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dc.contributor.author
Voller, Vaughan R.
dc.contributor.author
Roscani, Sabrina Dina
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dc.date.available
2024-04-08T13:40:31Z
dc.date.issued
2023-03
dc.identifier.citation
Voller, Vaughan R.; Roscani, Sabrina Dina; A general non-Fourier Stefan problem formulation that accounts for memory effects; Pergamon-Elsevier Science Ltd; International Journal Of Heat And Mass Transfer; 209; 3-2023; 1-10
dc.identifier.issn
0017-9310
dc.identifier.uri
http://hdl.handle.net/11336/232366
dc.description.abstract
The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a gen- eral model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. On shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in con- trast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result con- firmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Pergamon-Elsevier Science Ltd
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dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
STEFAN PROBLEM
dc.subject
MEMORY EFFECT
dc.subject
FRACTIONAL DERIVATIVE
dc.subject
ENTHALPY METHOD
dc.subject.classification
Matemática Aplicada
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
A general non-Fourier Stefan problem formulation that accounts for memory effects
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-04-08T11:17:53Z
dc.journal.volume
209
dc.journal.pagination
1-10
dc.journal.pais
Estados Unidos
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dc.description.fil
Fil: Voller, Vaughan R.. University of Minnesota; Estados Unidos
dc.description.fil
Fil: Roscani, Sabrina Dina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
dc.journal.title
International Journal Of Heat And Mass Transfer
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0017931023002478
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.ijheatmasstransfer.2023.124094
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