Non-Oberbeck–Boussinesq effects in two-dimensional Rayleigh–Bénard convection of different fluids

Abstract

Non-Oberbeck–Boussinesq (NOB) effects in three representative fluids are quantitatively investigated in two-dimensional Rayleigh–Bénard convection. Numerical simulations are conducted in air, water, and glycerol with Prandtl numbers of Pr=0.71,4.4, and 2547, respectively. We consider Rayleigh number Ra∈[106,109] involving temperature difference (Δθ̃) of up to 60 K. The velocity and temperature profiles are found to be top-bottom antisymmetric under NOB conditions. As Pr increases, the time-averaged temperature of the cavity center ⟨θc⟩t increases under NOB conditions and the value of ⟨θc⟩t is only weakly influenced by Ra for all fluids. For Pr = 4.4 and 2547, with the enhancement of NOB effects, ⟨θc⟩t linearly increases and the maximum θ rms decreases/increases, and its location shifts toward/away from the wall near the bottom/top wall. Dispersed ⟨θc⟩t points and opposite phenomenon are observed in Pr = 0.71. The Nusselt number (Nu) and thermal boundary layer thickness at hot and cold walls (λ¯h,cθ) of the three fluids are comparable, and the Reynolds number (Re) significantly decreases as Pr increases. Under the NOB conditions with Pr = 4.4 and 2547, Nu decreases, Re increases, and λ¯hθ (λ¯cθ) thins (thickens) in an approximately linear fashion. Furthermore, the NOB effects on Nu, Re, and λ¯h,cθ are relatively small for Pr = 0.71 and 4.4, whereas the modifications caused by NOB effects at Pr = 2547 are more significant. The power-law scaling factors of Nu, Re, and λ¯h,cθ are demonstrated to be robust to Pr, as well as NOB effects.