Axial annular flow of a Giesekus fluid with wall slip above the critical shear stress

Analytical solutions for axial annular flow of viscoelastic fluid obeying the Giesekus model are obtained including effect of slip condition at both walls. A power-law relation between wall shear stress and wall slip velocity called nonlinear Navier model was employed for the slip equation. The wall slip condition is assumed to be the same for both walls because both walls have similar properties. For the slip model it is considered that wall slip occurs only when a critical value is reached which is known as slip critical shear stress. Results indicate that slip initially occurs at the inner wall and then at the outer wall. Thus there are three flow regimes: no slip condition, slip only at the inner wall and slip at both walls. The flow regime is characterized by the value of slip critical shear stress. Results show that increasing slip effect causes pressure gradient, shear and normal stresses to decrease but, they increase by increasing slip critical shear stress. Also increasing elasticity decreases slip velocity at walls.