Approximate solutions to the Stefan problem with internal heat generation |
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Authors: | John Crepeau Ali Siahpush |
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Institution: | (1) Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83402, USA;(2) Idaho National Laboratory, P.O. Box 1625, MS 3760, Idaho Falls, ID 83415-3760, USA |
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Abstract: | Using a quasi-static approach valid for Stefan numbers less than one, we derive approximate equations governing the movement
of a phase change front for materials which generate internal heat. These models are applied for both constant surface temperature
and constant surface heat flux boundary conditions, in cylindrical, spherical, plane wall and semi-infinite geometries. Exact
solutions with the constant surface temperature condition are obtained for the steady-state solidification thickness using
the cylinder, sphere, and plane wall geometries which show that the thickness depends on the inverse square root of the internal
heat generation. Under constant surface heat flux conditions, closed form equations can be obtained for the three geometries.
In the case of the semi-infinite wall, we show that for constant temperature and constant heat flux out of the wall conditions,
the solidification layer grows then remelts. |
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Keywords: | |
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