A one-dimensional mathematical model is developed describing ice growth due to supercooled fluid impacting on a solid substrate. When rime ice forms, the ice thickness is determined by a simple mass balance. The leading- order temperature profile through the ice is then obtained as a function of time, the ambient conditions, and the ice thickness. When glaze ice forms, the energy equation and mass balance are combined to provide a single first-order nonlinear differential equation for the ice thickness, which is solved numerically.
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