The study of convection heat and mass transfer in a non-Newtonian fluid saturated porous medium has attracted many investigators due to its wide range of applications in geophysics and energy related problems. The effects like stratification, melting, double dispersion, dissipation, variable viscosity and radiation are important phenomena, understanding the effect of these on coupled convection in porous media is very important. In the existing literature, most of the researchers considered the porous media saturated with Newtonian fluid while studying aforesaid second order effects. This motivates to elaborate these second order effects in non- Newtonian fluid saturated non-Darcy porous media. This book aims at theoretical investigation of some of the above second order effects on natural and mixed convection heat transfer or coupled heat and mass transfer process by considering porous media saturated with non-Newtonian fluids. In each case, the non-dimensional governing equations are solved numerically by similarity and local non-similarity methods wherever applicable.