Linear stability of the Rayleigh–Bénard Poiseuille flow for thermodependent viscoplastic fluids

This work investigates the Rayleigh–Bénard Poiseuille flow of a Bingham fluid with temperature-dependent plastic viscosity according to the model μˆp=aexp⁡(−bˆTˆ). In fully developed situation, the temperature profile is purely conductive and the axial velocity profile, determined numerically, is skewed toward the lower viscosity region. The linear stability analysis of this primary flow is performed, and the critical conditions above which the flow becomes unstable are determined. It is found that the critical conditions decrease with increasing |k|=|bˆ|δTˆ and that the critical Rayleigh number scales as exp⁡(−0.8|k|)exp⁡(−0.8|k|). It is shown that this destabilization is mainly due to the asymmetry of the basic flow. As well as the basic flow, the perturbed flow is also asymmetric. Indeed, the amplitude perturbation of the least stable mode is much higher in the yielded region having the largest width.