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

TL;DR

This study uses the QUICK finite volume scheme to numerically analyze steady 2-D free convection with heat and mass transfer in an inclined rectangular domain, examining effects of inclination and Rayleigh number on flow and transfer rates.

Contribution

The paper applies the QUICK scheme with the SIMPLE algorithm to simulate heat and mass transfer in inclined domains, providing detailed insights into flow behavior and transfer rates at various Rayleigh numbers.

Findings

Pressure increases with inclination angle.

Streamline patterns change with inclination, forming secondary cells.

Nusselt and Sherwood numbers vary non-monotonically with Rayleigh number and inclination.

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 $\lambda=45^{\circ}$.