Determining a simplified version and application of Stefan's ice formation equation

by Katrina Haarmann

Submitted : Fall 2020

A simplified version of Stefan’s equation was derived using a simplified relationship between the number of days the average temperature is below freezing and the thickness of ice. Since this relationship was shown as a differential equation, separation of variables and integration were used to further simplify the equation. The derived equation was then used to approximate if a body of water has accumulated enough ice to be safe to walk across. The result is a simplified equation that can relate the number of days the average temperature is below freezing to the thickness of ice of a body of water. An example with a given temperature provides the full integration of the equation. Based on the result from the derived equation, it was determined that it can roughly approximate the thickness of ice under given conditions.

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