Modelling and simulation of ice/snow melting
Modelling and simulation of ice/snow melting
Modelling and simulation of ice/snow melting
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<strong>Modelling</strong><br />
interface movement<br />
◮ TS(h(t), t) = TL(h(t), t) = TM (<strong>melting</strong> point)<br />
◮ domain Ω = [0, l] separated by interface into<br />
[0, h(t)) <strong>and</strong> (h(t), l]<br />
◮ one-dimensional Stefan condition:<br />
∂TS<br />
∂TL<br />
kS (h(t), t) − kL (h(t), t)<br />
�<br />
∂x<br />
��<br />
∂x<br />
�<br />
heat flux difference<br />
h(0) = 0 slap initially frozen<br />
L - latent heat (e.g. water: 334 J/g)<br />
= ρL dh<br />
dt<br />
����<br />
velocity<br />
<strong>Modelling</strong> <strong>and</strong><br />
<strong>simulation</strong> <strong>of</strong> <strong>ice</strong>/<strong>snow</strong><br />
<strong>melting</strong><br />
Sabrina W<strong>and</strong>l -<br />
University <strong>of</strong> Linz<br />
Tuomo<br />
Mäki-Marttunen -<br />
Tampere UT<br />
Sigmund Vestergaard -<br />
TU Danmark<br />
Patrick Kürschner -<br />
TU Chemnitz<br />
Trond Kvarnsdal -<br />
NTNU Trondheim<br />
Introduction<br />
<strong>Modelling</strong><br />
Melting point<br />
depression<br />
Solution<br />
Exact<br />
Numerical<br />
Further issues
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