Stability of a Rayleigh-Bénard Poiseuille flow for yield stress fluids-Comparison between Bingham and regularized models

► Comparison between the Bingham and regularized models on the stability of the RBP flow. ► The effective viscosity is not defined in the plug zone for the Bingham model. ► Regularized models lead to the Newtonian critical conditions for weak values of yield stress. ► Convergence of the critical conditions between the simple and the Bingham models is not obtained. ► The Bercovier and Papanastasiou models can tend to the exact Bingham results.