- #1
leoflc
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Homework Statement
a rectangular plate (15 x 30) with the following boundary conditions:
u_y(x,0) = 0
u_y(x,30) = 0
u_x(0,y) = 0
u_x(15,y) = y(20-y)
the derivative B.Cs describe the heat flux through the boundaries.
solve the the steady-state temp u(x,t)
Homework Equations
steady-state: [tex]\nabla[/tex]^2 * u =0
The Attempt at a Solution
I set u(x,y)=F(x)G(y)
with the BCs, I got
G'(0)=0
G'(30)=0
F'(0)=0
F'(15)=y(20-y)
let F=A*cos(px) + B*sin(px)
F'(0)=0; so B=0
F'(15)=-A*sin(15*p)=y(20-y)
this is where I got stock.
How can I solve for 'p' or A with the B.C. that has 'y' in there?
Am I doing the right thing?
Thank you very much!