Abstract
This paper investigates the non-isothermal stationary flow of waxy crude oil in a two-dimensional axisymmetric pipe, focusing on the transition from Newtonian to non-Newtonian fluid behavior. The viscosity and yield stress of crude oil are strongly influenced by temperature fluctuations. During hot pumping through a buried pipeline, heat transfer to the surrounding soil creates a non-isothermal flow, leading to decreased flow temperature, increased viscosity, the appearance of yield stress, wax crystallization, and solid particle deposition on the inner pipeline wall. This accumulation narrows the flow area and creates a stagnant, thermally insulated zone near the wall. As a result, the waxy crude oil transits from Newtonian behavior at lower temperatures to non-Newtonian. Traditional one-dimensional modeling, which averages temperature and velocity across the pipeline cross-section, cannot fully explain these phenomena. Thus, this work develops a two-dimensional model to capture the flow and heat transfer of crude oil. The results demonstrate the transition of a Newtonian fluid to a non-Newtonian one due to heat exchange with the environment.