Velocity-vorticity formulation for 2D natural convection in an inclined cavity by the DQ method

Abstract

The aim of this paper attempts to apply the differential quadrature (DQ) method for solving two-dimensional natural convection in an inclined cavity. The velocity-vorticity formulation is used to represent the mass, momentum, and energy conservations of the fluid medium in an inclined cavity. We employ a coupled technique for four field variables involving two velocities, one vorticity and one temperature components. In this method, the velocity Poisson equation, continuity equation, vorticity transport equation and energy equation are all solved as a coupled system of equations so as to we are capable of predicting four field variables accurately. The main advantage of present approach is that coupling the velocity and the vorticity equations allows the determination of the boundary values implicitly without requiring the explicit specification of the vorticity values at the boundary walls. A natural convection in a cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 and H/L aspect ratios varying from 1 to 3 is investigated. It is shown that with the use of the present algorithm the benchmark results for temperature and flow fields could be obtained using a coarse mesh grid.