A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance
In a theoretical analysis, a lump-integral model for freezing and melting of the bath material onto a cylindrical additive having its thermal resistance negligible with respect to that of the bath is developed. It is regulated by independent nondimensional parameters, namely the Stefan numb...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Belgrade, Technical Faculty, Bor
2013-01-01
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| Series: | Journal of Mining and Metallurgy. Section B: Metallurgy |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-5339/2013/1450-53391300028S.pdf |
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| Summary: | In a theoretical analysis, a lump-integral model for freezing and melting of
the bath material onto a cylindrical additive having its thermal resistance
negligible with respect to that of the bath is developed. It is regulated by
independent nondimensional parameters, namely the Stefan number, St the heat
capacity ratio, Cr and the modified conduction factor, Cofm. Series solutions
associated with short times for time variant growth of the frozen layer and
rise in interface temperature between the additive and the frozen layer are
obtained. For all times, numerical solutions concerning the frozen layer
growth with its melting and increase in the interface temperature are also
found. Time for freezing and melting is estimated for different values of Cr,
St and Cofm. It is predicted that for lower total time of freezing and
melting Cofm<2 or Cr<1 needs to be maintained. When the bath temperature
equals the freezing temperature of the bath material, the model is governed
by only Cr and St and gives closed-form expressions for the growth of the
frozen layer and the interface temperature. For the interface attaining the
freezing temperature of the bath material the maximum thickness of the frozen
layer becomes ξmax-√Cr(Cr+St). The model is validated once it is reduced to a
problem of heating of the additive without freezing of the bath material onto
the additive. Its closed-form solution is exactly the same as that reported
in the literature. |
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| ISSN: | 1450-5339 |