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–Bénard 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.

Ellis 模型描述了剪切稀化流体的表观粘度，在极小的剪切应力的极限内没有奇点。特别是，当剪应力非常小时，该模型与牛顿行为相匹配。当在水平多孔层中规定产生基本通流的水平压力梯度时，研究了瑞利-贝纳不稳定性的出现。该系统线性不稳定性的阈值条件是通过分析和数值获得的。在流速可忽略不计的情况下，对于饱和多孔介质的牛顿流体文献中报道的相同参数条件，会发生不稳定性。另一方面，当考虑高流速时，