Heat Transfer of Crude Waxy Oil with Yield Stress in a Pipe

This article is devoted to the study of heat exchange of a heated flow of waxy oil in a pipe. Heat exchange between the waxy oil flow and the surrounding environment decreases the oil temperature and sharply increases the rheological properties. The appearance of a solid-like region within the yield-stress fluid flow is a non-trivial problem. This flow property greatly complicates the numerical solution of the system of equations governing the flow and heat transfer of viscoplastic fluids. The Bingham–Papanastasiou model allows one to solve the problem by regularizing the formula for effective molecular viscosity. The novelty of this work lies in establishing the dependence of the Nusselt number on the Reynolds and Bingham numbers for the flow of viscoplastic fluid in a pipe. Via calculations, velocity, temperature, and pressure distributions in the flow were obtained for Bingham numbers ranging from 1.7 to 118.29 and Reynolds numbers ranging from 104 to 2615. The Nusselt number dependence increases with the increase in the Reynolds number and decreases with the decrease in the Bingham number along the pipe length.