Modelling and simulation of ice/snow melting

Numerical Solution
1. Temperature distribution
Using matrix notation
⎡ ⎤
TA
⎢
T2(t) ⎥
⎢
. ⎥
. ⎥
⎢ . ⎥
⎢ ⎥
T (t +∆t)= ⎢Tn(t)
⎥+
⎢ ⎥
⎢ TF ⎥
⎢ ⎥
⎢ .
⎣ .
⎥
. ⎦
TF
∆t
h2 ⎡
0
⎢
1
⎢
⎣0
0
�
−2
1
. . .
1
. ..
−2
. . .
��
=A
0
1
. ..
⎡
⎤
⎤ T1(t + ∆t)
0
⎢
0⎥
⎢
. ⎥
. ⎥
⎥ ⎢ . ⎥
⎥ ⎢
⎥
⎥ ⎢Tn−1(t
+ ∆t) ⎥
⎥ ⎢
⎥
⎥ ⎢ Tn(t + ∆t) ⎥
⎥ ⎢
⎥
⎥ ⎢Tn+1(t
+ ∆t) ⎥
⎥ ⎢
⎥
0⎦
⎢ .
⎣ .
⎥
. ⎦
0
� TN+1(t + ∆t)
leads to update step algorithm:
T (t +∆t)=(IN+1−A) −1 [TA,T2(t),· · · ,Tn(t),TF ,· · · ,TF ] T
Modelling and
simulation of ice/snow
melting
Sabrina Wandl -
University of Linz
Tuomo
Mäki-Marttunen -
Tampere UT
Sigmund Vestergaard -
TU Danmark
Patrick Kürschner -
TU Chemnitz
Trond Kvarnsdal -
NTNU Trondheim
Introduction
Modelling
Melting point
depression
Solution
Exact
Numerical
Further issues