Solidification of a liquid about a cylindrical pipe

The temperature distribution and the rate of removal of heat by a coolant are predicted for the process of solidification of a liquid about a cold, isothermal pipe. The heat balance integral method incorporating spacial sub-division is used. It is found that acceptable results can be obtained by using only a small number of sub-divisions together with a piece-wise, linear profile. Furthermore, the results illustrate that the sensitivity which is normally associated with the heat balance integral method is overcome.