Effects of Mach Number and Prandtl Number on Plane Couette Flow

If the flow is compressible, heat due to friction as well as temperature change due to compression must be taken into account. In addition, it is necessary to consider the effects of the variation of viscosity with temperature. This dependence of temperature with viscosity and density makes the calculation of problems in viscous compressible flow much more difficult than that for the case of in-compressible flow. It?s necessary to consider equation of continuity momentum energy and reduced Navier-stokes equation to the the phenomenon of plane couette-flow for different values of Mach number and Prandtl numbers. The significance of four important Controlling parameters in viscous compressible fluids need to be discussed and illustrated.