Stability of the horizontal throughflow of a power-law fluid in a double-diffusive porous layer under convective boundary conditions

Abstract

Double-diffusive convective instability of a horizontal througflow in a power-law fluid-saturated porous layer lying between infinitely extended two plane horizontal boundaries is investigated by considering internal heating associated with the viscous dissipation. These boundaries are assumed to be impermeable, isosolutal and are subjected to the third kind thermal boundary conditions which are characterized by different Biot numbers B0,B1. The linear stability analysis of basic flow for pseudoplastic and dilatant fluids is analyzed for the longitudinal and transverse rolls in both aiding and opposing buoyancy cases. The eigenvalue problem is solved numerically using the bvp4c in Matlab. It is shown that the longitudinal rolls are the most unstable mode for dilatant fluids, whereas the transverse rolls are the most unstable mode of disturbance for pseudoplastic fluids. In both these cases, an increase in either of these Biot numbers is enhancing the stability of power-law fluids. Increasing Pèclet number destabilized the transverse rolls for the pseudoplastic fluid while the longitudinal rolls are stabilized in case of the dilatant fluid. The effect of viscous dissipation on the onset of instability is also presented. A discussion on the onset of oscillatory convective instability (ω≠0) in this double-diffusive process, under third kind thermal boundary conditions is also presented. Further, the instability of power-law fluid is discussed for two limiting cases of thermal boundary conditions; the first one is B0=0,B1→∞ which corresponds to the constant heat flux at the bottom boundary while the second one is B0→∞,B1→∞, that corresponds to isothermal walls. As Pe=0 is a singularity for the eigenvalue problem, a detailed asymptotic analysis of Pe→0 is presented for all these cases.