Mathematical simulation of the freezing time of water in small diameter pipes

• Mathematical simulation of the freezing of water in circular pipes.
• A one-dimensional, finite-length scale, transient heat conduction model approach was developed.
• Comparison of predictions of finite-length scale model and experiments were conducted.
• Model results compared well to experimental results.
• Application of the model to practical scenarios was considered and explored.

The cooling and freezing of stagnant water in cylindrical pipes were investigated under conditions of varying ambient air temperatures. Experiments were conducted to measure the transient temperature of water in a 50.8 mm nominal Schedule 80 steel pipe that was exposed to stagnant and forced air at temperatures ranging from −25 °C to −5 °C. There was a 10 vol.% air gap in the pipe to avoid excessive increase of fluid pressure during the freezing process. A one-dimensional transient heat conduction mathematical model was developed to estimate the freezing time of the liquid in the pipe. The model was based on the separation of variables method for a finite length-scale solidification problem, and was verified with the experimental transient temperature data. It was found that the model predicted the solidification time of the water in the pipe to within 15% of that which was measured by experiments for most of the tests that were conducted. The model was applied to predict the cooling and freezing behaviors of water in steel and copper pipes of various inner diameters and in insulated pipes. The results of the model and their agreement with experimental data suggest that a separation of variables method for a finite length-scale heat conduction problem may be applied to moving or free boundary problems to predict phase change phenomena.