Information Technology Reference
In-Depth Information
T
1
T
2
T?
Fig. 7.4
The
top figure
shows two metal pieces, at different temperatures T
1
and T
2
, insulated
on all sides except for one (
thinner line
), being brought into contact with each other in the
lower
figure
. The initial jump in temperature from T
1
to T
2
is smoothed out in time, see Fig.
7.5
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
1
0
1
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
1
0
1
Fig. 7.5
The evolution of the temperature in a medium composed of two pieces of metal, at differ-
ent initial temperatures. In the
gray-scale plots
,
dark
is hot and
white
is cool. The plots correspond
to t
0:25 (
lower right
).
Since all boundaries are insulated, the temperature approaches a constant value, equal to the aver-
age .T
1
C
D
0 (
upper left
), t
D
0:001 (
upper right
), t
D
0:025 (
lower left
), and t
D
T
2
/=2 of the initial temperature values. The simulations are based on a three-dimensional
mathematical model
in time, we actually deal with a three-dimensional problem. For convenience we
may, nevertheless, want to introduce a one-dimensional model. Imagine a horizontal
line through the center axis of the can of beer. We could compute the heat trans-
port along this line, disregarding heat transport in the other space directions. Since
the can of beer is cylindrical, we could in fact compute the heat transport in the
