The paper shows the applicability of a regular perturbation method for predicting the transient development of the ice layer thickness inside a cooled planar channel subjected to laminar flow. Applying the perturbation expansion to the conservation equations, closed-form solutions for the velocity and temperature distributions in the fluid for an arbitrarily shaped channel could be derived under the assumption that the axial variation in solid layer thickness is small. The distributions obtained for the steady-state ice layer thickness and the velocity were checked by numerical calculations and compared with the measurements of Kikuchi et al. (1986) and a generally good agreement was found.
A Perturbation Analysis of Transient Freezing of a Laminar Liquid Flow in a Cooled Two-Dimensional Channel
Weigand, B., Ho¨hn, W., and Beer, H. (May 1, 1993). "A Perturbation Analysis of Transient Freezing of a Laminar Liquid Flow in a Cooled Two-Dimensional Channel." ASME. J. Heat Transfer. May 1993; 115(2): 294–301. https://doi.org/10.1115/1.2910679
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