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## Homework Statement

Heat transfer problem with 3 insulated sides and heat flux in and out on one boundary.

given values: q & k

## Homework Equations

Governing Equation:

[tex]

\frac{\partial^{2}{T}}{\partial{x}^{2}} + \frac{\partial^{2}{T}}{\partial{y}^{2}} = 0

[/tex]

Boundary Conditions:

[tex]

@ x = 0 ;

\frac{\partial{T}}{\partial{x}} = 0

[/tex]

[tex]

@ x = L ;

\frac{\partial{T}}{\partial{x}} = 0

[/tex]

[tex]

@ y = 0 ;

\frac{\partial{T}}{\partial{y}} = 0

[/tex]

[tex]

@ y = H ;

\frac{\partial{T}}{\partial{y}} = \frac{q}{k} ; 0 < x < \frac{L}{2}

[/tex]

[tex]

@ y = H ;

\frac{\partial{T}}{\partial{y}} = \frac{-q}{k} ; \frac{L}{2} < x < L

[/tex]

## The Attempt at a Solution

I did the separation of variable method and applied the first 3 boundary conditions, @ x=0,L and @ y=0.

I'm stuck at this.

[tex]

T(x,y) = \sum_{n=0}^\infty C_n \cos{\frac{n \pi x}{L}} \cosh{\frac{n \pi y}{L}}

[/tex]

n = 0,1,2,3.....

How do i solve for Cn, and apply the piecewise boundary condition?

I know i have to use the Orthogonality property of Cosine.

Thanks.