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Even though you may not know how to solve the diffusion equation for a particular case, but you at least should be able to check
Even though you may not know how to solve the diffusion equation for a particular case, but you at least should be able to check a given solution to see if it satisfies the diffusion equation and the initial and boundary conditions. Explore the solution for the plane source. Check if it satisfies the diffusion equation, IC and BCs, and if the symmetry conditions are met. Examine how c(0)/c(x) at a given x varies as a function of time. For IC, please use this integral: Problem 2 In discussing the superposition solution, Glicksman argued in his book (p49) that "the linearity of the diffusion equation permits the use of superposition to produce new solutions for different geometric arrangement of the sources", while Shewmon argued in his book (p19) that "the fact that there is solute in the adjacent slices does not in any way affect this (the plane source solution) result, and the actual solution is thus given by a superposition of the distribution from the individual slabs." According to what you have learned about diffusion in this class, offer your physical argument about the validity of the superposition solution. Of course, one can always check the solution to see
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