Analysis of heat transfer dynamics within surface-mounted insulated cooled water pipeline

Objective: to determine the comparative contributions of convective and molecular heat-transfer mechanisms between the fluid and the pipeline walls during the cooling of an above-ground thermally insulated water pipeline subjected to subzero ambient environmental temperatures. To obtain analytical expressions that correlate the Nusselt numbers with the mean bulk temperature of the fluid undergoing cooling and the physical parameters of the pipeline’s infrastructure. Furthermore, the study proposes the adoption of Nusselt numbers, averaged across the specific thermal range of the cooling phase, as the definitive metrics for quantifying the cooling rate. Methods: a mathematical model of the water-pipeline cooling process was performed based on hydromechanics and thermal conductivity equations. The analytical resolution of this model employed a quasi-stationary approximation. This methodological approach is predicated on the physical observation that the thermal decay of the water mass occurs on a significantly longer time scale than the rapid thermal equilibration within the pipe material and its insulating layers. Numerical calculations were carried out to represent typical operational and environmental parameters. Results: analytical expressions for Nusselt numbers under convective and molecular mechanisms of heat transfer between the water and the pipeline walls have been obtained. The efficiency of these mechanisms has been compared, showing that the convective mechanism is the dominant mechanism of cooling water. Explicit expressions have been derived for the difference between the average water temperature in the pipeline and the temperature of its inner surface. It has been demonstrated that ice nucleation on the inner surface of the pipeline initiates prior to the entire water volume reaching the phase-transition temperature. A predictive formula has been developed to calculate the average water temperature at which this internal icing commences. Numerical calculations applied to this formula over a broad spectrum of ambient temperatures provided further validation for typical pipeline configurations. Practical significance: the obtained results permit the formulation of a high-fidelity mathematical model describing the thermal behavior of insulated hydraulic systems. The use of such a model enables precise calculation of cooling dynamics, specifically allowing operators to determine the critical time window available before the onset of ice formation on the pipeline walls.