Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Abstract

To accurately describe the distribution law of the temperature field formed by a single freezing pipe under the action of a seepage field, the shape of the freezing front was simplified using a segmentation-equivalent method. The analytical solution of the steady-state temperature field was derived, and the accuracy was verified using a physical model test. Combined with the results of the model test and the calculation results of the analytical solution, the distribution law of the freezing temperature field formed by a single pipe under different seepage velocities was analyzed. It was found that compared with the no flow rate, when the seepage velocity was 3, 6, and 9 m/day, the frozen area was reduced from 17.97 × 104 mm2 to 15.77 × 104, 3.84 × 104, and 3.05 × 104 mm2, respectively. The proportion of frozen area below −5°C increased from 39.43% to 40.19%, 49.84%, and 51.52%, respectively. The average freezing temperature field reduced from −5.78 to −5.86, −7.31, and −7.50°C, respectively. As the seepage velocity increased, the frozen area formed by a single pipe decreased while the proportion of the low-temperature zone increased and the average temperature of the temperature field decreased.

Thermodynamic Analysis of Coupled Seepage and Thermal Conduction Effects in Earth-Rock Dams

“…However, despite the practical significance of research on coupling mechanisms, existing studies still have some deficiencies in theory and methodology. Current models often overlook the interaction between the temperature and seepage fields or simplify some key influencing factors in the simulation process [16][17][18], such as insufficient consideration of convective heat transfer, leading to inaccurate predictions of dam behavior under different environmental conditions [19][20][21]. Moreover, many studies use parameters and boundary conditions that are too idealized, differing from real operational environments, which limits the widespread application of the models and their predictive capabilities for actual effects.…”

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