heat source, the fluid flow is stable for $Le≥3$ while the influence of a heat source destabilizes the flow for $Le>2$⁠. In high and low shear flows with increasing solutal gradient, the solutal Rayleigh number shows a highly destabilizing nature for all $Le$⁠. Moreover, smaller relaxation and higher retardation time are the most unstable characteristics of the heat source system. In convective longitudinal rolls, the unicellular streamline patterns tend to become bi-cellular by the influence of positive Soret parameters and energy sources.