Terminal Falling Characteristics of a Sand Grain with Dufour and Soret Effects

Abstract

The transient effect of double diffusive natural convection of flow in a differentially heated sand grain with Soret and Dufour coefficients is studied numerically. The right vertical wall has constant temperature T_c. The lower inlet opening is heated uniformly with fixed temperature T_h and the velocity at the inlet of the fluid domain is set to the falling velocity V_i. The condition T_h > T_c is maintained all over the domain. The concentration in right wall is maintained higher than inlet opening (C_c < C_h). The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite-element method. Solutions are obtained for fixed Prandtl number (Pr = 1.73), Rayleigh number (Ra = 10⁴), Dufour coefficient (D_f = 0.5) and Soret coefficient (S_r = 0.5). Transient analysis of the streamlines, isotherms, iso-concentration, falling velocity and forces on sand grain, the local and average Nusselt number and Sherwood number, temperature and concentration at subdomain centre as well as average form, subdomain horizontal and vertical velocities are presented graphically. It is found that the rate of heat transfer and mass transfer in the sand grain enhances and reduces respectively for shorter time periods and then they become almost steady.

© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v5i1.10003        J. Sci. Res. 5 (1), 91-103 (2013)