CHE 441 ______

LAST NAME, FIRST

Problem set #7

1. A concentric tube heat exchanger uses water (Cp = 4178 J/kg.K) , which is available at 15oC to cool ethylene glycol (Cp = 2650 J/kg.K) from 100 to 60oC. The water flow rate is 0.5 kg/s and glycol flow rate is 1.0 kg/s. Determine the effectiveness of the exchanger.

2. (Ref. 1) A single-pass shell-and-tube heat exchanger contains 80 steel tubes (k = 25 Btu/hr×ft×oF). The ID of the tubes is 0.732 in., and the OD is 1.0 in. The shell side of the exchanger contains saturated steam at 330oF, and water passes through the tubes. The unit is designed with sufficient tube area to permit 15,000 gph of water to be heated from 70 to 140oF. In the course of this design, a dirt coefficient hd of 1000 Btu/hr×ft2×oF was assumed to allow for scaling on the water side of the tube. The film coefficient for the steam is 2000 Btu/hr×ft2×oF. The film coefficient for the water is 600 Btu/hr×ft2×oF. No safety factor other than the one scale value was used in carrying out the exchanger design. Estimate the temperature of saturated steam which must be used when the exchanger is new (i.e., no scale present) if the water enters the unit at a rate of 15,000 gph and is heated from 70 to 140oF. Cp of water = 1Btu/lb×oF× 1ft3 = 7.48 gal. Water density = 62.3 lb/ft3.

= = + + + +

3. (Ref. 2) Hot oil at a flow rate of 3.00 kg/s (Cp = 1.92 kJ/kg×oK) enters an existing counter flow exchanger at 400oK and is cooled by water entering at 325oK and flowing at a rate of 0.70 kg/s. The overall U = 350 W/m2×oK and area A = 12.9 m2. Calculate the heat transfer rate and the exit oil temperature.

4. (Ref. 2) In a single-pass counterflow heat exchanger, 10,000 lb/hr of water enters at 60oF and cools 20,000 lb/hr of oil having a specific heat of 0.50 Btu/lb×oF from 200oF to 150oF. If the overall heat transfer coefficient is 50 Btu/hr×ft2×oF, determine the surface area required.

5. Ethylene glycol and water, at 80 and 10°C, respectively, enter a shell-and-tube heat exchanger for which the total heat transfer area is 15 m2. With ethylene glycol and water flow rates of 3 and 5 kg/s, respectively, the overall heat transfer coefficient is 800 W/m2×K. Ethylene glycol: cp = 2470 J/kg×K, water: cp = 4180 J/kg×K. The effectiveness of this shell-and-tube heat exchanger can be determined from the following expression

e = 2

a) Determine the effectiveness of the heat exchanger.

b) If e = 0.8 determine the outlet temperature of water.

6. Run the program Microplant as a Novice Troubleshooter and turn in the last display of the program.

7. Estimate the temperature of saturated steam that is required in the shell of a new (i.e. no scale deposit) single-pass shell-and-tube heat exchanger when water on the tube side, for either the new design or the original design that included scale formation, is heated from 21 to 65.5oC at a flow rate of 15.75 kg/s. The exchanger contains 60 steel tubes, each with an inside diameter of 0.0186 m and an outside diameter of 0.0254 m. The unit is designed with sufficient tube area to permit the heating of the water as specified. In the original design, an hd of 8250 W/m2∙K was used to allow for scaling on the water side of the tube. The film coefficient for the steam was taken as 11,400 W/m2∙K, and the temperature of the saturated steam required to account for the heating of the water was found to be 153.3oC. No scaling factor for the shell side was used in the original design, and it can be neglected in the new design.

Data: cp,w = 4179 J/kg×K, mw = 0.00063 Pa×s, rw = 991 kg/m3, kw = 0.641 W/m×K, ksteel = 45 W/m×K. The inside heat transfer coefficient can be estimated from

hi = (0.023)Re0.8Pr1/3

8. The rate of fermentation of glucose (A) to ethanol (B) by Saccharomyces cerevisiae (C) at 303oK is given by:

- rA = k

where k = 1.53´10-3 / s, = 93 kg/m3, and CM = 1.7 kg/m3.

The cell yield is 0.06 kg Saccharomyces cerevisiae produced per kg of glucose consumed. The ethanol yield is 0.47 kg ethanol/kg of glucose consumed.

a) Evaluate the time required for 95 percent conversion of glucose in a batch reactor with an initial charge of 10 kg/m3 glucose and initial cell concentration of 0.01 kg/m3 in a 10-m3 batch reactor filled to 70 percent.

b) Determine the required flow rate to produce the same glucose conversion for a PFR of equal volume with the same glucose-feed concentration, but with 0.9 kg/m3 of Saccharomyces cerevisiae in the feed.

References:

(1) Peters and Timmerhaus, Plant Design and Economics for Chemical Engineers, Fourth Edition, McGraw Hill

(2) Incropera and DeWitt, Fundamentals of Heat Transfer.