Steady flow of visco-plasto-elastic fluids in pipes

The objective of the paper is to analyze the main dynamic characteristics of steady pipe flow for the case of a fluid whose constitutive is determined by a linear superposition of a viscoelastic Phan-Thien-Tanner fluid and a Bingham-type plastic fluid. The combined effects of viscoelasticity and yield stress are explored through some variables of the flow, such as velocity, and plug region. The fluid is considered incompressible and laminar, and the pipe circular. One main motivation of this work is the study of possible relevant interaction among the physical properties of the fluid. The elasticity of the fluid is expressed by means of two parameters that include the relaxation time. The plasticity is modelled though the Bingham constitutive equation, which involves, in general, a constant yield stress and a non-linear viscosity, when the flow is non-axisymmetric. Analytical expressions for the dependent variables are presented, and their plots in terms of the constants of the fluid, as well. This paper is a continuation of previous work by the authors, mainly related to investigating the structure of secondary flow and of the associated heat transfer in non-circular ducts, for the case of a purely viscoelastic fluid.