Question: Problem 5.1. Consider the partial differential equation K(Cxx + zz) - uC = 0 (5.74) in the region above z = h(x), with h(x) =

Problem 5.1. Consider the partial differential

Problem 5.1. Consider the partial differential equation K(Cxx + zz) - uC = 0 (5.74) in the region above z = h(x), with h(x) = Hmax cos kr. The boundary conditions are C(x, hmax cos kx) = C. and C(x,z) O as z 00. (i) Describe a physical situation governed by this boundary value prob- lem. (ii) Solve the problem with hmax = 0. (iii) Based on your exact solution, non-dimensionalize the problem with non-zero hmax and determine the non-dimensional control parameters. (iv) Use perturba- tion theory to find the first effects of small non-zero hmax on the "inventory" 27/ A C(x, 2) dx dz. (5.75) 27 roo def k Louise (I think you'll have to go to second order in hmax.) Problem 5 2 Consider the diffusion

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