Abstract
Numerical Investigations of Heat and Mass Transfer in Saturated Porous Cavity with
Soret and Dufour Effects
Khaled Abdulhussein Jebear Al-Farhany, 2012 Doctor of Philosophy, the University of
Manchester
The mass and thermal transport in porous media play an important role in many
engineering and geological processes. The hydrodynamic and thermal effects are two
interesting aspects arising in the research of porous media. This thesis is concerned with
numerical investigations of double-diffusive natural convective heat and mass transfer in
saturated porous cavities with Soret and Dufour effects. An in-house FORTRAN code,
named ALFARHANY, was developed for this study. The Darcy-Brinkman-Forchheimer
(generalized) model with the Boussinesq approximation is used to solve the governing
equations. In general, for high porosity (more than 0.6), Darcy law is not valid and the
effects of inertia and viscosity force should be taken into account. Therefore, the
generalized model is extremely suitable in describing all kinds of fluid flow in a porous
medium. The numerical model adopted is based on the finite volume approach and the
pressure velocity coupling is treated using the SIMPLE/SIMPLER algorithm as well as
the alternating direction implicit (ADI) method was employed to solve the energy and
species equations.
Firstly, the model validation is accomplished through a comparison of the numerical
solution with the reliable experimental, analytical/computational studies available in the
literature. Additionally, transient conjugate natural convective heat transfer in twodimensional porous square domain with finite wall thickness is investigated numerically.
After that the effect of variable thermal conductivity and porosity investigated
numerically for steady conjugate double-diffusive natural convective heat and mass
transfer in two-dimensional variable porosity layer sandwiched between two walls. Then
the work is extended to include the geometric effects. The results presented for two
different studies (square and rectangular cavities) with the effect of inclination angle.
Finally, the work is extended to include the Soret and Dufour effects on double-diffusive
natural convection heat and mass transfer in a square porous cavity.
In general, the results are presented over wide range of non-dimensional parameters
including: the modified Rayleigh number (100≤ Ra* ≤1000), the Darcy number (10-6≤
Da≤ 10-2), the Lewis number (0.1≤ Le≤ 20), the buoyancy ratio (-5≤ N ≤ 5), the thermal
conductivity ratio (0.1≤ Kr ≤ 10), the ratio of wall thickness to its height (0.1≤D ≤ 0.4),
the Soret parameter (-5≤ Sr ≤ 5), and the Dufour parameter (-2≤ Df ≤ 2) .