Natural convection in a fluid saturating an anisotropic porous medium in LTNE: effect of depth-dependent viscosity

Abstract Thermal convection in a fluid saturating an anisotropic porous medium local thermal nonequilibrium (LTNE) is investigated, with specific attention to the effect of variable viscosity on onset convection. Many fluids show remarkable dependence temperature that cannot be neglected. For this reason, we take into account whose decreases exponentially depth, according Straughan (Acta Mech. 61:59–72, 1986), Torrance and Turcotte (J. Fluid 47(1):113–125, 1971). The novelty paper highlight how coupled LTNE assumption affects A numerical procedure shows destabilising depth-dependent viscosity. Moreover, it comes out hypothesis makes influence more intense. Linear instability analysis conduction solution carried by means Chebyshev-tau method QZ algorithm, which provides critical Rayleigh number for straightforward way. energy employed order study nonlinear stability. optimal result coincidence between linear threshold global stability obtained. permeability conductivity, weighted conductivity ratio, interaction coefficient highlighted.