Abstract
A closed-form expression is presented to find the location of solid-liquid interface motion in convection-dominated solidification and melting problems. In this regard, the solutions are expressed in terms of the generalized representations of error functions,E (u, v) andF (u, v), which are useful to heat-conduction problems with convective-type boundary conditions. It is demonstrated that for constant surface temperature, the interface solution reduces to the classical Neumann solution.
Zusammenfassung
Es wird eine geschlossene Formel hergeleitet, die den jeweiligen Ort der Grenze zwischen fester und flüssiger Phase bei konvektionsdominierten Erstarrungs- und Schmelzproblemen zu bestimmen gestattet. Die Lösungen lassen sich unter Verwendung der verallgemeinerten FehlerintegralfunktionenE(u, v) undF (u, v) formulieren, welche sich bei Wärmeleitungsproblemen mit konvektiven Randbedingungen als sehr nützlich erweisen. Im Falle konstanter Oberflächentemperatur resultiert die klassische Neumannsche Lösung.
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Abbreviations
- C p J/kg·k:
-
specific heat at constant pressure
- h W/m2·k:
-
convective heat-transfer coefficient
- k W/m·k:
-
thermal conductivity
- L f J/kg:
-
latent heat of fusion
- s m:
-
solid-liquid interface location
- Ste Stefan number:
-
[Ste=C p,s(T f-T ∞/L f]
- t s:
-
temperature
- x m:
-
spatial variable
- α m2/s:
-
thermal diffusivity (α=kρC p)
- λ :
-
dimensionless interface location (λ=s/2√α1 t)
- X :
-
dimensionless heat-transfer coefficient (X=hs/k s )
- Xi:
-
dimensionless heat-transfer coefficient at the interface (Xi =his/k s )
- θ sc :
-
dimensionless subcooling temperature [(T f-T i)/(T f-T ∞)]
- ρ kg/m3 :
-
density
- f:
-
freezing
- i:
-
interface or initial
- l:
-
liquid phase
- s:
-
solid
- ∞:
-
ambient
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The authors acknowledge the support provided by the King Fahd University of Petroleum and Minerals for this research project.
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Zubair, S.M., Chaudhry, M.A. Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions. Warme- und Stoffubertragung 30, 77–81 (1994). https://doi.org/10.1007/BF00715013
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DOI: https://doi.org/10.1007/BF00715013