Pressure-drop and Trouton ratio for Oldroyd-B fluids in hyperbolic converging channels

We present new theoretical developments on the incompressible viscoelastic flow of an Oldroyd-B fluid in a hyperbolic contracting symmetric channel. We show uniformity of the effect of viscoelasticity in hyperbolic planar and cylindrical axisymmetric geometries by revealing a modified Deborah number according to which the lubrication solutions for the pressure drop and the Trouton ratio are simplified. We also develop an expression for the Trouton ratio in terms of the fluid velocity at the midplane only, valid beyond the lubrication limit. Using the Newtonian velocity as a first approximation, we show the enhancement of the Trouton ratio with increasing the fluid elasticity.