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Effect of asymmetry on the steady thermal convection in a vertical torus filled with a porous medium

Adrian Postelnicu
Department of Thermal Engineering and Fluid Mechanics, Transilvania University of Brasov, Brasov, Romania

Nicoleta Scurtu
Numerical Mathematics and Scientific Computing, Weierstrass-Institute for Applied Analysis and Stochastic (WIAS), Mohrenstrasse 39, 10117 Berlin, Germany

Sinopsis

The paper deals with a study on the thermal convection in a fluid saturated porous medium confined in a vertical oriented toroidal loop heated from below and cooled from above, subjected to a vertically uniform temperature gradient. In fact, Sano, O., Journal of the Physical Society of Japan (1987 and 1988) studied such a configuration for clear fluids. We take the steady heat conduction state under a constant vertical temperature gradient (−k) as a fundamental solution. A cylindrical system of co-ordinates (r, φ, s) is considered for the loop of 2πR length and cross sectional diameter 2a, where the ratio a/R is assumed to be very small. We expand all quantities in terms of double Fourier series in φ and θ, where θ = s/R. First-order perturbed fields from steady heat conduction state are examined and various plots are given: isotherms in ring and meridian plane, stream lines and velocities. Finally, an attempt is made in order to identify other fundamental solutions: S-type (cellular thermal convection) and A-types (coaxial flow, bidirectional flow and antisymmetric cellular flow).

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