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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Analytical Solution<br />
If the initial temperature distribution is<br />
⎧<br />
⎪⎨<br />
T (x, 0)=<br />
⎪⎩ TA−(TA−TM)<br />
�<br />
x<br />
erf<br />
2 √ �<br />
αt0<br />
erf(λ) , 0≤x ≤h(0)<br />
TM, x > h(0)<br />
with:<br />
λ - the solution <strong>of</strong> equation λeλ2 =⇒ solution <strong>of</strong> the Stefan problem:<br />
h(t) = 2λ � α(t + t0)<br />
erf<br />
T (x, t) = TA − (TA − TM)<br />
erf(λ) = CL(TA−TM )<br />
√ πL<br />
�<br />
x<br />
2 √ α(t+t0)<br />
erf(λ)<br />
<strong>and</strong> t0 = h(0)2<br />
4λ 2 α<br />
�<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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