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 />
Simplification: solid phase at uniform temperature Tinit = TM,<br />
only liquid phase is active, Ω = [0, ∞)<br />
=⇒ one phase Stefan problem<br />
Find T (x, t) <strong>and</strong> h(t) such that<br />
Heat equation: Tt = αLTxx, 0 < x < h(t), t > 0,<br />
Interface conditions<br />
for t > 0 :<br />
Initial condition: h(0) = 0.<br />
�<br />
T (h(t), t) = TM,<br />
h ′ (t) = −βTx(h(t), t), β := kL<br />
ρL<br />
Boundary condition: T (0, t) = TA(t) = TA > TM : t > 0.<br />
similar processes: solidification, flows through porous media,<br />
combustion, reactions<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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