Axisymmetric Solutions of the Equations of Motion of Non-Linear Viscous Flows

The Navier-Stokes equations of motion of viscous fluids arise from the assumption of a linear constitutive relation between the stress and the rate of strain tensors. By postulating the non-linear constitutive relation$t_{ij}=-p\ \delta _{ij}+2\mu d_{ij}+2\mu _{c}d_{ia}d_{aj}$between the stress and the rate of strain tensors, one arrives at the equations of motion of non-Newtonian viscous liquids in which there is a coefficient of cross viscosity$\mu _{c}$present besides the usual coefficient μ. We obtain here some axisymmetric solutions of the equations of non-Newtonian viscous motion and point out certain solutions which are admissible in both the two distinct cases of linear and non-linear viscous flow.