Our research focuses on the development of mathematical and computational models for fluids flow and heat and mass transfer problems. It is a theoretical investigation where we seek to develop appropriate mathematical models to interpret and enhance understanding of fluid flow characteristics to help elucidate and explain experimental findings and observed phenomena. The numerical solutions obtained provide a means for which other exact or approximate solutions can be vindicated and validated. Further, the exact solutions obtained provide an interesting and complete benchmark to verify numerical schemes for different complex flow situations.