The specifi c fl ow exergies of milk into and out of the heat exchanger are
( ) ( )
( ) ( ) ( )
= − − −
= − − + × −
=
c,i m,i m0 m0 m,i m0
503.7 100.7 [kJ/kg] 25 273 [K] 1.5276 0.3534 [kJ/kgK]
53.1 kJ/kg
h h T s s
y
= =
c,o m0 0 (The reference temperature is the outlet temperature of the milk.)
y y
During heat exchange, the heat loss from the steam equals the heat gain by the milk. That is,
(
−)
=(
−)
c c,o c,i h h,i h,o
m h h m h h
From Equation 7.21, the energy effi ciency of the heat exchanger is
( )
( )
η −
= × =
−
c c,o c,i
En
h h,i h,o
100% 100%
m h h
m h h
From Equation 7.22, the exergy effi ciency of the heat exchanger is
( )
( )
( )
( )
= − ×
−
× −
= ×
× −
=
c c,o c,i
Ex
h h,i h,o
100%
1000 [kg/h] 53.1 0 [kJ/kg]
184.6 [kg/h] 637.7 63.87 [kJ/kg] 100%
50.13%
m m
y y
h y y
It can be seen from the above example that although the energy effi ciency of a heat exchanger is 100% if the heat loss is negligible, the exergy effi ciency is only 50.13%. This means that the quality of the energy into the heat exchanger is degraded through the heat exchanger.
7.4 ENERGY CONSERVATION TECHNOLOGIES
vibration, and fl uid vibration. In some cases, two or more techniques may be used simultaneously (Zimparov, 2002). Heat transfer enhancement techniques can be used to
Improve the performance of an existing heat exchanger
•
Reduce the size and cost of a new heat exchanger
•
Increase the energy and exergy effi ciencies of the heat exchangers, thus
•
reducing operating cost
The heat transfer rate of a pipe may be limited by the inside convective heat transfer coeffi cient, outside convective heat transfer coeffi cient, or the heat conduction of the pipe wall. Enhancement of heat transfer means to increase the heat transfer coeffi -cients. Applications of heat transfer techniques should assess the limiting factor on heat transfer.
Example 7.6
Following Examples 7.2 and 7.5, if the inside convective heat transfer coeffi cient or the outside convective heat transfer coeffi cient is doubled, what will be the increase in the overall heat transfer coeffi cient?
Solution 7.6
From Example 7.2, the overall heat transfer coeffi cient before enhancement is Ui = 92.53 W/m2 °C.
1. If the inside convective heat transfer coeffi cient is doubled from 100 to 200 W/m2 °C, the overall heat transfer coeffi cient is determined by
( )
= + +
×
i
0.0175 0.0125ln
1 1 0.0125 0.0125
200 45 1000 0.0175
U
Thus, the new overall heat transfer coeffi cient is Ui = 172.18 W/m2 °C. The overall heat transfer coeffi cient is increased by 86% from 92.53 to 172.18 W/m2 °C.
2. If the outside convective heat transfer coeffi cient is doubled from 1000 W/m2 °C to 2000 W/m2 °C, the overall heat transfer coeffi cient is determined by
( )
= + +
i ×
0.0175 0.0125ln
1 1 0.0125 0.0125
100 45 2000 0.0175
U
Thus, the new overall heat transfer coeffi cient is Ui = 95.69 W/m2 °C. The over-all heat transfer coeffi cient is increased by 3.4% from 92.53 to 95.69 W/m2 °C.
From the above example, we can see that the enhancement of heat transfer should be applied to the side with dominant thermal resistance or a smaller heat transfer coeffi cient.
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EXAMPLE 7.7
Following Examples 7.2 through 7.6, enhanced heat transfer pipes with double inside convective heat transfer coeffi cient are used to replace the pipes in the heat exchanger, and other conditions remain the same. Exergy effi ciency can be improved by reducing steam temperature. What could be the steam temperature and exergy effi ciency for the new heat exchanger? The properties of the fl uids are given in Table 7.5. The reference temperature, T0 = 25°C.
Solution 7.7
From Example 7.4, the total inside area of the pipes of the heat exchanger is Ai = 30.8 m2.
