Abstract
This study investigates non-isothermal laminar flow of waxy crude oil in a pipe. Due to heat exchange with the surroundings, the flow cools along the pipe length, resulting in a gradual transformation of the oil rheology from Newtonian to viscoplastic behavior. The mathematical model is based on the generalized Navier–Stokes equations coupled with the Shvedov–Bingham rheological model and the effective viscosity approach. The governing equations were solved numerically using the control volume method in the velocity–pressure formulation. The numerical simulations produced velocity, temperature, and effective viscosity fields, as well as pressure-drop data characterizing the rheological state of the waxy crude oil throughout the pipe flow domain. It was established that, in the central region of the inlet flow, the oil retains Newtonian behavior, whereas viscoplastic behavior begins to develop near the pipe wall. Further downstream, the flow progressively transforms into a viscoplastic state over the entire pipe cross-section, accompanied by the formation of stagnant near-wall regions and a plug-flow core.