A numerical model for the simulation of double-diffusive natural convection in a triangular cavity using equal order and control volume based on the finite element method

A numerical model is presented for the study of natural convective heat and mass transfer in a triangular cavity. This configuration is encountered in greenhouse solar stills where vertical temperature and concentration gradients between the saline water and transparent cover induce flows in a confined space. This phenomenon plays a decisive role in the water distillation process and in the biological comfort. In this double-diffusion problem, the ratio N of the relative magnitude thermal and solute Rayleigh numbers is a key parameter. The two-dimensional flow equations, expressed here in a velocity–pressure (UVP) formulation, along with the energy and concentration equations, are solved by control volume based a finite elements method using the equal–order method without pressure correction. Due to the relative low values of the Rayleigh numbers encountered under realistic conditions (≤106), mostly laminar flow conditions prevail. The numerical solutions yield a two-cellular flow field with the size of cells depending on the Rayleigh number for a fixed Lewis number. For a positive value of N, the solution is qualitatively similar to the case with only thermal buoyancy present (N = 0). However, for negative values, more complex phenomena arise. The relationship between the pressure gradient and the other variables were investigated.