Freezing Flow in a Subcooled Permeable Medium

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Abstract
Analytical similarity solutions are derived for the problem of transient one-dimensional flow and freezing of a liquid in an initially dry permeable half-space. The structure of the flow consists of three regions: a liquid zone in which the temperature decreases to the freezing temperature, a central two-phase zone where the temperature is at the freezing point, and a leading gas-filled region in which the temperature is nearly undisturbed. The propagation velocity of this intrusion is determined as a function of the subcooling, latent heat, and other process parameters. As the inlet temperature approaches the freezing temperature, the governing equations admit a pair of solutions having propagation velocities that sometimes differ by more than an order of magnitude.

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