DRBEM solution of the thermo-solutal buoyancy induced mixed convection flow problems

Mixed convective heat and solutal transport is important in engineering applications such as nuclear waste disposal, crystal growth and oceanography. Mixed convective in a lid-driven cavity and through channels with backward-facing step is studied by solving the equations of conservation of mass, momentum, energy and solutal concentration numerically. The governing equations are solved by using dual reciprocity boundary element method (DRBEM) with constant elements in terms of stream function, vorticity, temperature and concentration. Vorticity, energy and concentration equations are transformed to the form of modified Helmholtz equations by utilizing forward difference with relaxation parameters for the time derivatives, and also approximating Laplacian terms at two consecutive time levels. The DRBEM application is carried out with the fundamental solution of modified Helmholtz equation, resulting in linear algebraic systems for the time dependent unknowns. Inhomogeneities in modified Helmholtz equations are approximated with the thin plated radial basis functions. Computations are carried out for several values of Richardson number, buoyancy ratio and Reynolds number. When the temperature and solutal concentration boundary conditions are changed, the thermal and solutal buoyancy forces can oppose or aid each other. The effects of these parameters on the flow behavior and heat transfer are shown in terms of graphics.