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hw4-011-ts

# hw4-011-ts - C HEMICAL E NGINEERING 1 20B H omework 4 due F...

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CHEMICAL ENGINEERING 120B Homework 4 - due Friday, February 18, 2011 1. A drop of water at 25 C is thrown onto a hot copper frying pan. How hot must the frying pan be in order for the drop to 'sizzle' (boil a thin layer) on contact? 2. Consider a plate of thickness d and thermal diffusivity CY. One edge (z = 0) is heated in an oscillatory fas hion, with T(z = 0, t) = To coswt J~ (e iwt ) . The other end is insulating (dT/dz = 0 at z = d). [,(1) a. Before doing any detailed calculations, from dimensional or scaling arguments, figure out a frequency where the solution will change qua litatively. That is - above a certain frequency scale, the temperature in the plate will look a certain way, 'whereas below that frequency scale, it looks completely different. What do you expect will happen? Describe it physically in terms of how long it conduction takes. (to) b. Non-dimensionalize the differential equations, choosing z = d(, T = Toe, and t = i/w, where t, (), and ( are dimensionless variables. v"hat dimensionless parameter appears? \\'hat does it correspond to?
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