On convection and flow in porous media with cross-diffusion.
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.