From Example 7.5, the overall heat transfer coeffi cient of the heat exchanger with the enhanced heat transfer pipes is Ui = 172.18 W11/m2 °C.
Using Equation 7.14, for the same heating load using the heat exchanger with the enhanced heat transfer pipes, the temperature difference between steam and milk can be reduced to
∆ = = = °
′ ° ×
LMTD 2 2
i i
111,467 [W]
21.02 C 172.18 [W/m C] 30.8 [m ]
T q
U A
Using the heat exchanger with the enhanced heat transfer pipes, the temperature difference decreases from 39.08°C to 21.02 °C.
Using Equation 7.1, we can fi nd the steam temperature for the heat exchanger with the enhanced heat transfer pipes:
= = °
h1 h2 122 C
T T
The specifi c fl ow exergies of saturated steam into the heat exchanger and satu-rated water out of the heat exchanger at 122°C are
( ) ( )
( ) ( ) ( )
= − − −
= − − + × −
=
s s s0 s0 s s0
2709.6 2545.4 [kJ/kg] 25 273 [K] 7.1088 8.5794 [kJ/kgK]
602.4 kJ/kg
h h T s s
y
TABLE 7.5
Properties of Fluids for Example 7.7
Temperature Enthalpy (kJ/kg) Entropy (kJ/kgK)
Saturated steam 122 2709.6 7.1088
Saturated steam 25 2545.4 8.5794
Saturated water 122 490.97 1.4405
Saturated water 25 100.7 0.3534
Milk 121 503.7 1.5276
Milk 25 100.7 0.3534
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( ) ( )
( ) ( ) ( )
= − − −
= − − + × −
=
w w w0 w0 w w0
490.97 100.7 [kJ/kg] 25 273 [K] 1.4405 0.3534 [kJ/kgK]
66.31 kJ/kg
h h T s s
y
At 122°C, the latent heat of steam increases from 2174 kJ/kg to 2219 kJ/kg. The mass fl ow of steam through the heat exchanger is decreased to
= = =
h ∆
v
111, 467 [W]
180.8 kg/h 2,219 [kJ/kg]
m q h
From Example 7.5, the specifi c fl ow exergies of milk into and out of the heat exchanger are
m1=53.1 kJ/kg y
and
= =
2 0 0
m m
y y
( )
(× − )
= =
× −
Ex
1000 [kg/h] 53.1 0 [kJ/kg]
54.78%
180.8 [kg/h] 602.4 66.31 [kJ/kg]
h
Using the heat exchanger with the enhanced heat transfer pipes, the exergy effi -ciency will be increased by 9.3% from 50.13% to 54.78%.
Enhanced heat transfer surfaces have been successfully used to obtain more compact and effi cient heat exchangers (Wang et al., 2000a,b). Several enhanced heat transfer rough surface confi gurations such as spirally fl uted pipes, as shown in Figure 7.4, have been widely used to enhance the convective heat transfer of a single phase fl ow, with an increase of about 50% in the inner convective heat transfer coeffi cient (Wang et al., 2000a). Swirl fl ow devices such as a twisted tape insert are also used to enhance the surface protuberances (Zimparov, 2002). A gas usually has lower convective heat transfer coeffi cients than a liquid. Therefore,
FIGURE 7.4 Schematic structure of the spirally fl uted tube. (Reprinted from Wang et al., Energ. Convers. Manage., 41: 993–1005, 2000a. With permission.)
β
p e
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methods should be developed to reduce the thermal resistance or increase the con-vective heat transfer coeffi cient on the gas side.
Fluid foods including both Newtonian and non-Newtonian fl uids such as fruit and vegetable juices and milk are often subjected to thermal treatment inside heat exchangers. The heat exchangers must have a high heat transfer rate, low friction losses, and easy cleaning and sanitizing. The shell and tube heat exchanger equipped with helically corrugated walls as shown in Figure 7.1 can meet these requirements (Rozzi et al., 2007). Helically corrugated tubes are particularly effective in enhancing convective heat transfer for Reynolds number ranging from about 800 to the limit of the transitional fl ow regime (Rozzi et al., 2007).
