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

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.

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