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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Belgrade, Technical Faculty, Bor
2013-01-01
|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568872356544512 |
|---|---|
| author | Singh U.C. Prasad A. Kumar A. |
| author_facet | Singh U.C. Prasad A. Kumar A. |
| author_sort | Singh U.C. |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cbedf7ac0c024ac2a27246592eea2c16 |
| institution | Kabale University |
| issn | 1450-5339 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | University of Belgrade, Technical Faculty, Bor |
| record_format | Article |
| series | Journal of Mining and Metallurgy. Section B: Metallurgy |
| spelling | doaj-art-cbedf7ac0c024ac2a27246592eea2c162025-02-02T23:57:13ZengUniversity of Belgrade, Technical Faculty, BorJournal of Mining and Metallurgy. Section B: Metallurgy1450-53392013-01-0149324525610.2298/JMMB120808028S1450-53391300028SA lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistanceSingh U.C.0Prasad A.1Kumar A.2Engineering Division, Tata Steel Limited, Business centre, Bistupur, Jamshedpur, IndiaDepartment of Mechanical Engineering, National Institute of Technology, Jamshedpur, IndiaDepartment of Mechanical Engineering, Birla institute of Technology Mesra, Ranchi, IndiaIn 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.http://www.doiserbia.nb.rs/img/doi/1450-5339/2013/1450-53391300028S.pdfadditive additionmelt-additive systemmathematical modelingfreezing and melting |
| spellingShingle | Singh U.C. Prasad A. Kumar A. A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance Journal of Mining and Metallurgy. Section B: Metallurgy additive addition melt-additive system mathematical modeling freezing and melting |
| title | A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| title_full | A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| title_fullStr | A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| title_full_unstemmed | A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| title_short | A lump-integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| title_sort | lump integral model based freezing and melting of a bath material onto a cylindrical additive of negligible resistance |
| topic | additive addition melt-additive system mathematical modeling freezing and melting |
| url | http://www.doiserbia.nb.rs/img/doi/1450-5339/2013/1450-53391300028S.pdf |
| work_keys_str_mv | AT singhuc alumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance AT prasada alumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance AT kumara alumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance AT singhuc lumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance AT prasada lumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance AT kumara lumpintegralmodelbasedfreezingandmeltingofabathmaterialontoacylindricaladditiveofnegligibleresistance |