Pattern Selection in Rayleigh-Bénard Convection with Nonlinear Viscoelastic Fluids

Rayleigh-Bénard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of nonlinear viscoelastic fluids represented by the Phan-Thien-Tanner (PTT) constitutive equation is investigated numerically. Governing equations are discretized by finite-difference methods in space and time. The momentum and PTT constitutive equations are written in a quasilinear formulation. Quasilinear terms are treated with the high-order upwind central (HOUC) method and velocity-pressure coupling is handled through the projection method. The developed model is validated for Oldroyd-B types of working fluids. The onset of time-dependent convection is observed and the critical Rayleigh number is determined for PTT types of fluids. The time-dependent flow pattern transition is investigated and explained. A transition from time-dependent flow to steady-state flow is observed at a higher Rayleigh number and the corresponding critical Rayleigh number is computed. The effect of the rheological parameters on heat transfer is investigated. © 2022 American Physical Society.