A Text book written completely for Post Graduate and Research Scholars in Applied Mathematics, Fluid Mechanics. This book mainly focuses on the unsteady MHD fluid/Dusty fluid through porous plates with or without an inclined magnetic field. The behavior of the unsteady MHD flow in the presence of inclined magnetic forces and the flow of fluid between parallel porous plates using the analytical method and differential transformation method is also investigated.The unsteady MHD dusty fluid flow between parallel plates through a porous medium with the heat source. The exact solution of the axial and transverse velocities in the porous medium is analytically derived; its behavior is computationally discussed with reference to the various governing parameters. The axial and transverse velocities of fluid and the temperature distribution are presented. The exact solution of the temperature distribution is analytically derived and discussed for different governing parameters in detail.