ISPH method for double-diffusive natural convection under cross-diffusion effects in an anisotropic porous cavity/annulus

Purpose - A study on heat and mass transfer behavior for an anisotropic porous medium embedded in square cavity/annulus is conducted using incompressible smoothed particle hydrodynamics (ISPH) method. In the case of square cavity, the left wall has hot temperature T-h and mass C-h and the right wall have cool temperature T-c and mass C-c and both of the top and bottom walls are adiabatic.While in the case of square annulus, the inner surface wall is considered to have a cool temperature T-c and mass C-c while the outer surface is exposed to a hot temperature T-h and mass C-h. The paper aims to discuss these issues. Design/methodology/approach - The governing partial differential equations are transformed to non-dimensional governing equations and are solved using ISPH method. The results present the influences of the Dufour and Soret effects on the fluid flow and heat and mass transfer. Findings - The effects of various physical parameters such as Darcy parameter, permeability ratio, inclination angle of permeability and Rayleigh numbers on the temperature and concentration profiles together with the local Nusselt and Sherwood numbers are presented graphically. The results from the current ISPH method are well-validated and have favorable comparisons with previously published results and solutions by the finite volume method. Originality/value - A study on heat and mass transfer behavior on an anisotropic porous medium embedded in square cavity/annulus is conducted using Incompressible Smoothed Particle Hydrodynamics (ISPH) method. In the ISPH algorithm, a semi-implicit velocity correction procedure is utilized, and the pressure is implicitly evaluated by solving pressure Poisson equation (PPE). The evaluated pressure has been improved by relaxing the density invariance condition to formulate a modified PPE.