Heat transfer and convection onset in a compressible fluid: He-3 near the critical point - art. no. 056310

Heat transport in He-3 above its critical temperature T-c was studied along the critical isochore in a flat Rayleigh-Benard cell (height h = 1 mm, dia meter D = 57 mm). The range of the reduced temperature epsilon was 5 x 10(- 4)less than or equal to epsilon less than or equal to2 x 10(-1). The temper ature difference DeltaT(t) across the fluid layer as a function of the time t was measured for different values of the heat current q until steady sta te was reached. The crossover was observed from the regime dominated by the Rayleigh criterion for the convection onset to that controlled by the adia batic temperature gradient (ATG), or "Schwarzschild criterion," in good qua ntitative agreement with predictions. The slope of the convective heat curr ent versus the reduced Rayleigh number was found to be independent of compr essibility and the same as for still less compressible fluids. Plots of Nu versus Ra, both corrected for the ATG effect, are presented for early-stage convective turbulence (1x10(5)<Ra<5x10(8)), with unexpected results for th e highest values of Pr approximate to 590. The evolution of the transients DeltaT(t) upon turning q on and off are described. In the nonconvective reg ime, the observed transient relaxation curve agrees quantitatively with pre dictions. In the convective regime, the shape of DeltaT(t) changes qualitat ively with increasing q and with epsilon. In the Appendix, new data for the thermal conductivity are presented, the impact of the "piston effect'' on the temperature profiles inside the fluid is described, and the derivation for DeltaT(t) in the diffusive regime is outlined.