Mathematical simulation of heating and melting of solid ice in a carbon steel pipe coated with a resistive heating system

Abstract

The heating and melting processes of solid ice inside a closed pipe were investigated by performing experiments and developing mathematical models. Several experiments were conducted in a cold room to measure the transient temperature and the times that were required to heat and melt ice inside a nominal 51-mm (2-inch) diameter Schedule 40 carbon steel pipe. The resistive heating system that was developed for this study consisted of several coating layers that were fabricated by using flame and cold spraying processes. By passing current through the coating heating system, sufficient heat was generated by way of Joule heating to heat and melt the ice in the closed pipe. One-dimensional transient heat conduction models were developed in cylindrical coordinates to predict the transient temperature of the ice during the heating process and the transient location of the moving solid-liquid interface during the melting process. The models were developed based on the separation of variables and the superposition methods. The data obtained from the models were compared with the results that were from the experiments. It was found that the models predicted the solid ice heating times to within 16%, 12%, and 15% and the melting times to within 6%, 8%, and 9% of those that were measured in experiments with supplied powers of 10 W, 20 W, and 40 W, respectively. The results suggest that the mathematical models that were developed based on one-dimensional transient heat conduction in cylindrical coordinates can be employed to provide reasonable predictions of the total time that is required for a thermal-sprayed coating heating system to heat and melt the ice within carbon steel pipes.