Computational analysis of the transition of a system between two non-equilibrium stationary states through two-dimensional laminar natural convection in a cylindrical cavity

Our work focuses on the numerical study of two-dimensional and transient natural convection in a fluid confined within a crescent-shaped space delimited by two horizontal cylinders. The upper wall is subjected to a non-uniform heat flux, while the lower wall experiences a uniform heat flux, thereby generating thermal natural convection. The transfer equations are solved in a bi-cylindrical coordinate system using the formalism of stream function and vorticity, and then integrated using the finite difference method. Subsequently, these transfer equations are integrated using S.V Patankar's finite difference method with an implicit scheme. The computational program is implemented using Maple V Release Student software. The discretization of the equations highlights the following parameters: the Prandtl number (Pr), the modified Grashof number (Gr), and the aspect ratio (r2/r1). The Prandtl number is fixed at 0.7. The results include temperature distributions, local and average Nusselt values, as well as graphs illustrating variations in various parameters based on slice indices.