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 />
Two-phase Stefan problem<br />
� Tt = αLTxx : 0 < x < h(t), αL := kL<br />
ρcL ,<br />
Heat-Equations:<br />
Tt = αSTxx : h(t) < x < l, αS := kS<br />
ρcS .<br />
�<br />
Interface conditions T (h(t), t) = TM,<br />
for t > 0 : ρLh ′ (t)<br />
�<br />
= kSTx(h(t), t)−kLTx(h(t), t).<br />
h(0)<br />
Initial conditions:<br />
T (x, 0)<br />
�<br />
= 0 (material initially solid),<br />
= Tinit < TM : 0 ≤ x ≤ l.<br />
Boundary conditions T (0, t) = TA > TM,<br />
for t > 0 : T (l, t) = TG < TM.<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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