DOI: 10.1615/ICHMT.2004.IntThermSciSemin
ISBN Print: 978-9-61913-930-1
Effect of asymmetry on the steady thermal convection in a vertical torus filled with a porous medium
ABSTRAKT
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).