Thin shear boundary layers in flow of hot aluminium

The flow of hot aluminium in channels is investigated. The constitutive relation considered for the flow stress is the inverse hyperbolic sine function of the Zener–Hollomon parameter. Analytical solutions for the flow are derived. At high strain rates, an exponential velocity profile close to the channel walls is predicted indicating the existence of a thin shear boundary layer characterized by strong shear. The characteristic length scale for the exponential velocity profile is a function of material parameters in the constitutive relation and the inverse of the local pressure gradient. The analytical prediction of a thin shear boundary layer close to the channel walls for large strain rates is consistent with the observed microstructure in an extruded section.