Traveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids

We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau, the Power-law rheology models, and a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and prove existence and uniqueness of solutions to the equations for validation of the models. We also provide numerical estimates of the shock thickness as well as maximum strain associated with the traveling waves.