Effect of departures from the Oberbeck-Boussinesq approximation on the heat transport of horizontal convecting fluid layers

Abstract

Measurements are presented of the Nusselt numbers N and Rayleigh numbers R for shallow layers of ⁴He gas heated from below. By choosing different temperatures between 2·3 K and 5·1 K and different pressures between 0·07 bar and 1 bar, the extent Q of departures from the Oberbeck-Boussinesq approximation was varied. When R was evaluated at the static temperature at the midplane of the cell, both the critical Rayleigh number R_c and the initial slope N₁ of the Nusselt number were found to be independent of Q within experimental scatter. This result agrees with the prediction of Busse (1967). When R was evaluated at the cold end temperature of the cell, both R_c and N₁ depended strongly upon Q.