This book is concerned with the study of the centrifugal force effect on Uranium enrichment and the Lorentz force effect on the plasma. Enriched uranium is a critical component for both civil nuclear power generation and military nuclear weapons. Plasmas has many important applications in the propulsion of spacecraft; Plasma processing; Understanding astrophysical phenomena, hypersonic flight . This book is related to fluid mechanics, plasma mechanics and nonequilibrium irreversible thermodynamic. The exact analytical solutions of nonlinear partial differential equations systems with variable and constant coefficients are presented in this book. Unsteady cylindrical Couette flow of rarefied gas (Uranium hexafluoride (UF6)) between two porous cylinders rotating with different angular velocities in the presence of centrifugal field is studied. The same flow of plasma between two cylinders rotating with different angular velocities is investigated. This book contains exact solutions, analytical methods and real geometries that help researchers in the relevant topics. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.