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Homework 9

CM3110

Heat Exchanger Effectiveness
Shell-and-tube heat exchangers

  1. You are asked to design a double-pipe heat exchanger for an application that will continuously heat a process stream (Cp=4.85kJ/kg K, mass flow rate=0.584 kg/s) from 25oC to 95oC. The heat-transfer fluid will be Thermatic® (Cp=12.8 kJ/kg K), which will be fed at 125oC. The mass flow rate of the Thermatic® is not specified and must be chosen in the design process. The viscosities of the process fluid and of the Thermatic® may be assumed to be constant (not a function of temperature).  Describe how you will estimate the overall heat-transfer coefficient U for the heat exchanger. Please write down all equations you will use and indicate how you will use them. Please list separately all the physical property data you will need and how you will determine any quantities (diameters, velocities, etc.) in your equations. If your solution is iterative, please outline your iterative strategy.   (SOLUTION)
  2. Design a double-pipe heat exchanger for an application that will continuously heat a process stream (Cp=4.85kJ/kg K, mass flow rate=0.584 kg/s) from 25oC to 95oC. The heat-transfer fluid will be Thermatic® (Cp=12.8 kJ/kg K), which will be fed at 125oC. The mass flow rate of the Thermatic® is not specified and must be chosen in the design process. The viscosities of the process fluid and of the Thermatic® may be assumed to be constant (not a function of temperature).  (no solution provided)

  3. (Based on example 4.9-2 from Geankoplis 3rd edition page 275) Water flowing at a rate of 0.667 kg/s enters a countercurrent, double-pipe heat exchanger at 308K and is heated by an oil stream entering at 383K at a rate of 2.85 kg/s (cp=1.89 kJ/(kg K).  The overall heat transfer coefficient of the heat exchanger is 300. W/(m2 K) and the heat transfer area in the exchanger is 15.0 m2.  Calculate the heat-tranfer rate and the exit water temperature, first using heat exchanger effectiveness (no solution given; plot for effectiveness versus NTU=UA/Cp,min is given in McCabe et al. p445 or in Geankoplis 3rd ed p274) and then without using the effectiveness. How well do your answers compare?  Note Geankoplis 3rd edition has the solution to the problem when effectivenes is used. (SOLUTION)
  4. From Figure 4.9-7 on page 274 of Geankoplis 3rd edition (given in lecture notes), at what values of  and NTU is it better to use co-current flow instead of counter-current flow? Please explain your answer. (SOLUTION)
  5. (based on Geankoplis 3rd edition 4.8-4) Steam at 1.00 atm pressure (absolute) and 100.oC is condensing on a bank of 5 vertical tubes each 0.305 m high and having an outer diameter of 1.00 in.  The tubes are arranged in a bundle spaced far enough apart so that they do not interfere with each other.  The surface temperature of the tubes is 97.78oC.  Calculate the average heat-transfer coefficient and the total mass flow rate of condenstate (kg/h). (SOLUTION)
  6. (based on Geankoplis 3rd edition 4.9-1) A 1-2 shell-and-tube heat exchanger with one shell pass and two tube passes is used to heat a cold fluid from 37.8oC to 121.1oC by using a hot fluid entering at 315.6oC.  The temperature of the hot fluid leaving the exchanger is measured to be 148.9oC.  Calculate the log-mean temperature difference in the exchanger and the mean temperature difference in the exchanger.  Comment on these answers - why are they different?  Are they different in the way you expected? (SOLUTION)
  7. (based on Geankoplis 3rd edition 4.9-2) Oil flowing at a rate of 5.04 kg/s (mean Cp=2.09 kJ/(kg K)) is cooled in a 1-2 shell-and-tube heat exchanger from 366.5K to 344.3K by water flowing at 2.02 kg/s entering at 283.2K.  The overall heat-transfer coefficient based on the outer area is 340. W/(m2 K).  Calculate the area required. (SOLUTION)
  8. (based on Geankoplis 3rd edition 4.9-4) Hot oil at a flow rate of 3.00 kg/s (heat capacity Cp=1.92 kJ/(kg K)) enters an existing counterflow exchanger at 400.K and is cooled by water entering at 325 K (under pressure) and flowing at a rate of 0.70 kg/s.  The overall heat-transfer coefficient is 350. W/(m2 K) and the heat-transfer area is 12.9 m2.  Calculate the heat-transfer rate and the exit oil temperature. (SOLUTION)
  9. A countercurrent, double-pipe heat exchanger (inner heat transfer area = 42.6 m2, overall heat-transfer coefficient based on the area given = 340. W/(m2 K)) was designed to cool a vegetable oil (mean heat capacity = 5.62 kJ/(kg K), flow rate = 5.3 kg/s) from 120.oC to 85oC using city water as the cooling fluid. The city water is supplied at a temperature of 18oC. (SOLUTION)
    1. What is the outlet temperature of the city water for the conditions given?
    2. After some years of use we know that the heat exchanger will become fouled. If we assume that the water temperatures (both inlet and outlet) and all flow rates do not change, what will be the new overall heat transfer coefficient and outlet temperature of the oil after fouling? The ratio of inner to outer diameter for the inside pipe of the heat exchanger is 0.887.
    3. How could we adjust the operating conditions of the heat exchanger to prevent this degradation of performance of the unit?

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