# Temperature of a Sheet of Metal

• Nov 19th 2010, 08:38 AM
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.
• Nov 19th 2010, 11:02 PM
CaptainBlack
Quote:

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
• Nov 29th 2010, 10:35 AM
mathmaniac234
Can this also be solved with complex analysis and finding harmonic functions?