Buoyancy-driven linear instability in a porous layer with contrasting heat sources

Double-diffusive linear instability of a power-law fluid flow through porous media with various heat source functions is studied with two permeable infinite parallel walls. The energy balance equation accounts for viscous dissipation, and the temperature and concentration on the boundaries are assumed to be isothermal and isosolutal, respectively. After non-dimensionalisation with appropriate scales, the governing equations are subjected to infinitesimal disturbances on the base flow, and are used to study the stability theory. The results obtained revealed that for large and small values of the Péclet number ( $\textit{Pe}$ ), an increasing source function ( $Q_{\textit{Is}}$ ) delays the onset of convective motion by diminishing the vertical temperature gradient and hence suppressing buoyancy, resulting in a higher critical Rayleigh number ( ${\textit{Ra}}_c$ ). In contrast, the non-uniform source ( $Q_{\textit{Ns}}$ ) can destabilise the system due to localised heating, which increases buoyancy and favours the growth of perturbations. Generally, increasing Lewis number ( ${\textit{Le}}$ ) tends to suppress the instability under opposing buoyancy conditions, whereas in the case of aiding buoyancy, a sufficiently large throughflow can counteract this stabilising effect. Under the influence of viscous dissipation and source parameters, a pseudo-plastic fluid is more stable compared to a dilatant fluid. In convective rolls, when thermal and solutal diffusivities are equal, dilatant fluids exhibit multicellular convection. Under aiding buoyancy, streamlines develop three counter-rotating vortices, whereas under opposing buoyancy, the pattern attains a symmetric structure.