A method for calculating transient flows of viscoelastic fluids in viscoelastic channels

Transient viscoelastic (VE) fluid flow in VE channels is investigated analytically, extending the analysis of Zielke (1968) to the linear VE fluids characterized by Rieutord (1981). Local linearized equations are employed to obtain an expression for the friction term in the integral form of the motion equation. Weighting functions are derived to account for the bidimensionality of the flow and to determine the local velocity, and the solution method for the resulting system of equations is based on the theory of characteristics. Results are presented graphically for flows of a three-parameter Oldroyd (1950) fluid in response to stepwise increases in velocity or pressure or to the progressive closing of a valve.