Abstract
The solution to many transient heat conduction problems, in particular problems with movable boundaries or heat sources, can be simplified by introducing new variables. Figure 5.1 shows an example of a heat source moving along x axis at velocity v, while Fig. 5.2 shows an ablation that occurs at velocity v(t). One can transform transient heat conduction equation
in an motionless coordinate system with origin 0 under the condition that either the coordinate system, which moves along with the heat source, or a movable boundary will be introduced. Once the new coordinate ξ is introduced, expressed by equation (Fig. 5.1 and Fig. 5.2)
one obtains
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Literature
Slattery JC (1999) Advanced Transport Phenomena. University Press, Cambridge
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© 2006 Springer-Verlag Berlin Heidelberg
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(2006). Variable Change. In: Solving Direct and Inverse Heat Conduction Problems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33471-2_5
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DOI: https://doi.org/10.1007/978-3-540-33471-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33470-5
Online ISBN: 978-3-540-33471-2
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