Numerical Simulations of 2-D Steady Free Convective flow with Heat and Mass Transfer in an Inclined Rectangular Domain

Abstract

In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh numbers in the range of $10^4 \le Ra \le 10^6$, for Prandtl number $Pr=7.2$, and Lewis number $Le=1$. We have used no-slip wall boundary conditions for the components of velocity and Neumann boundary conditions for temperature and concentration. We have used the QUICK scheme to discretize the governing equations along with the boundary conditions chosen in the present problem. The SIMPLE algorithm is adopted to compute the numerical solutions of flow variables, $U$-velocity, $V$-velocity, pressure, temperature, and concentration as well as the local and average Nusselt and Sherwood numbers at different Rayleigh numbers in the range mentioned above. Our numerical solutions for $U$-velocity along the vertical line through the geometric center has been compared with benchmark solutions available in the literature for $\lambda=15^{\circ},\, Ra=10^4,\, Pr=7.2$, and $Le=1$ and it has been found that it is in the good agreement. Pressure increases with increasing the angles of inclination. When the angles of inclination increase from $\lambda=15^{\circ}$ to $\lambda=45^{\circ}$, the intensity of streamlines decreases near the center and secondary cells are formed at the top and bottom of the center of the domain. As the Rayleigh number is increased from $10^4$ to $10^6$, the average Nusselt number is decreased for $\lambda=15^{\circ}$, and decreases and then increases for $\lambda=45^{\circ}$, whereas, the average Sherwood number increases for $\lambda=15^{\circ}$ and decreases for $\lambda=45^{\circ}$.