Double-diffusive natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder (Part I: Heat and mass transfer)

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a heated enclosure with an inner cold cylinder filled with non-Newtonian Carreau fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 10⁴ and 10⁵), Carreau number (Cu = 1, 10, and 20), Lewis number (Le = 2.5, 5 and 10), Dufour parameter (D_f = 0, 1, and 5), Soret parameter (S_r  = 0, 1, and 5), Eckert number (Ec = 0, 1, and 10), the Buoyancy ratio (N = −1, 0.1, 1), the radius of the inner cylinder (R_d  = 0.1 L, 0.2 L, 0.3 L, and 0.4 L), the horizontal distance of the circular cylinder from the center of the enclosure (Ω = −0.2 L, 0 and 0.2 L), the vertical distance of the circular cylinder from the center of the enclosure (δ = −0.2 L, 0 and 0.2 L). Results indicate that the increase in Rayleigh number enhances heat transfer for various studied parameters. The increase in power-law index provokes heat and mass transfer to drop gradually. The increase in the Lewis number declines the mass transfer considerably while causes heat transfer to drop marginally. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different Rayleigh numbers. The augmentation of the buoyancy ratio number enhances heat and mass transfer. The increase in Eckert number affects heat and mass transfer; especially, at Ra = 10⁵. The rise of Carreau number causes heat and mass transfer to drop gradually. The movement of the center of the cylinder from the bottom to the top side of the enclosure vertically (δ  = −0.2 L, 0 and 0.2 L) decreases heat and mass transfer significantly while the effect of power-law index drops. The increase in the radius of the cylinder enhances heat and mass transfer. The alteration of the center of the cylinder horizontally (Ω) to the left and right sides enhance heat and mass transfer although this augmentation is different in various power-law indexes.