Non-Oberbeck-Boussinesq effects on a water-filled differentially heated vertical cavity

In this study, we examined non-Oberbeck-Boussinesq (NOB) effects on a water-filled differentially heated vertical cavity through two-dimensional direct numerical simulations. The simulations encompassed a Rayleigh number (Ra) span of 10⁷-10¹⁰, temperature difference ( Δ θ ̃ ) up to 60 K, and a Prandtl number (Pr) fixed at 4.4. The center temperature ( θ cen ) was found to be independent of Ra and to increase linearly with Δ θ ̃ , as presented by θ cen ≈ 1.18 × 10 − 3 K − 1 Δ θ ̃ . The thermal boundary layer (BL) thicknesses near the hot and cold walls ( λ ¯ h θ and λ ¯ c θ , respectively) are found to scale as λ ¯ h , c θ ∼ R a γ λ ¯ h , c , where the scaling exponent γ λ ¯ h , c ranges from −0.264 to −0.262. For more detail, the scaling exponent γ λ ¯ h displays an increasing trend, while γ λ ¯ c demonstrates a decreasing trend. However, the sum of the hot and cold thermal BL thicknesses was found to be constant at a fixed Ra in the presence of NOB effects. Our detailed investigation of the Nusselt number (Nu) and Reynolds number (Re) revealed that N u ∼ R a 0.258 and R e ∼ R a 0.364 , showing insensitivity to NOB effects. These exponents were smaller than those for Rayleigh-Bénard convection. The NOB modifications on Nu and Re were less than 1.2% and 2.5%, respectively, even at Δ θ ̃ = 60 K. Our results also revealed that key parameters such as θ cen and normalized ratios [ ( λ ¯ NOB θ / λ ¯ OB θ ) h , c , N u NOB / N u OB , and R e NOB / R e OB ] exhibit universal correlations with Δ θ ̃ . Remarkably, these relationships are consistent across varying Ra values. This observation underscored the influence of NOB effects on these parameters could be confidently forecasted using just the temperature difference ( Δ θ ̃ ) for R a ∈ [ 10 7 , 10 10 ] .