Effect of asymmetry on the steady thermal convection in a vertical torus filled with a porous medium - Adrian, Postelnicu (Strojniški vestnik, 2005)
The paper deals with a study on the thermal convection in a fluid saturated porous medium confined in a vertical oriented toroidalloop heated from below and cooled from above, subjected to a vertically uniform temperature gradient.In fact, Sano, O., Journal ofthe Physical Society of Japan (1987 and 1988) studied such a configuration for clear fluids. We take the steady heat conduction stateunder a constant vertical temperature gradient (-k) as a fundamental solution. A cylindrical system of co-ordinates (r, f, s) is considered for the loop of 2pR length and cross sectional diameter 2a, where the ratio a/R is assumed to be very small. We expand allquantities in terms ofdouble Fourier series in f and q, where q = s/R. First-order perturbed fields from steady heat conduction stateare examined and various plots are given: isotherms in ring and meridian plane, stream lines and velocities. Finally, an attempt ismade in order to identify other fundamental solutions: S-type (cellular thermal convection) and A-types (coaxial flow, bidirectional flow and antisymmetric cellular flow).
Keywords: prevod toplote; tok fluida; mediji porozni; modeli matematični; prenos toplote; konvekcija; porozni mediji; cilindi; matematični modeli