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Prove The Solution of a Rectangular Reactor Core

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A reactor core is in the form of a rectangular prism of height h with a rectangular base having sides of length a and b. Assuming that the boundary condition is psi = 0 at the sides of the reactor show, by direct substitution or otherwise, that the solution has the form

psi = A cos(pi*x / a) cos(pi*x / b) cos(pi*z / h)

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We solve the partial differential equation corresponding to the radiation intensity psi inside a rectangular reactor core.

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