Double-diffusive thermosolutal Hadley–Prats flow: stability analysis

Abstract

ABSTRACT A mathematical model is formulated to study the onset of double-diffusion fluid flow through an infinite permeable channel with internal heat source and viscous dissipation effects under the influence of convection conditions. Numerically, the dimensionless emerging eigenvalue problem is tackled using the fourth-order Runge–Kutta scheme, specifically applied to longitudinal roll disturbances. Critical values of wave number and vertical thermal Rayleigh number are determined. A higher value of Gebhart number is observed to correlate significantly with the destabilizing phenomena in Hadley–Prats flow. Concentration-based internal heat generation also strongly modifies the critical thermal Rayleigh number. Also, it is found that the horizontal mass flow and viscous dissipation exert a substantial influence on the onset of instability in the flow regime. Linear instability analysis indicates that greater values of Lewis number in the porous medium stabilize the convection process for both values of mass diffusion parameter ( C z ) . Enhancing C z from negative to positive values diminishes the critical thermal Rayleigh ( R z ) value and consequently induces instability in the porous medium. Increased concentration-based internal heat generation generates the destabilization process in the flow region.