implementing the oldroyd-b model in three different rheometric shear flows start-up through an innovative step-by-step approach

The rheological characteristics of the oldroyd-b model concerning the initiation of drag couette flow, pressure driven axial pipe as well as annular flows were examined using the emergent step-by-step method. this technique dissects the evolution of the stress tensor independently by employing the differential form of the viscoelastic constitutive equation analogous to the micro-macro approaches. the method demonstrated the capacity to replicate transient velocities across the aforementioned geometries, as corroborated by comparisons with relevant analytical expressions, thereby affirming the efficacy of the proposed step-by-step approach in addressing flow challenges associated with more intricate yet descriptive viscoelastic constitutive equations pertinent to polymeric fluids.