By Zygmunt Lipnicki
This monograph comprehensively describes phenomena of warmth stream in the course of section swap in addition to the dynamics of liquid solidification, i.e. the improvement of a solidified layer. The ebook presents the reader with easy wisdom for sensible designs, in addition to with equations which describe strategies of strength transformation. the objective viewers essentially includes researchers and specialists within the box of warmth move, however the publication can also be worthwhile for either working towards engineers and graduate students.
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Additional resources for Dynamics of Liquid Solidification: Thermal Resistance of Contact Layer
By substituting the above temperature function to Eq. 34), the following is obtained expðÀb Á sÞ ¼ ~d Á d~d 1 d~d þ : ds BiCON ds ð4:38Þ Integration of the above equation from s ¼ 0 to s ¼ 1 allows to deﬁne parameter b Zs expðÀbsÞ Á ds ¼ ~d2 ~d þ BiCON 2 0 Z1 expðÀbsÞ Á ds ¼ ) 0 ) b ¼ ~2 dmax 2 1 þ ~dmax BiCON : ~d2 ~dmax max þ 2 BiCON ð4:39Þ 42 4 Solidiﬁcation on a Rectangular Geometrics In this case, the thickness of the solidiﬁed layer varies from ~d ¼ 0 to ~d ¼ ~dmax , and constant b is deﬁned by ~dmax .
C. The boundary case of solidiﬁcation Since the surface of the solidiﬁed layer is assumed adiabetic, there is not a thermal contact layer ðq_ ¼ 0; r ¼ 0; ~dt ¼ 0Þ in the flowing liquid. The liquid flowing above an adiabatic surface is not overheated, and its temperature equals that of solidiﬁcation TF. A model of this phenomenon was presented (Fig. 8). In the discussed case, the heat balance Eq. 2 Fig. 26) ~d ¼ pﬃﬃﬃﬃﬃﬃ pﬃﬃﬃ 2# s: ð4:30Þ The obtained solution in comparison with another case was shown in Fig.
But the influence of the hydraulic and the thermal boundary layers in the solidiﬁcation process has been less analysed. The thermal resistance of the contact layer in the process of a liquid solidiﬁcation on a cold plate was by some authors theoretically investigated, among others by Ignaszak et al. (2002), Lipnicki (2003), Lipnicki et al. (2005), Lipnicki and Bydałek (2005, 2008). Some interesting experiments connected with the measurement of the heat flowing through a contact layer were conducted by Wang and Matthyes (1994) and Loulou et al.
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