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Homework 7

CM3110

Note:  some solutions use physical property data that were taken from Geankoplis 3rd edition. 
This information is also available in your text, in Felter and Rousseau, or in Perry's Hancbook of Chemical Engineering.

  1. Derive the overall heat-transfer coefficient, U, for heat flux in a rectangular slab of thermal conductivity, k, with Newton's law of cooling boundary conditions at both surfaces (i.e. the heat-transfer coefficient at the left side is h1, the heat-transfer coefficient at right side is h2, the fluid on left side is at temperature Tb1, the fluid at right side is at temperature Tb2, and the slab is of thickness B). (Hint: we did the case for U in a hollow tube in class). (SOLUTION)
  2. Create a summary list of all the correlations for heat transfer coefficient given in your text. (SOLUTION)
  3. (adapted from Geankoplis 3rd edition 4.3-8 p319)  Water at an average temperature of 70oF is flowing in a 2-in, schedule 40 steel pipe.  Steam at 220oF is condensing on the outside of the pipe.  The convective coefficient for the water inside the pipe is h=5.00 x 102 BTU/(h ft2 oF) and the condensing steam coefficient on the outside is h=1.5 x 103 in the same units.  a) Calculate the heat loss per unit length of 1.0 ft of pipe; b) repeat using the overall heat transfer coefficient U based on the inside area; c) repeat using the overall heat transfer coefficient U based on the outside area. (SOLUTION)
  4. (adapted from Geankoplis 3rd edition 4.5-3 p321)  A reaction mixture having a mean heat capacity of 2.85 kJ/(kg K) is flowing at a rate of 7260 kg/h and is to be cooled from 377.6K to 344.3K.  Cooling water at 288.8 K is available and the flow rate is 4536 kg/h.  The overall heat transfer coefficient based on the outer area is 653 W/(m2 K).  a) for counterflow, calculate the outlet water temperature and the heat-transfer area of the exchanger; b)  repeat for cocurrent flow. (SOLUTION)
  5. (adapted from Geankoplis 3rd edition 4.5-5)  Oil flowing at the rate of 7258 kg/h with a mean heat capacity of 2.01 kJ/(kg K) is cooled from 394.3 K to 338.9 K in a counterflow heat exchanger by water entering at 294.3K and leaving at 305.4 K.  Calculate the flow rate of the water and the overall heat transfer coefficient based on the inner area Ui if the inner area is 5.11 m2. (SOLUTION)

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