Natural convection inside vertical enclosures is governed by the cavity aspect ratio \(H/L\) and the Rayleigh number based on the width \(L\):

\[Ra_L = \frac{g \beta (T_h - T_c) L^3}{\nu \alpha}\]

Convection Transition Regimes

  • Conduction Regime (\(Ra_L < 1000\)): Bouyancy forces are balanced by viscous shear. Heat transfer is dominated by pure conduction: \(Nu \approx 1.0\).
  • Transition Regime (\(1000 < Ra_L < 10^5\)): Fluid starts circulating, forming a unicellular boundary layer loop. Heat transfer increases linearly.
  • Turbulent Boundary Layer (\(Ra_L > 10^5\)): Separate boundary layers form along hot and cold walls. Core fluid stabilizes thermally. Nusselt correlation matches:
    \[Nu_L = 0.18 Ra_L^{0.25} \left( \frac{H}{L} \right)^{-0.3}\]

References

  • Catton, I. (1978). Natural convection in enclosures. Proc. 6th Int. Heat Transfer Conf., Vol. 6, pp. 13-31.