Coexistence of Single-Roll and Two-Roll Oscillations for Rayleigh–Bénard Convection in Trapezoidal Cavities Filled With Oldroyd-B Fluids

Abstract Bottom-heated viscoelastic fluids in a cavity transit from conduction to convection through periodic oscillations or steady-states of flow patterns, depending on the Rayleigh number and other fluid parameters. It is in contrast to the Newtonian fluids, where the transition is always to steady-state convection. The trapezoidal cavities filled with Oldroyd-B fluid have been explored with side walls inclined from 80 deg to 100 deg using OPENFOAM-based RheoTool simulations. The obtuse angle trapezoidal cavities have five different types of solutions. Four of these solutions consist of one-roll and two-roll solutions (TRS) with and without oscillations. The fifth solution is the conduction-dominated solution with low flow and heat transfer. However, since it lacks two-roll solutions, there are only three kinds of solutions for Rayleigh–Bénard convection (RBC) in an acute angle trapezoidal cavity (AATZC). The bifurcation maps and heat transfer characteristics are presented for various types of rolls. One-roll periodic solution exists beyond the viscosity ratio of 0.5 in AATZCs, while it is up to 0.5 in square and obtuse angle trapezoidal cavity (TZCs). Moreover, two-roll periodic solutions are observed beyond the viscosity ratio of 0.5 in obtuse angle TZCs. Isotherms and flow patterns are presented to illustrate the dynamics of each flow regime. The effect of sidewall angles on the stabilization of the flow is also investigated. The periodic oscillations are observed up to higher Rayleigh numbers for trapezoidal cavities with smaller cavity angles compared to those with higher cavity angles.