Enhanced heat transfer surface confi gurations have also been developed to improve the heat transfer with phase changes of condensation and evaporation (Wang et al., 2000a,b). The heat transfer coeffi cient of a turbulent fl ow in rough tubes is as high as 250% of that in smooth tubes. The performance of a condenser with enhanced heat transfer tubes can increase up to 400%. However, the pressure drop of a fl uid fl owing through the rough surface of the enhanced heat transfer tubes may be signifi -cantly increased depending on the confi guration of the enhanced heat transfer sur-face (Zimparov, 2002).
7.4.2 ENERGY CONSERVATIONTHROUGH CLEANINGOF FOULING LAYER
Fouling and cleaning of heat exchangers are serious industrial problems. It was reported that fouling caused an increase of up to 8% in the energy consumption in fl uid milk plants and about 21% of the total energy was used to clean milk pasteuri-zation plants (Ramirez et al., 2006). Although the chemistry of the fouling process is still not understood, the complex interaction between the chemistry and the fl uid mechanics of heat exchangers makes it diffi cult to deal with the fouling problem (Fryer and Belmar-Beiny, 1991; Visser and Jeurnink, 1997). The dairy industry has been confronted with fouling on the metal surface of plate heat exchangers. In the dairy industry, fouling deposits are mainly caused by heat-sensitive whey proteins and heat-induced precipitation of calcium phosphate salts. Fouling may cause an increased pressure drop, heat transfer resistance, and microbial growth at the fouling places (Visser and Jeurnink, 1997; Changani et al., 1997).
If a fouling layer is generated on the inside wall of pipes, heat transfer will need to overcome four layers of resistance in a series: inside boundary layer, fouling layer, pipe wall, and outside boundary layer. The overall resistance is thus deter-mined by
t i f w o
R =R +R +R +R (7.23)
The overall heat transfer coeffi cient (based on the inside area) can be calculated using
f 0 w0
fi wi
fi fi fi fi f w w0 w0
ln ln
1 1 1
2 2
r r
r r
U A h A k L k L h A
⎛ ⎞ ⎛ ⎞
⎝ ⎠ ⎝ ⎠
= + + +
π π
(7.24) or
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f 0 w0
fi fi fi wi fi
fi f f w w0 w0
ln ln
1 1
i
r r
r r r r r
U h k k h r
⎛ ⎞
⎛ ⎞
⎝ ⎠
⎝ ⎠
= + + + (7.25)
Example 7.8
Following Examples 7.2 through 7.7, if a 1 mm thick fouling layer at a thermal con-ductivity of 0.5 W/m°C is formed on the inside wall of the pipe, what will be the overall heat transfer coeffi cient? What would be the steam temperature and exergy effi ciency of the heat exchanger after fouling occurs?
Solution 7.8
From Example 7.4, the total inside area of the pipes of the heat exchanger is Ai = 30.8 m2.
The overall heat transfer coeffi cient (based on the inside area) after fouling can be determined by Equation 7.25:
( ) ( )
= + + +
fi ×
0.0125 0.0175
0.0115ln 0.0115ln
1 1 0.0115 0.0125 0.0115
100 0.5 45 1000 0.0175
U
The overall heat transfer coeffi cient is thus
= 2°
fi 78.98 W/m C U
Therefore, due to the fouling, the overall heat transfer coeffi cient is decreased from 92.53 W/m2 °C (from Example 7.2) to 78.98 W/m2 °C.
Due to the formation of a fouling layer, the inside surface area is reduced to
= ⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞
= × ⎜⎝ ⎟⎠
=
2 fi wi fi
wi
2 2
2
0.0115 m 30.8 m
0.0125 m 26.1 m
A A r r
Due to the decrease in overall heat transfer coeffi cient and inside surface area, in order to supply the same amount of heat to milk, q = 111,467 W, the temperature difference between steam and milk should be increased to
∆ ′ = = = °
° ×
′
LMTD 2 2
i i
111,467 [W]
54.07 C 78.98 [W/m C] 26.1 [m ]
T q
U A
The temperature difference is increased from 39.08°C (from Example 7.3) to 54.07°C.
