Finite-wall effect on buoyant convection in an enclosure with pulsating exterior surface temperature

A numerical study is made of the finite-wall effect in the benchmark-configuration buoyant convection in a square cavity at large Rayleigh number. A general formulation, with one vertical sidewall of finite thickness and thermal conductivity, is presented. Firstly, the finite-wall effect for the case of non-pulsating boundary temperature condition is delineated. The energy balance consideration, together with the preceding empirical correlations, leads to a simple formula to predict the temperature at the interior surface of the finite-thickness wall. The analytical predictions are shown to be consistent with the results of full-dress Navier–Stokes numerical solutions. Secondly, the finite-wall effect for the case of pulsating boundary temperature condition is explored. The numerical results illustrate that the amplitude of oscillating Nusselt number, A(Nu), at the central plane peaks at a particular pulsation frequency. This has been interpreted to be a manifestation of resonance. The finite-wall effect on the shift of resonance frequency is discussed. The temperature oscillation at the interior surface of the solid wall is examined, and the convection-modified model is introduced to describe the alteration in the temperature contrast across the fluid portion. The estimation of the resonance frequency, based on the internal gravity oscillations, is shown to be in accord with the Navier–Stokes numerical solutions.