This article investigates a generalised solution approach for transient viscoelastic flows employing consistent dynamic boundary conditions. Such a procedure vaunts three key properties-independence of reference frame, problem dimension and constitutive equation type. Three different boundary condition protocols have been investigated, two transient and one steady, through a time-dependent incremental pressure-correction formulation with a hybrid finite element/finite volume scheme. These procedures are compared and contrasted through application to pressure-driven start-up flow in 4:1 planar rounded-corner contractions for two fluid models, Oldroyd and pom-pom. Some novel differences are highlighted in the dynamic evolution of flow structure and the impact upon stress generation, as a consequence of protocol, whether steady or transient, under flow-rate or force-driven control. Overshoot-undershoot kinematics observed under any particular flow protocol have been mutually linked to the precise boundary conditions imposed. Under flow-rate controlled protocols, large oscillations are stimulated in pressure, which may disturb computational tractability. Comparatively, the evolution of force-driven flow can provide considerably smoother development patterns in pressure, with largest attached vortices and strong oscillatory vortex structure features. Specifically under transient flow-rate control, some distinct complex flow features have emerged, including reversed flow, followed by vortex detachment and reattachment. For pom-pom SXPP-fluids and force-driven protocol, transient flow development is observed to be relatively smooth and non-oscillatory at a Weissenburg number of unity. At larger levels of Weissenburg number, transient overshoots have been detected in characteristic variables of stress and molecular backbone-stretch. In addition, Weissenburg number continuation to steady state, has been shown to disconnect the dynamics between velocity and stress, which prevents highly elastic localised regions from developing. (C) 2008 Elsevier B.V. All rights reserved.