The development of a wax layer on the interior wall of a circular pipe transporting heated oil: the effects of temperature-dependent wax conductivity

• Published in: Journal of engineering mathematics Vol. 131; no. 1
• Main Authors: Mason, Sophie Lauren, Meyer, John Christopher, Needham, David John
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Pipes; Temperature dependence; Temperature effects; Theoretical and Applied Mechanics; Thermal analysis; Transportation; Waxes; 80A22; Heated oil pipeline; 76T99; Generalised Stefan problem; Wax layers; Asymptotic limit; 80M35; Quasi-linear parabolic PDE; 80M20
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-021-10171-x

In this paper, we develop and significantly extend the thermal phase change model, introduced in Needham et al. (QJMAM 67:93–125, 2014), describing the process of paraffinic wax layer formation on the interior wall of a circular pipe transporting heated oil, when subject to external cooling. In particular, we allow for the natural dependence of the solidifying paraffinic wax conductivity on local temperature. We are able to develop a complete theory, and provide efficient numerical computations, for this extended model. Comparison with recent experimental observations is made, and this, together with recent reviews of the physical mechanisms associated with wax layer formation provide significant support for the thermal model considered here.