Onset of Multilayer Convection in a Partially Heated Circular Cavity

In this article, the time-dependent double-diffusive natural convection is investigated inside a circular cavity containing stably stratified brine solution. The container is heated partially through its sidewalls by a constant heat flux rate. By using Galerkin finite element method, numerical solutions to the Navier-Stokes equations under the Boussinesq flow assumptions have been systematically organized and developed. The evolutions of the stream function, temperature and concentration fields are presented in each evaluated case. Steep and sharp concentration variation in the interfaces together with wavy distribution of temperature within the layers is observed. At first a length scale, which is the vertical displacement of a heated element of the fluid, in a stably stratified solution under Neumann boundary condition is defined. Then a special form of Rayleigh number based on the length scale is obtained and named as universal Rayleigh number. A categorization based on single, two and multilayer formation is established. Temperature distribution along the cavity in the different cases shows a correlation between heat transfer coefficient and the rate of formation and degradation of the layers.