  Unlike the power-law model, the Ellis model describes the apparent viscosity
of a shear-thinning fluid with no singularity in the limit of a vanishingly
small shear stress. In particular, this model matches the Newtonian behaviour
when the shear stresses are very small. The emergence of the Rayleigh-B\'enard
instability is studied when a horizontal pressure gradient, yielding a basic
throughflow, is prescribed in a horizontal porous layer. The threshold
conditions for the linear instability of this system are obtained both
analytically and numerically. In the case of a negligible flow rate, the onset
of the instability occurs for the same parametric conditions reported in the
literature for a Newtonian fluid saturating a porous medium. On the other hand,
when high flow rates are considered, a negligibly small temperature difference
imposed across the horizontal boundaries is sufficient to trigger the
convective instability.
