  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.
