Numerical study of heat and mass transfer in a relief pipeline with variable diameter

In this work, a comprehensive numerical and analytical investigation of hydrodynamic and thermal processes in closed pipelines of variable diameter is carried out, taking into account the terrain profile and external temperature effects. The scientific novelty of the study lies in the development of an improved quasi-one-dimensional model that allows for an integral assessment of the influence of geometric parameters (diameter, inclination angle, internal surface roughness) and thermophysical properties (material thermal conductivity, ambient temperature) on the distribution of pressure and temperature along the pipeline. The developed model was validated by comparing it with numerical simulations based on the SST turbulence model and calculations using the Darcy-Weisbach equation. The maximum deviation between the results did not exceed 2 %, confirming the high accuracy of the proposed method. It was established that hydraulic losses are predominantly determined by the pipe diameter and flow velocity, whereas thermal losses depend mainly on the thermal conductivity of the material and the spatial orientation of the pipeline. The proposed approach provides a reliable and computationally efficient foundation for predicting the energy characteristics of liquid transportation systems, optimizing structural parameters, and improving the energy efficiency of industrial, municipal, and thermal networks.