Energetic variational approaches for non-Newtonian fluid systems

We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized compressible non-Newtonian fluid system. We also derive the generalized incompressible non-Newtonian fluid system by using our energetic variational approaches.