Thermal convection in a cylindrical annulus heated laterally

Details Thermal convection in a cylindrical annulus heated laterally Thermal convection in a cylindrical annulus heated laterally

2001-10-18

arxiv.org/abs/math/0110195v2

Mathematics

Analysis of PDEs

17 pages, Latex, 13 figures. Version improved in the physical results. To appear in Journal of Physics A: Mathematical and gen

Scientific paper

10.1088/0305-4470/35/18/306

In this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. As the temperature gradient reaches a critical value a stationary or oscillatory bifurcation may take place. The problem is modelled with a novel method which extends the one described in (numerico). The Navier Stokes equations are solved in the primitive variable formulation, with appropriate boundary conditions for pressure. This is a low order formulation which in cylindrical coordinates introduces lower order singularities. The problem is discretized with a Chebyshev collocation method easily implemented and its convergence has been checked. The results obtained are not only in very good agreement with those obtained in experiments, but also provide a deeper insight into important physical parameters developing the instability, which has not been reported before.

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