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Non-Oberbeck-Boussinesq effects in Rayleigh-Benard convection

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The problem of Rayleigh-Benard convection is commonly analyzed within the so-called Oberbeck-Boussinesq (OB) approximation, in which the fluid properties are assumed to be temperature independent, apart from the density for which a linear temperature dependence is assumed. Under normal conditions, i.e., small temperature differences between the bottom and top plate, this approximation is rather good. However, in order to achieve ever larger Rayleigh numbers for given cell height and fluid properties the temperature difference is quite frequently increased to such an extent that the OB approximation has to be expected to fail. Non-Oberbeck-Boussinesq (NOB) effects on the mean center cell temperature, the Nusselt number Nu, and the Reynolds number Re then have to be expected at the largest Rayleigh numbers.

We report on our recent experimental, theoretical, and numerical results on these NOB corrections. For water and glycerol they are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient: With increasing NOBness, for water and glycerol Nu goes down and the center temperature goes up, whereas for ethane gas in general Nu goes up and the center temperature goes down. However, for ethane close to the critical point the main origin of NOB corrections lies in the strong temperature dependence of the isobaric thermal expansion coefficient, namely in the nonlinear temperature dependence of the density, leading to NOB corrections which presently cannot be described by our extended Prandtl-Blasius boundary layer theory.

Related Links * – Web page Phyiscs of Fluids group Twente

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