- #1
joelcponte
- 5
- 0
Homework Statement
Heat equation in a annulus, steady state solution.
u(a,θ,t) = Ta
u(b,θ,t) = Tbcos(θ)
Homework Equations
Using separation of Variables
[itex]\frac{}{}\frac{1}{r}\frac{d}{d r}(r\frac{d R}{d r}) + \frac{1}{r^2}\frac{d^2\Theta}{d \theta} = 0[/itex]
The Attempt at a Solution
I found
u(r,θ,t) = [itex] \alpha_0 + \beta_0 ln(r) + \sum (\alpha_n r^n + \beta_n r^{-n})(\gamma_n cos(n\theta) + \sigma_n sin(n\theta)) [/itex]
but the answer is
u(r,θ,t) = [itex] \alpha_0 + \beta_0 ln(r) + \sum (\alpha_n r^n + \beta_n r^{-n})cos(n\theta)[/itex]
(this is before applying the boundary conditions)