%0 Book Section %1 statphys23_0018 %A Araujo, F. Fontenele %A Ahlers, G. %A Brown, E. %A Funfschilling, D. %A Grossmann, S. %A Lohse, D. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K boundary convection layers rayleigh-benard self similarity statphys23 topic-3 %T Thermal convection with variable transport properties %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=18 %X Thermally driven fluid motion usually involves significant variations in transport properties like viscosity and thermal conductivity. In the context of Rayleigh-Bénard convection (flow in a container heated from below and cooled from above), such variations can break the top-down symmetries of the velocity, temperature, and density profiles. This symmetry breaking is indicated by the difference $T_c - T_m$, where $T_c$ is the temperature in the center of the convection container and $T_m = (T_b + T_t)/2$ is the mean temperature between the bottom ($T_b$) and top ($T_t$) plates. On the basis of boundary-layer equations with variable transport properties 1-2, we compute $T_c - T_m$ as function of $\Delta = T_b - T_t$. Two different fluids are considered: gaseous ethane close to its critical point 1 and water 2. The latter exhibits $T_c > T_m$ for increasing $\Delta$, meaning that the top boundary-layer becomes thicker than its counterpart at the bottom plate. In contrast, when working fluid is gaseous ethane, the opposite symmetry breaking is observed. In both cases, our theoretical results are in reasonable agreement with experimental measurements (see figure 1). References 1) G. Ahlers, F. Fontenele Araujo, D. Funfschilling, S. Grossmann, and D. Lohse. Physical Review Letters 98, 054501 (2007).\\ 2) G. Ahlers, E. Brown, F. Fontenele Araujo, D. Funfschilling, S. Grossmann, and D. Lohse. Journal of Fluid Mechanics 569, 409 (2006)

@incollection{statphys23_0018, abstract = {Thermally driven fluid motion usually involves significant variations in transport properties like viscosity and thermal conductivity. In the context of Rayleigh-B\'enard convection (flow in a container heated from below and cooled from above), such variations can break the top-down symmetries of the velocity, temperature, and density profiles. This symmetry breaking is indicated by the difference $T_{c} - T_{m}$, where $T_{c}$ is the temperature in the center of the convection container and $T_m = (T_{b} + T_{t})/2$ is the mean temperature between the bottom ($T_{b}$) and top ($T_{t}$) plates. On the basis of boundary-layer equations with variable transport properties [1-2], we compute $T_{c} - T_{m}$ as function of $\Delta = T_{b} - T_{t}$. Two different fluids are considered: gaseous ethane close to its critical point [1] and water [2]. The latter exhibits $T_{c} > T_{m}$ for increasing $\Delta$, meaning that the top boundary-layer becomes thicker than its counterpart at the bottom plate. In contrast, when working fluid is gaseous ethane, the opposite symmetry breaking is observed. In both cases, our theoretical results are in reasonable agreement with experimental measurements (see figure 1). References 1) G. Ahlers, F. Fontenele Araujo, D. Funfschilling, S. Grossmann, and D. Lohse. Physical Review Letters 98, 054501 (2007).\\ 2) G. Ahlers, E. Brown, F. Fontenele Araujo, D. Funfschilling, S. Grossmann, and D. Lohse. Journal of Fluid Mechanics 569, 409 (2006)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Araujo, F. Fontenele and Ahlers, G. and Brown, E. and Funfschilling, D. and Grossmann, S. and Lohse, D.}, biburl = {https://www.bibsonomy.org/bibtex/2e45d6733f1e038b3440628291008161b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {dd7e05c20cad29e754871a0b5532a84c}, intrahash = {e45d6733f1e038b3440628291008161b}, keywords = {boundary convection layers rayleigh-benard self similarity statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:09.000+0200}, title = {Thermal convection with variable transport properties}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=18}, year = 2007 }