Computation of Chebyshev spectral analysis approximation has been developed in order to solve coupling of Navier-Stokes and heat equations for a differentially heated annular cavity under axisymmetric conditions. A domain decomposition technique introduced by Hugues and Randriamampianina in [4] has been used to solve coupling between pressure and velocity in N-S equations. A detailed description of the solution method is provided in this paper. Preliminary results are presented for temperature field and stability of the system under two different heat transport regimes: conduction and advection. This paper attempts to describe fundamentals for further investigations that are being developed for this system in axisymmetric and three-dimensional conditions.

Chebyshev spectral analysis approximation, Navier-Stokes and heat equations, spectral iterative domain decomposition technique.