Energy-Efficient Process Cooling Homework
1. Consider a 1 ft2 uninsulated tank at 50 F surrounded by plant air at 90 F. The
total thermal resistance of the metal tank and air film is 2 hr-ft2-F/Btu. Calculate
the annual reduction in cooling load (mmBtu/yr), cooling energy cost savings
($/yr), and simple payback (months) for adding R-6 insulation to the tank if the
cooling is provided by an air cooled chiller at a cooling cost of $10 /mmBtu and
the installed cost of the insulation is $2.00 /ft2.
2. Consider a system that heats 100 gpm of milk from 70 to 200 F then cools it to
38 F for packaging. The density of the milk is 8.32 lb/gal and the specific heat is 1
Btu/lb-F. The overall efficiency of the boiler system delivering the required heat
is 60% and the electrical power requirement of the air cooled chiller that delivers
the required cooling is 1.2 kW/ton. Calculate the reduction in the rate of boiler
fuel use (Btu/hr) and chiller electrical power (kW) if a 70% effective heat
exchanger where added between the heating and cooling operations. If the
overall conductance of the heat exchanger is 12 Btu/hr-ft2-F, calculate the
required surface area (ft2) of the heat exchanger.
3. Consider cross flow heat transfer between extruded plastic and cooling water.
Currently the volume flow rate of water is 2 gpm and the mass flow rate of
plastic is 30 lb/min. The density of water is 8.32 lb/gal and the specific heat is
1.00 Btu/lb-F. The specific heat of plastic is 0.26 Btu/lb-F. The effective UA is
1,000 Btu/hr-F. The temperature of the extruded plastic entering the heat
exchanger is 200 F and the temperature of chilled water entering the heat
exchanger is 40 F. Calculate the rate of heat transfer (Btu/hr), and the required
entering water temperature if the mode of heat transfer were converted from
cross flow to counter flow.
4. A continuous cooling process requires 20 tons of 60 F chilled water and returns
the water at 68 F. The water is supplied by a water-cooled chiller using 0.65
kW/ton of process cooling. Using binned weather data for Boulder, CO shown
below determine annual chiller electricity use savings (kWh/yr) from operating
the cooling tower operating at 3 gpm/ton instead of the chiller whenever
possible.
StrTemp
========
95
90
85
80
75
70
EndTemp
========
99
94
89
84
79
74
T(F)
========
95.7
92.2
87.9
82.2
77
72.4
Twb(F)
========
61.7
59.8
59.4
58.1
56.9
54.7
hrs1-24
========
22
64
147
382
440
362
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-5
-10
69
64
59
54
49
44
39
34
29
24
19
14
9
4
-1
-6
67.9
62.5
57
52.1
47.4
43
37.5
32.1
27.7
23.1
17.7
12.1
7.2
2.8
-1.9
-6.6
53.7
51.7
47.1
43.2
40.1
37.2
34.2
30.9
28
25
21.2
17.4
14.3
11.3
8.3
5.4
630
907
698
754
620
775
834
717
542
320
201
130
89
74
37
15
5. A cooling tower with a design flow rate of 3 gpm/ton-chiller capacity has a
single-speed 40-hp fan that cycles on and off to deliver cooling water at a setpoint temperature of 90 F. When running, the fan is 80% loaded and 90%
efficient. The wet-bulb temperature is 65 F and the temperature range of the
cooling water is 8 F. Determine the fan power savings (kW) from adding a
variable frequency drive to the cooling tower fan and modulating fan speed to
achieve the desired set-point temperature.
6. A cooling tower is sized to cool condenser water from an 80-ton chiller plant,
with a design flow rate of 3 gpm/ton-chiller capacity. The cooling tower
operates 5,000 hours per year. The water utility charges $2.00 per ccf for water
discharged to sewer, and assumes that all water entering the plant is discharged
to sewer. Assuming the evaporation rate is 0.75%, calculation the annual sewer
cost savings ($/yr) from applying for a “sewer exemption” for water evaporated
from the cooling tower.
7. A critical, 5,000 hour per year, cooling load in a facility with aging chillers is 400
tons. The company is considering replacing the two 400-ton standard-efficiency
water-cooled constant-speed chillers with two 400-ton high-efficiency watercooled variable-speed chillers. Chiller performance is given by the “StandardEfficiency” and High-Efficiency” performance maps in the text. The chillers
operate at the coldest possible condensing water temperature. Determine the
annual electricity savings (kWh/yr) from replacing the current constant-speed
chillers with variable-speed chillers if both chillers in each system were operated
at 50% of full load.
8. For this problem consider a single plant visit. For this plant, the avoided cost of
demand is $14 /kW-month and the avoided cost of energy is $0.02 /kWh.
Compressed air to the plant is supplied by a 75-hp air-cooled rotory-screw
compressor with a 93% efficiency motor that generates 4 scfm/hp. The
compressor runs in load/unload mode and draws 60% of full load power when
unloaded. The plant and compressor run 5,000 hr/yr. A production line uses 10
copper tubes with nominal diameters of 1/8-inch and inside diameters of 0.125
inch to blow moisture off a product. Air-saver nozzles that consume 10 scfm of
compressed air are found to perform just as well as the open tubes. Calculate
the annual cost savings from installing air-saver nozzles on the open tubes.
Assume the compressed air pressure is 100 psig at the tubes and ambient
pressure is 15 psia.