Modelling of flow and transport is an essential component of many scientific and engineering applications, with increased interests in recent years. Application areas vary widely and include groundwater contamination, carbon dioxide sequestration, air pollution, petroleum exploration and recovery, weather prediction, and chemical separation processes. However, accurate mathematical and numerical simulation of flow and transport remains a challenging topic from many aspects of physical modelling, numerical analysis, and scientific computation. In the present book, a study is made to understand the flow dynamics in porous medium and its transition behavior in a horizontal layer.