Effects of aspect ratio on Rayleigh–Bénard convection under non-Oberbeck–Boussinesq effects in glycerol

This study investigates the non-Oberbeck–Boussinesq (NOB) Rayleigh–Bénard convection inside a two-dimensional rectangular cavity for a fluid with a high Prandtl number (Pr = 2547.0). The parametric study focuses on the aspect ratio (Γ , 0.3 ≤ Γ ≤ 8) dependence of heat transfer and fluid flows on the Rayleigh number (Ra) ranging from 5 × 10 ³ to 10 ⁸ and an NOB assumption with a temperature difference (Δ θ~) of up to 50 K. We numerically find that the critical Ra (Ra _c) for convection onset decreases as Δ θ~ increases for small Γ , while it increases as Δ θ~ increases for large Γ . Four flow regimes are classified based on kinetic and thermal energy dissipation rates in the Γ –Ra plane. The aspect ratio dependency of the Nusselt number (Nu), Reynolds number (Re), and top and bottom thermal boundary layer (BL) thicknesses (λ¯h,cθ) is also investigated under both OB and NOB conditions. It is found that the Γ effect on Re (up to 61%) is more serious than that on Nu (up to 4.5%), while Γ does not obviously affect the generality of the classical NOB effects on scaling exponents of Nu, Re, and λ¯h,cθ for fully chaotic regimes. Top–bottom λ¯h,cθ asymmetry is confirmed, where the top BL is always thicker than the bottom one, and their ratio is up to 1.8 for Δ θ~ = 50 K at Ra = 10 ⁸ . Although λ¯hθ+λ¯cθ increases with an NOB effect enhancement for all aspect ratios, the compensation between λ¯hθ and λ¯cθ leads to small deviation (up to 7.0%) of λ¯hθ+λ¯cθ from unity. This contributes to the robustness of Nu because it is confirmed that the NOB effects on Nu are dominated by the change in λ¯hθ+λ¯cθ .