# Thread: Temperature of a Sheet of Metal

1. ## Temperature of a Sheet of Metal

Hello,

A large (effectively infinite) sheet of metal, insulated above and below, occupies the
infinite strip B = {(x, y) | 0 <= x <= pi/2, y >= 0}. The y-axis is maintained at room
temperature (20◦) but ice placed along the x-axis and the line y = pi/2 keeps the
temperature at 0◦ there. Find the steady-state temperature at the point (x, y).

Any help would be greatly appreciated! Thanks.

Hello,

A large (effectively infinite) sheet of metal, insulated above and below, occupies the
infinite strip B = {(x, y) | 0 <= x <= pi/2, y >= 0}. The y-axis is maintained at room
temperature (20◦) but ice placed along the x-axis and the line y = pi/2 keeps the
temperature at 0◦ there. Find the steady-state temperature at the point (x, y).

Any help would be greatly appreciated! Thanks.
Well what PDE does the temperature distribution follow?

CB

3. Can this also be solved with complex analysis and finding harmonic functions?