Modelling Heat and Mass Transfer in a Relief Pipeline with Constant and Varying Diameters
DOI:
https://doi.org/10.71310/pcam.3_73.2026.07Keywords:
fluid flow, heat transfer, pipe flowAbstract
This work presents a comprehensive numerical and analytical study of hydrodynamic and thermal processes in closed pipelines of variable diameter, taking into account terrain relief and external thermal influences. The novelty lies in an improved quasi-onedimensional model that assesses the impact of geometric parameters (diameter, inclination angle, internal roughness) and thermophysical characteristics (material thermal conductivity, ambient temperature) on the pressure and temperature distribution along the pipeline. The model was validated against SST-turbulence-model simulations and Darcy–Weisbach calculations, with a maximum deviation below 2%. Hydraulic losses were found to depend mainly on pipe diameter and flow velocity, whereas thermal losses depend on the material’s thermal conductivity and the pipeline orientation. The proposed approach provides a reliable and computationally efficient basis for predicting the energy characteristics of fluid-transport systems and optimizing thermal networks.
References
Lapshin V. Analysis of heat exchange processes on the surface of the aboveground pipeline with heat insulation // Bulletin of Scientific Research Results. – 2023. – Vol. 2023. – №3. – P. 147–156.
Sharikov Y.V., Markus A.A. Mathematical modeling of heat transfer in pipelines and pipe’s objects // Journal of Mining Institute. – 2013. – Vol. 202. – P. 233–238.
Bulovich S.V. Mathematical modeling of gas flow in the vicinity of an open end of a pipe with oscillations of a piston at the other end of the pipe according to the harmonic law at a resonant frequency (in Russian) // Journal Technical Physics. – 2017. – Vol. 87. – №11. – 1632 p.
Kurbatova G.I., Filippov B.V., Filippov V.B. Non-isothermal turbulent flow of compressible gas // Mathematical Modeling. – 2003. – Vol. 15. – №3. – P. 92–108.
Ermolaeva N.N., Kurbatova G.I. Analysis of approaches to modeling thermodynamic processes in gases at high pressures // Vestnik of St. Petersburg University. Episode 10. Applied mathematics. Informatics. Management Processes. – 2013. – №2. – P. 36–45.
Kurbatova G.I., Popova E.A., Filippov B.V. Models of offshore gas pipelines // Saint Petersburg. – 2005.
Grunicheva Y.V., Kurbatova G.I., Popova Y.A. Nonstationary nonisothermal flow of gas mix in offshore gas pipelines // Mathematical Models and Computer Simulations. – 2011. – Vol. 3. – №6. – P. 751–758.
Vasiliev O.F., Bondarev E.A., Voevodin A.F., Kanibolotsky M.A. Non-Isothermal Gas Flow in Pipes // Novosibirsk: Nauka. – 1978.
Tevyashev A.D., Smirnova V.S. Method of approximate solution of the Cauchy problem for the system of equations of steady gas flow in a pipeline // Radioelectronics and Information Science. – 2009. – №1. – P. 81–87.
Khujaev I., Bozorov J., Akhmadjonov S. Investigation of the propagation of waves of sudden changes in mass flow rate of fluid and gas in a “short” pipeline approach // IEEE Dynamics of Systems, Mechanisms and Machines (Dynamics). – 2019.
Charny I.A. Unsteady Motion of Real Fluid in Pipes // Moscow: Nedra. – 1975.
Grachev V.V., Shcherbakov S.G., Yakovlev E.I. Dynamics of Pipeline Systems // Moscow: Nauka. – 1987.
Khuzhaev I.K., Mamadaliev K.A., Kukanova M.A. Analytical solution of the problem of the propagation of a compaction wave in an inclined pipeline caused by the deceleration of a fluid // Problems of Computational and Applied Mathematics. – 2015. – №2. – P. 65–79.
Khujaev I.K., Akhmadjonov S.S., Mahkamov M.K. Modeling the stages of verification of the suitability of a short section of a gas pipeline for operation // Mathematical Models and Computer Simulations. – 2022. – Vol. 14. – №6. – P. 972–983.
Zaitsev A.V., Pelenko F.V. Modeling of viscous fluid flow in a pipe // Scientific journal of SPbGUNiPT. Series: Processes and Equipment of Food Production (Electronic Journal). – 2012.
Zaitsev A.V. Development of an algorithm for solving the Navier-Stokes equations for the flow of cryogenic liquid in a pipe // Bulletin of MAX. – 2011. – №3. – P. 37–42.
Bozorov O.S., Mamatkulov M.M. Analytical Studies of Nonlinear Hydrodynamic Phenomena in Media with Slowly Changing Parameters // Tashkent: TITLP. – 2015.
Chu S., Marensi E., Willis A.P. Modelling the transition from shear-driven turbulence to convective turbulence in a vertical heated pipe // Mathematics. – 2025. – Vol. 13. – №2. – 293 p.
Chu S., Willis A.P., Marensi E. The minimal seed for transition to convective turbulence in heated pipe flow // Journal of Fluid Mechanics. – 2024. – Vol. 997. – 46 p.
Wibisono A.F., Addad Y., Lee J.I. Numerical investigation on water deteriorated turbulent heat transfer regime in vertical upward heated flow in circular tube // International Journal of Heat and Mass Transfer. – 2015. – Vol. 83. – P. 173–186.
Idelchik I.E. Handbook of Hydraulic Resistance // Moscow: Mashinostroenie. – 1975.
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