Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Maths and Mathematical Physics



+44 (0)20 7594 8369d.papageorgiou Website




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BibTex format

author = {Moore, MR and Mughal, MS and Papageorgiou, DT},
doi = {10.1017/jfm.2017.100},
journal = {Journal of Fluid Mechanics},
pages = {455--489},
title = {Ice formation within a thin film flowing over a flat plate},
url = {},
volume = {817},
year = {2017}

RIS format (EndNote, RefMan)

AB - We present a model for ice formation in a thin, viscous liquid film driven by aBlasius boundary layer after heating is switched off along part of the flat plate. Theflow is assumed to initially be in the Nelson et al. (J. Fluid Mech., vol. 284, 1995,pp. 159–169) steady-state configuration with a constant flux of liquid supplied atthe tip of the plate, so that the film thickness grows like x1/4in distance alongthe plate. Plate cooling is applied downstream of a point, Lx0, an O(L)-distancefrom the tip of the plate, where L is much larger than the film thickness. Thecooling is assumed to be slow enough that the flow is quasi-steady. We present athorough asymptotic derivation of the governing equations from the incompressibleNavier–Stokes equations in each fluid and the corresponding Stefan problem for icegrowth. The problem breaks down into two temporal regimes corresponding to therelative size of the temperature difference across the ice, which are analysed in detailasymptotically and numerically. In each regime, two distinct spatial regions arise, anouter region of the length scale of the plate, and an inner region close to x0 in whichthe film and air are driven over the growing ice layer. Moreover, in the early timeregime, there is an additional intermediate region in which the air–water interfacepropagates a slope discontinuity downstream due to the sudden onset of the ice atthe switch-off point. For each regime, we present ice profiles and growth rates, andshow that for large times, the film is predicted to rupture in the outer region whenthe slope discontinuity becomes sufficiently enhanced.
AU - Moore,MR
AU - Mughal,MS
AU - Papageorgiou,DT
DO - 10.1017/jfm.2017.100
EP - 489
PY - 2017///
SN - 0022-1120
SP - 455
TI - Ice formation within a thin film flowing over a flat plate
T2 - Journal of Fluid Mechanics
UR -
UR -
VL - 817
ER -