The study of solute transport phenomena in laminar and turbulent flow situations has a wide range of applications in different fields of engineering sciences and this is the reason that modern fluid dynamics has become a common platform of mathematicians, physicists, chemists, biologists, physiologists, geologists and engineers. Since the pioneer work of Sir G. I. Taylor in 1953, the study of solute transport in longitudinal direction has been extensively studied by different researchers. This book is written for the researchers and post graduate students who are working in the field of time-dependent convection-diffusion problems. A clear view on basic fluid dynamics is given in the first chapter of the book. Three research problems have been carefully chosen to understand the basic mechanism of solute transport phenomena in longitudinal direction, and to predict the dispersion coefficient, mean concentration distribution for all time period using finite-difference technique.