Thermal convection in a cylindrical annulus heated laterally
Abstract
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.
Cite
@article{arxiv.math/0110195,
title = {Thermal convection in a cylindrical annulus heated laterally},
author = {S. Hoyas and H. Herrero and A. M. Mancho},
journal= {arXiv preprint arXiv:math/0110195},
year = {2009}
}
Comments
17 pages, Latex, 13 figures. Version improved in the physical results. To appear in Journal of Physics A: Mathematical and general