Examination One, MSE 855, Monday, January 22, 2007 3 – 3:50 pm in Room 1202 Engineering Building 1.Write down Fick’s First law, the continuity equation and Fick’s Second law in coordinate invariant form. Give Fick’s Second law for two cases (i) D a function of C, and (ii) D is not a function of C. Define every symbol you use in each equation and give appropriate physical units for each symbol. (20 pts) 2. Beginning with Fick's First Law and the continuity equation, derive Fick's Second Law. Express ALL equations in coordinate-invariant form. Show the two cases (i) D a function of C, and (ii) D is not a function of C (15 points). 3. (a) State Laplace’s equation in coordinate invariant form and discuss the particular connections between Laplace’s equation, the heat equation and the solution of solid state diffusion problems. Be explicit. Discuss particular diffusion equations that are involved (15 points).
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