Heat transport in a pure fluid near the critical point: Steady state and relaxation dynamics

The steady-slate conditions and relaxation dynamics of a fluid layer during heat transport experiments near the liquid-vapor critical point are studied theoretically. The application is to He-3 along the critical isochore and under normal gravity-where experimental data are available-as well as zero gravity. First, the steady-state density stratification from gravity and from heat flow is calculated The resulting observable thermal conductivity <(lambda)over bar>(obs) is obtained as a function of the temperature difference Delta T (or the heat current Q) across the fluid layer and becomes a strong non-linear function of Delta T as T-c is approached The calculated <(lambda)over bar>(obs) is compared with that from experiments both above and below T-c. Second, the spatial profiles of temperature and density and their temporal evolutions are calculated above T-c as Delta T is established after Q is switched on, or conversely as Delta T decays to zero after Q has been switched off From the calculations, done both from a closed-form expression and from simulations, the "observable" and "asymptotic" relaxation times for reaching the steady state are calculated as a function of Q, and compared with the experiments above T-c.