Diffusion from an instantaneous point source, at time t = 0, a mass m_A of species A is injected into a large body of fluid B. Take the point of injection to be the origin of coordinates. The material A diffuses radially in all directions. The solution may be found in Carslaw and Jaeger: ²

(a) Verify that Eq. 20B.5-1 satisfies Fick's second law. 

(b) Verify that Eq. 20B.5-1 satisfies the boundary conditions at r = ∞.

(c) Show that Eq. 20B.5-1, when integrated over all space, gives m_A, as required. 

(d) What happens to Eq. 20B.5-1 when t → 07

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