Can someone help me with this?
An infinitely long plate of width L has its two parallel sides maintained at temperature zero and its other side at constant temperature T. What is the rate of change?
I have that Laplace's equation holds and u(x,0) = T, u(0,y) = 0, u(L,y) = 0 with the lim as y goes to infinity of u(x,y) finite.
I know how to do the separable equations stuff, but can someone help me with the eigenfunctions (i.e. what are X(x) and Y(y) for u(x,y) = XY). Thanks.