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Objective: transport infrastructure facilities include a variety of water supply systems. In the event of an emergency, after stopping the movement of water in the pipeline, it is cooled first, and then there is a risk of freezing and destruction of water pipelines. This work is devoted to the calculation of the cooling time of water in the above-ground water conduit with thermal insulation from the specified temperature value in the initial state to the freezing temperature. Methods: when building a mathematical model of the water cooling process, an approach is used based on averaging the equations of hydrodynamics by the volume of water in the pipeline and averaging the equations of thermal conductivity in the wall of the pipeline and in the layer of the heat insulator by the polar angle. To obtain a quasi-stationary form of equations, a comparative analysis of the rates of thermal processes in different layers of the water conduit is used. Results: a new mathematical model for cooling the water pipeline is formulated — a model of average temperatures. The applicability of the quasi-stationary form of the equations of the model is justified and its analytical solution is found. Explicit formulas are obtained for cooling time of water conduit as a function of its parameters. Cooling time was calculated in a wide range of parameters. The results of model calculations are compared with calculations according to traditional semi-empirical formulas. Practical importance: the formulas obtained in the work can be used to estimate the cooling time of water in an above-ground water pipeline with heat insulation to the freezing temperature in the case when the ambient temperature drops to negative values.
V. F. Lapshin (Fri,) studied this question.