Pattern selection and heat transfer in the Rayleigh–Bénard convection near the vicinity of the convection onset with viscoelastic fluids

Abstract

The effect of viscoelasticity on the flow and heat transport in the Rayleigh–Bénard convection (RBC), a frequently encountered phenomenon in nature and industry, in a rectangular enclosure with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by a finitely extensible nonlinear elastic-Peterlin constitutive model almost all important features of viscoelastic fluid flow. Numerical simulations are conducted at a low concentration [Formula: see text], where [Formula: see text], μs is the solvent viscosity, and [Formula: see text] is the sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β, and the extension length L on the oscillating mode of the viscoelastic RBC. The results indicate that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the strongly elastic nonlinearity makes the flow transition irregular and even brings about the relaminarization or lead to the convection cells traveling in the horizontal direction. The increasing extension length L induces multiple pairs of roll flow patterns at a specific setting of ( Ra, Wi). Heat transport is reduced (up to 8.5%) by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.