Non-Newtonian fluid flow through a sudden pipe contraction under non-isothermal conditions

A steady-state laminar flow of a viscoplastic fluid through an axisymmetric sudden pipe contraction under non-isothermal conditions has been studied numerically. Mathematical formulation of the problem is given using stream function - vorticity - temperature variables. Rheological properties of the fluid are described by the Herschel-Bulkley model, which implies an unyielded region formation in the flow. Viscous dissipation effects and temperature dependence of the viscosity are taken into account when simulating the process. An asymptotic time solution of unsteady flow equations is used to obtain a steady-state solution to the initially formulated problem. The finite-difference method based on the alternative directions scheme is applied to solve the problem numerically. Regularization of the rheological equation is performed to provide a through computation of the flow with unyielded regions. A parametric investigation of the flow structure, which includes dead zones and yielded/unyielded regions, is implemented in order to show the impact of main dimensionless parameters.