Prediction of the center temperature for compressible non-Oberbeck-Boussinesq thermal convection

Thermal convection in gaseous ethane at high pressure is theoretically analyzed, focusing on non-Oberbeck-Boussinesq (NOB) effects. On the basis of boundary-layer equations with variable transport properties, it is shown that the top-down symmetry of the velocity, temperature, and density profiles is broken. In particular, we predict that the temperature $T_{c}$ in the center of the convection container is less than the mean temperature $T_{m} = (T_{t} + T_{b})/2$ between the top ($T_{t}$) and bottom ($T_{b}$) plates, in contrast to the corresponding NOB effect in liquids. We also characterize the temperature profile across the top boundary-layer, as $T_{t}$ approaches the gas-liquid coexistence curve and the corresponding thermal conductivity is enhanced.