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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. [ABSTRACT FROM AUTHOR]

Highlights • This paper presents a methodology to infer the rheology of a fluid from free surface velocity measurement. • Rheology is reconstructed by minimizing the difference between simulated and measured data. • The method is tested on synthetic and real experimental data for the dam-break flow problem. • Particle Tracking Velocimetry is used to measure the free surface velocity. • Models based on the Navier–Stokes equations and the lubrication approximation with an Ellis rheology are presented. Abstract This study presents a new rheometry technique which requires a free surface velocity field as an input. By minimising the difference between observed and simulated data, we show here that it is possible to estimate the three parameters of an assumed Ellis rheological law. The dam-break problem is considered here with molasses as the working fluid. The free surface velocity is evaluated by seeding the free surface with buoyant particles and using particle tracking velocimetry. The parameter identification is successfully tested with "synthetic" data produced by the numerical model. The parameter identification algorithm is shown to be robust even when significant noise is added to the synthetic dataset. For true experimental data, the reconstructed flow curve is within 25% of the actual one, demonstrating the potential of the method for circumstances where standard rheometry does not apply. [ABSTRACT FROM AUTHOR]

The determination of temperature and auxiliary quantities such as local and average Nusselt numbers for thermally developing flow is referred as the Graetz problem. In the classical Graetz problem, the fluid entering the tube or channel is Newtonian in nature. Here, an extension of the classical Graetz problem is presented by assuming that the fluid entering the tube or channel obeys the Ellis constitutive equation. The energy equation for the considered problem is solved using the separation of variables technique supplemented with the MATLAB routine bvp4c for computation of the eigenvalues and numerical solution of the associated Sturm-Liouville boundary value problem. The problem is solved for two types of thermal boundary conditions, namely, uniform surface temperature and uniform surface heat flux for both flat and circular geometries. Expressions for bulk mean temperature and local and average Nusselt numbers are presented and discussed through tables and graphs. [ABSTRACT FROM AUTHOR]

The accuracy of the Ostwald-de Waele model in solving the problem of roll flow has been assessed by comparing with the "reference" solution for an Ellis fluid. As a result of the analysis, it has been shown that the model based on a power-law equation leads to substantial distortions of the flow pattern. [ABSTRACT FROM AUTHOR]

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