# Extend the considerations of the preceding problem to particle diffusion, and assume that there is a net

## Question:

n(x, y, z, t) ∞ exp (t/t1) cos(kxx) cos (kyy) cos (kzz),

where kxL, kyL and kzL are integer multiples of π. Give the functional dependence of the net time constant t1 on kx, ky, kz and t0, and show that for at least one of the solutions of the form (67) the neutron concentration grows with time if L exceeds a critical value Lcrit. Express Lcrit as a function of Du and t0. In actual nuclear reactors this increase is ultimately halted because the neutron generation rate gu decreases with increasing temperature.

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