Numerical Simulation of Laminar Flow and Heat Transfer of Waxy Oil with Yield Stress in a Pipe with Sudden Enlargement

Abstract

This study investigates the non-isothermal laminar flow and heat transfer of waxy oil in a pipe with a sudden enlargement, emphasizing its transition from a Newtonian to a viscoplastic state during cooling. Using the Schwedoff-Bingham rheological model, the motion and heat transfer governing equations were numerically solved via Patankar’s control volume method in “velocity components-pressure” variables. A significant transformation is observed in the flow structure. In isothermal conditions with Reynolds numbers of 1046 and 2092 and Bingham numbers of 0.05 and 0.025, reverse flow zones and negative pressure distributions are observed. However, under non-isothermal conditions with Bingham numbers ranging from 8.5 to 59.14, reverse flow zones disappear, replaced by a stagnation zone with zero velocity due to increased plastic viscosity and yield stress during oil cooling. The study also demonstrates an enhanced convective heat transfer arising from the sudden pipe enlargement. The novelty of this work lies in its focus on the temperature-dependent rheological transformation of waxy oil, extending beyond previous studies by providing detailed insights into the interplay between flow structure and thermal effects in viscoplastic fluids. These findings are critical for optimizing pipeline operations and ensuring efficient transport of waxy oils.