Taylor-Couette flows in a horizontal annular gap between finite coaxial
cylinders in rotor-stator configuration are numerically investigated. The
inner cylinder (rotor) rotates at a constant angular velocity while the
outer cylinder (stator) is at rest. They are limited at their extremities by
two fixed walls that prevent axial fluid flow. In addition, a heat transfer
is generated by an imposed temperature difference, with the rotor hotter
than the stator while the end-walls are adiabatic. The fluid physical
properties are temperature dependent. This non-linear physics problem, with
a strong coupling of the conservation equations and boundary conditions, is
solved by a finite volume method with numerical schemes of second order
space and time accuracies. The radius and aspect ratios and the Taylor,
Grashof and Prandt numbers are the control parameters. The developed
numerical code has been tested for different meshes and perfectly validated.
Extensive calculations have been made in large ranges of the Taylor and
Grashof numbers to analyze the Taylor-Couette flow in convection modes. The
results highlight the dynamic and thermal instabilities generated in the
Taylor Couette flow from the appearance of Ekman cells to the Taylor vortex
propagation in the entire annulus. The combined effect of these vortices
with the secondary flow improves the heat transfer. Furthermore, the
influence of the physical properties in the radial direction is more marked
in the vicinity of the walls. Finally, we propose an empirical correlation
of the Nusselt number in the studied parameter ranges.