Abstract
A simple, analytical, approximate solution is given for calculating the time-dependent development of the ice-layer thickness inside a parallel-plate channel with forced-convection, laminar flow. The upper and the lower walls of the channel are cooled by uniform external convection. By ignoring the effect of acceleration on the shape of the velocity profile, which is due to the converging ice-layers in the axial direction, an analytical solution for the variation of the ice-layer thickness with time and axial position could be obtained.
The approximate solution was compared with numerical calculations and good agreement was found. The resulting closed-form solution for the ice-layer thickness shows that several solutions can exist. An analysis of the results shows which of the possible solutions is the physically relevant one.
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References
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© 1999 Springer-Verlag
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Weigand, B., Arnal, M., Lipnicki, Z. (1999). An analytic solution prescribing the time-dependent formation of a solid crust inside a convectively cooled plane channel. In: Hutter, K., Wang, Y., Beer, H. (eds) Advances in Cold-Region Thermal Engineering and Sciences. Lecture Notes in Physics, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104179
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DOI: https://doi.org/10.1007/BFb0104179
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Publisher Name: Springer, Berlin, Heidelberg
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