- #1
itisali
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Homework Statement
I have applied separation of variables to a transient radial heat equation problem.
T is a function of r and t.
I have reached the following step:
Homework Equations
[itex]
T_2(t,r) = \sum_{m=1}^ \infty c_m e^{-\alpha_2\lambda_m^2t}\left(\dfrac{-Y_0(\lambda_mb)J_0(\lambda_m r)}{J_0(\lambda_mb)}+Y_0(\lambda_mr)\right)
[/itex]
The Attempt at a Solution
I need to find [itex]c_m[/itex] which is usually found using orthogonality condition. This is done by multiplying both sides with [itex]rJ_0(λ_nr)[/itex] and integrating both sides with respect to r. But here in above equation I can't apply the orthogonality condition due to presence of [itex]Y_0(λ_mr)[/itex] on right side of equation.
How do I apply orthogonality condition in this case?
I just want to find out the coefficient [itex]c_m[/itex] and somehow get rid of the summation sign.
Please help!