Effects of co-rotating cylinders and boundary conditions on heat and mass transfer in a trapezoidal enclosure

Source abstract

This study investigates the effects of rotational speed $(\Omega)$, Richardson number $\left(Ri\right)$, and Lewis number $\left(Le\right)$ on heat and mass transfer (HMT) around two co-rotating cylinders symmetrically situated in a trapezoidal enclosure. In the double-diffusive mechanism, the bottom wall of the trapezium is at a high temperature $\left(T_h\right)$ and concentration $\left(C_h\right)$, while the top wall is at a low temperature $\left(T_c\right)$ and concentration $\left(C_c\right)$. The side walls are perfectly insulated with zero mass flux, while the buoyancy ratio $\left(Br\right)$ is fixed at 1.0. Two thermal-mass boundary scenarios are considered. Scenario 1: Cylinders are thermally insulated with zero mass flux, and scenario 2: Cylinders have fixed mass and thermal boundary conditions of $\varphi =C=0.5$. The relevant dimensionless transport equations were solved using the finite element scheme. Results show that increasing $\Omega$ and decreasing $Ri$ enhance flow strength and improve HMT. In scenario 2, the average Sherwood number $\left(Sh_{av}\right)$ and Nusselt number $\left(Nu_{av}\right)$ decrease by $11.6\%$ when $Le=1.0$, $Br=1.0$, $Ri=10$, and $\Omega=300$; this is due to diffusion interference causing HMT loss to the cylinder walls. Increasing $\Omega$ from 100 to 300 raises the mid-plane peak velocity by $253.4\%$, indicating flow enhancement. Correspondingly, $Sh_{av}$ and $Nu_{av}$ increase by $36.9\%$ when $Le=Br=1.0$ and $Ri=0.01$. For both boundary conditions, increasing $Le$ boosts mass transfer with a marginal impact on heat transfer. This research has significant practical and theoretical implications for heat exchangers, rotary machinery, nuclear reactors, electronic cooling systems, and related applications.