Rayleigh–Bénard convection of a viscoplastic liquid in a trapezoidal enclosure

Abstract

The objective of this paper is to clarify the role of sloping walls on convective heat transport in Rayleigh–Bénard convection within a trapezoidal enclosure filled with viscoplastic fluid. The rheology of the viscoplastic fluid has been modeled with Bingham fluid model. The system of coupled nonlinear differential equations was solved numerically by Galerkin's weighted residuals scheme of finite element method. The numerical experiments are carried out for a range of parameter values, namely, Rayleigh number (5.103 ≤ Ra ≤ 105), yield number (0 ≤ Y ≤ Yc), and sidewall inclination angle (ϕ = 0, π/6, π/4, π/3) at a fixed Prandtl number (Pr = 500). Effects of the inclination angle on the flow and temperature fields are presented. The results reveal that inclination angle causes a multicellular flow and appears as the main parameter to govern heat transfer in the cavity. The heat transfer rate is found to increase with the increasing angle of the sloping wall for both Newtonian and yield stress fluids. On the other hand, the plug regions also found to increase with increasing φ, which is unusual but perhaps not unexpected behavior. In the yield stress fluids, the flow becomes motionless above a critical yield number Yc because the plug regions invade the whole cavity. The critical yield number Yc is also affected by the change of inclination angle and increases significantly with the increase of φ.