hw10a - , and heat capacity, C p , are all constant. a. For...

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CBE 320 November 2, 2009 Transport Phenomena Problem Session X 1. Fiber spinning In the fiber-spinning process shown in the figure below, the cylindrical fiber flows through a nozzle with uniform speed V o , and enters into a cooling water bath of constant, uniform temperature T . At large z (the direction of flow), far away from the nozzle, the fiber temperature is the same as that of the bath. Assume that the heat transfer coefficient between the fiber and the water bath, h , the thermal conductivity of the fiber, k , the fiber density,
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Unformatted text preview: , and heat capacity, C p , are all constant. a. For a small fiber radius, R , one may assume that the fiber temperature and velocity does not vary in the r-direction. Use the shell energy balance method to derive the differential equation for the temperature profile in the fiber T ( z ) for this situation. b. Indicate the boundary conditions you should use to solve this differential equation. c. Solve this differential equation to determine the temperature profile. 2. Work problem 11B.2 (a) and (b) in BSL. 1...
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