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Using Equation 7.1, the steam temperature for the heat exchanger with the enhanced heat transfer pipes is Th1′ =Th2′ =140.5 C° .
The enthalpy and entropy of steam at 140.5°C are given in Table 7.6. Using Equation 7.17, the specifi c fl ow exergies of saturated steam into the heat exchanger and saturated water out of the heat exchanger at 140.5°C are
( ) ( )
( ) ( ) ( )
ψ = − − −
= − − + × −
=
s s s0 s0 s s0
2733.9 2545.4 [kJ/kg] 25 273 [K] 6.9299 8.5794 [kJ/kgK]
680.05 kJ/kg
h h T s s
( ) ( )
( ) ( ) ( )
ψ = − − −
= − − + × −
=
w hw hw0 Tw0 sw sw0
589.13 100.7 [kJ/kg] 25 273 [K] 1.7391 0.3534 [kJ/kgK]
75.49 kJ/kg
At 140.5°C, the latent heat of steam is 2145 kJ/kg. The mass fl ow of steam through the heat exchanger is
= = =
h ∆
v
111, 467 [W]
187.1 kg/h 2,145 [kJ/kg]
m q h
From Example 7.5, the specifi c fl ow exergies of milk into and out of the heat exchanger are
1=53.1 kJ/kg ym
and
= =
2 0 0
m m
y y
( )
(× − )
= =
× −
Ex
1000 [kg/h] 53.1 0 [kJ/kg]
46.94%
187.1 [kg/h] 680.05 75.49 [kJ/kg]
h
The exergy effi ciency decreases by 6.4% from 50.13% to 46.94%.
TABLE 7.6
Properties of Fluids for Example 7.8
Temperature Enthalpy (kJ/kg) Entropy (kJ/kgK)
Saturated steam 140.5 2733.9 6.9299
Saturated steam 25 2545.4 8.5794
Saturated water 140.5 589.13 1.7391
Saturated water 25 100.7 0.3534
Milk 121 503.7 1.5276
Milk 25 100.7 0.3534
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7.4.3 ENERGY CONSERVATIONTHROUGH OPTIMIZATION OF HEAT EXCHANGER DESIGN
Traditional design of heat exchangers involves many trials by changing one variable at a time and using a trial–error or a graphical method to meet design specifi cations.
The design variables may include Inside heat transfer coeffi cient
•
Outside heat transfer coeffi cient
•
Temperature difference
•
Tube surface area
•
With the combination of exergy analysis and life cycle analysis, an exergy optimiza-tion of a heat exchanger can be obtained. There is a trade-off between exergy saving during operation and exergy consumption during construction of a heat exchanger (Cornelissen and Hirs, 1999; Unuvar and Kargici, 2004).
7.4.4 ENERGY CONSERVATIONTHROUGH HEAT
EXCHANGER NETWORK RETROFIT
Process integration technology for improving energy effi ciency has been widely used around the world. The fi nancial benefi t comes from both reduced energy costs and debottlenecking for increase in throughput. It can also reduce fl ue gas emission. Sys-tematic methods for the design of heat exchanger networks have been developed (Wang et al., 1990; Silva and Zemp, 2000; Smith, 2000). The network retrofi t usually starts by identifying the bottlenecking exchangers within an existing heat exchanger network structure using thermodynamic methods. To overcome the network pinch, a modifi cation in the network structure is required by relocation of an existing heat exchanger to a new duty or addition of a new exchanger or change of stream splitting arrangement.
However, it is not straightforward to identify the most appropriate structural modifi cation. The relationship among heat transfer coeffi cient, pressure drop, and exchanger area is complex. The retrofi t area target should be implemented as a nonlinear optimization problem to minimize the requirement for additional area.
Mathematical models are usually needed to identify the most benefi cial structural changes (Smith, 2000). The minimum temperature difference in heat exchangers can be optimized, and trade-off between the capital costs and the energy saving revenue can be determined by mathematical models (Wang et al., 1990). In addition, besides the increased heat transfer coeffi cients, pressure drop constraints due to the addi-tional heat exchanger area during retrofi t of heat exchanger networks should also be considered (Silva and Zemp, 2000).