Geometric confinement and fluid properties effects on stability and heat transfer of thermal convection in lateral heated cavities

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A numerical study is performed to investigate two-dimensional natural convection in a laterally heated cavity, with particular emphasis on the coupled effects of the aspect ratio ( A ), Rayleigh number ( R a ), and Prandtl number ( P r ). The simulations cover mainly the ranges 1 0 4 ≤ R a ≤ 1 0 6 , 0 . 01 ≤ A ≤ 10 , and 0 . 01 ≤ P r ≤ 10 . A fourth-order compact finite-difference scheme combined with a third-order TVD Runge–Kutta time integration is employed to ensure numerical stability and adequate resolution of unsteady flow features. The results reveal that heat transfer is strongly influenced by the Prandtl number. As P r increases, the flow transitions from unsteady to steady behavior and the overall heat transfer is enhanced. For low-Prandtl-number fluids ( P r < 1 ), such as gases and liquid metals, nonlinear solution bifurcations emerge, becoming increasingly pronounced at larger aspect ratios and higher Rayleigh numbers. The onset of unsteadiness is associated with a critical Rayleigh number R a c , marking the transition from steady to unsteady convection. Scaling analyses show that R a c ∼ A − 10 / 3 for air and R a c ∼ A − 7 / 3 for water, indicating a reduced sensitivity to geometric confinement for high- P r fluids. The aspect ratio is found to exert a non-monotonic influence on heat transfer. The average Nusselt number ( N u av ) attains its maximum at an optimal aspect ratio A m that shifts toward smaller values as R a increases. Additionally, the heat transfer follows a power-law dependence on the Rayleigh number, N u av = c R a β , where 0 . 14 ≤ c ≤ 0 . 20 and 0 . 25 ≤ β ≤ 0 . 30 , with the coefficients depending on the Prandtl number.