Double diffusive buoyancy induced convection in stepwise open porous cavities filled nanofluid

Two-dimensional study has been performed for the buoyancy induced flow in a stepwise opening cavity heated from the left vertical wall. The governing equations subject to the imposed boundary conditions are solved by using the higher order finite element technique. A finite element method involving the cubic polynomials (ℙ₃) has been implemented for the discretization of velocity, temperature and concentration fields while the pressure is approximated by utilizing the quadratic (ℙ₂) finite element space of functions. The adaptive Newtons method is availed for the linearization of the discrete system of algebraic equations and the corresponding linear system in each step is computed using the Gaussian elimination method. The governing parameters are chosen as Rayleigh number 10³ ≤ Ra ≤ 10⁷, Darcy number 10⁻⁶ ≤ Da ≤ 10⁻², buoyancy ratio 0.1 ≤ Br ≤ 1, aspect ratio 0.5 ≤ AR ≤ 1 and Brownian motion parameter 0.1 ≤ Nb ≤ 1. It is noted that both heat and mass transport are function of the aspect ratio. Heat transfer is increased and mass transfer is reduced by decreasing the geometrical ratio depending on the different studied parameters.