On convection and flow in porous media with cross-diffusion.
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Date
2012
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Abstract
In this thesis we studied convection and cross-diffusion effects in porous media.
Fluid flow in different flow geometries was investigated and the equations for momentum, heat and mass transfer transformed into a system of ordinary differential
equations using suitable dimensionless variables. The equations were solved using a
recent successive linearization method. The accuracy, validity and convergence of the
solutions obtained using this method were tested by comparing the calculated results
with those in the published literature, and results obtained using other numerical
methods such as the Runge-Kutta and shooting methods, the inbuilt Matlab bvp4c
numerical routine and a local non-similarity method.
We investigated the effects of different fluid and physical parameters. These
include the Soret, Dufour, magnetic field, viscous dissipation and thermal radiation
parameters on the fluid properties and heat and mass transfer characteristics.
The study sought to (i) investigate cross-diffusion effects on momentum, heat and
mass transport from a vertical flat plate immersed in a non-Darcy porous medium
saturated with a non-Newtonian power-law fluid with viscous dissipation and thermal
radiation effects, (ii) study cross-diffusion effects on vertical an exponentially stretching surface in porous medium and (iii) apply a recent hybrid linearization-spectral
technique to solve the highly nonlinear and coupled governing equations. We further
sought to show that this method is accurate, efficient and robust by comparing it with established methods in the literature.
In this study the non-Newtonian behaviour of the fluid is characterized using the
Ostwald-de Waele power-law model. Cross-diffusion effects arise in a broad range
of fluid flow situations in many areas of science and engineering. We showed that
cross-diffusion has a significant effect on heat and mass-transfer processes and cannot
be neglected.
Description
Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.
Keywords
Heat--Convection., Fluid dynamics., Theses--Mathematics.