Etude analytique et numérique du transfert thermique autour d'un cylindre vertical chauffé.

Abstract

In this work, we study, theoretically and numerically the axisymmetric natural convection along a vertical cylinder that is isothermal or heated by a constant heat flux. The length of the cylinder is six times its radius. The Prandtl number is equal to 0.7. The Grashof number is varied: it is equal to 104, 105 and 106. Regarding the numerical simulation, the conservation equations of mass, Navier-Stokes and energy are solved by the finite volume numerical method with a space and time second order accurate numerical discretization. It is demonstrated, with a theoretical approach, that the cylinder local Nusselt number is close to that of the vertical plate in the case when the ratio of the boundary layer thickness and the cylinder radius is very weak. This result is confirmed by the numerical results which show that the difference between the cylinder and the plate local Nusselt numbers is apparent in the case of the weak Grashof number. For high Grashof numbers, the difference is relatively weak and is manifested only at the axial positions where the ratio of the boundary layer thickness and the cylinder radius is relatively considerable.