Exact solution of the problem on a six-constant Jeffreys model of fluid in a plane channel

An exact analytic solution of the problem of a generalized viscoelastic Jeffreys fluid flow in a plane channel under the action of a pressure gradient is found. The velocity profiles are obtained in a parametric form with a velocity gradient taken as a parameter. The critical values of the pressure gradient are determined, which, when exceeded, lead to weak tangential discontinuities in the longitudinal velocity profile. When the pressure gradient changes smoothly over some range of parameters, a hysteresis loop emerges on the graph of the flow rate versus the pressure gradient.