11.14. Suppose that two parallel planes are
perpendicular to the z plane and pass
through the horizontal lines
and that the temperature is held constant at the
values and , respectively,
on these planes. Then
is given by
Figure 11.17 The temperature between parallel planes where .
Explore Solution 11.14.
Show that is the harmonic conjugate of .
Enter the formula for the temperature function. This is similar to Example 11.1, and Example 11.18.
Solve to get the isothermals.
Solve to get the heat flow lines.
For illustration we choose .
Use Mathematica to make a contour plot of the temperature.
Hence the temperature function T[x,y] = 50 - 20
(-1+y) is harmonic in the horizontal
has the desired boundary values.
(c) 2006 John H. Mathews, Russell W. Howell