Natural convection in an enclosed vertical air layer with large horizontal temperature differences

Abstract

Steady-state two-dimensional results obtained from numerical solutions to the transient Navier-Stokes equations are given for laminar convective motion of a gas in an enclosed vertical slot with large horizontal temperature differences. We present results for air using the ideal-gas law and Sutherland-law transport properties, although the results are also valid for hydrogen. Wide ranges of aspect-ratio, Rayleigh-number and temperature-difference parameters are examined. The results are compared in detail with the exact solution in the conduction and fully developed merged boundary-layer limits for arbitrary temperature difference, and to the well-established Boussinesq limit for small temperature difference. It is found that the static pressure, and temperature and velocity distributions are very sensitive to property variations, even though the average heat flux is not. In addition we observe a net vertical heat flux to be the same as that obtained from the Boussinesq equations. We concentrate on the boundary-layer regime, but we present a rather complete picture of different flow regimes in Rayleigh-number, aspect-ratio and temperaturedifference parameter space. We observe that, with increasing temperature difference, lower critical Rayleigh numbers for stationary and oscillatory instabilities are obtained. In addition we observe that in some cases the physical nature of the instability changes with increasing temperature difference.