Natural Steady Convection in a Space Annulus Between Two Elliptic Confocal Ducts: Influence of the Slope Angle

The authors express the Boussinesq equations of the laminar thermal and natural convection, in the case of permanent and bidimensional flow, in an annular space between two confocal elliptic cylinders. The latter is oriented at an arbitrary angle $α$ with respect to the gravity force, using the elliptic coordinates system. A new calculation code using the finite volumes with the primitive functions (velocity-pressure formulation) is proposed. The Prandtl number is fixed at 0.7 (case of the air) with varying the Rayleigh number. The effect of the system inclination is examined.