Specific roles of fluid properties in non-Boussinesq thermal convection at the Rayleigh number of 2× 10

We demonstrate the specific non-Boussinesq roles played by various fluid properties in thermal convection by allowing each of them to possess, one at a time, a temperature dependence that could be either positive or negative. The negative temperature dependence of the coefficient of thermal expansion hinders effective thermal convection and reduces the Nusselt number, whereas the negative dependence of fluid density enhances the Nusselt number. Viscosity merely smears plume generation and has a marginal effect on heat transport, whether it increases or decreases with temperature. At the moderate Rayleigh number examined here, the specific heat capacity shows no appreciable effect. On the other hand, the conductivity of the fluid near the hot surface controls the heat transport from the hot plate to the fluid, which suggests that a less conducting fluid near the bottom surface will reduce the Nusselt number and the bulk temperature. Copyright c © EPLA, 2009 Introduction. – The flow generated by the buoyancy force in a fluid column between two horizontal plates maintained at different temperatures has been a topic of intense research [1,2]. An important control parameter for the problem is the Rayleigh number Ra≡ α∆TgH/νκ, where α is the isobaric thermal expansion coefficient of the fluid; ∆T , the temperature difference between the top and bottom plates separated by a vertical height H; g, the acceleration due to gravity; ν, the kinematic viscosity; and κ, the thermal diffusivity of the fluid. It is also known that the flow characteristics depend on the geometry and the Prandtl number Pr= ν/κ. If the temperature difference ∆T is small so that the resulting density differences in the flow are small as well, it is traditional to account for the effects of density variations only through the gravitational body force and to assume, in so far as all other effects are concerned, that constant density is a good approximation. This is the Boussinesq approximation. If this approximation is invalid, one has to account for the temperature variations of all fluid properties. A comprehensive account of the nonBoussinesq effects near the onset of the primary instability (a)E-mail: [email protected] of the flow can be found in [3,4], but our understanding of their precise role in the turbulent regime, which began with ref. [5] and explored more recently [6–13], is still inadequate. Reference [9] attempts to understand the effect of the non-Boussinesq effects in water and glycerol experimentally. The temperature dependence of kinematic viscosity and thermal diffusion coefficient were found to have a dominant influence on center temperature. However, they did not isolate the role of individual physical properties in determining the heat transport or center temperature. Reference [10] uses ethane gas and notes that the center temperature decreases for gases and the Nusselt number increases for large non-Boussinesq values at Rayleigh numbers that are higher than that reported in this paper. For gases, it is noted that the center temperature is less than the algebraic mean of the top and bottom temperatures, as obtained in [10,11,13], but a physical reason is not elucidated. Two-dimensional DNS in refs. [11,12] of Rayleigh-Bénard convection with properties of glycerol and ethane, respectively, tries to dwell into the non-Boussinesq effects on the center temperature at low Rayleigh numbers, and again falls short of giving a physical picture of the role of fluid properties.