Abstract
Solidification of a liquid at its fusion temperature as it penetrates into an initially empty tube maintained at constant temperature was treated theoretically and experimentally. An approximate method was introduced which involves postulating a reasonable functional form for the instantaneous shape of the frozen layer along the tube wall. This approximate crust profile method was verified theoretically using a numerical approach in which the governing integro-differential equation of liquid motion was rigorously solved on a digital computer. The good agreement obtained between the numerically exact solution and the crust profile assumption in the special case of constant wall temperature encourages exploitation of the crust profile method to predict the effects of a finite heat transfer coefficient when the flow tube is immersed in a liquid coolant bath. This system has been used in previous experimental studies of freezing of an advancing flow.
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