2010 International Conference on Digital Manufacturing & Automation
Experimental Study on Heat Dissipation Performance of Forced Convector with U Shaped Fin-Tube
Xiaozhou Wu, Jianing Zhao School of Municipal and Environmental Engineering, Harbin Institute of Technology,Harbin, China Email:
[email protected] Abstract—Forced convector, which is one of the low temperature heating end users, not only high efficient but also conveniently adjustable, fits for low temperature metering heating system which can raise energy efficiency. So in this paper, in order to convenient for engineering application of forced convector, heat dissipation calculation method and heat dissipation characteristic equation are put forward. Heat dissipation performances of forced convector were studied with the two parameters of heat transfer coefficients and mean temperature differences when inlet water temperature is from 45 to 60 and water flow rate is from 50 kg/h to 170 kg/h. Experimental results show that: the heat transfer coefficients are almost independent of the mean temperature difference under constant water flow rate, but have significant exponential relationship with variable water flow rate. The final calculation results of heat dissipation characteristic equation of forced convector are closed to experimental data. Keywords-forced convector ； U shaped fin-tube ； heat dissipation calculation method; heat dissipation characteristic equation
Although some researchers have studied heat dissipation performance of U shaped fin-tube under natural air convection [9], the heat dissipation performance under forced air convection is lack of relative research in the world. So in this paper, in order to convenient for its engineering application, experimental studies were made on heat dissipation performances of forced convector under forced air convection. II. EXPERIMENTAL METHOD A. Measurement Apparatus The measurement of heat dissipation performance of forced convector is carried out on hot water test board for radiators and convectors, which was built on the basis of international standard (Code: ISO 3147—3150), as shown in Fig.1.
boiler
I. INTRODUCTION
heater radiator or convector
Recently, heat metering, as one of the most important part of energy conservation in heating buildings in China, is paid great attention to and vigorously supported by Chinese government, and will be gradually popularized in northern heating cities. At the same time, the renewable technology such as heat pumps and solar panels that allow us to use the earth’s natural energy to heat our water, are more easily available and more viable, so the modern low temperature heating systems are used more and more in the world [1-3]. So as to raise the efficiency of present energy and meet the requirements of heat metering, the low temperature heating end users should be required not only high efficient but also conveniently adjustable. Forced convector is one of the suitable low temperature heating end users, named heating fan coil in China and fan convector in Europe. Forced convector has short launch-time, easy to control, convenient to adjust and can use many low temperature heat sources, and is gradually adopted in low temperature heating systems [4-6]. Although forced convector is developed from traditional fan-coil which has mature technique, in order to meet the requirement of heating system it has big difference in structure, such as single-row U shaped fin-tube instead of multi-row snake shaped, small air volume fan instead of large air volume, no condensation-plate, and so on, resulting in great change in its heat dissipation performance [7,8]. 978-0-7695-4286-7/10 $26.00 © 2010 IEEE DOI 10.1109/ICDMA.2010.382
supply air
water tank
supply water pump
return water
closed chamber
electric switching valve
refrigerator
balance
water tank
return air
Fig.1 Heat dissipation of radiator or convector measurement system
B. Forced Convector The structure of forced convector with U shaped fin-tube is shown in Fig.2, its size is 800 × 112 × 400 (mm), and main heating component is fin-tube, which consists of L shaped aluminum fin and U shaped brass pipe. air outlet water inlet
air outlet fin-tube
water outlet U shaped fin-tube
cross-flow fan
air inlet impeller Fig.2 Structure of forced convector with U shaped fin-tube
motor
705 706
C. Measurement Method After the test board operating in a stable state, the measurement parameters are recorded every 10 minutes for 6 times, which includes indoor air temperature, inlet air temperature, outlet air temperature, water flow rate, inlet water temperature and outlet water temperature. Substituting water flow rate, inlet water temperature and outlet water temperature for heat dissipation calculation equation, we can obtain the heat dissipation of forced convector under a certain experimental condition. The heat dissipation calculation equation is as follows.
Q = cw ⋅Gw ⋅(tw,in −tw,out )
velocity is about 1.18m/s when fan under high rotation speed。
B. Mean Temperature Difference of Forced Convector with U Shaped Fin-tube The flow pattern of U shaped fin-tube is cross flow with both passes unmixed, as shown in Fig.4.
MP2
MP3
MP4
MP5
MP6
MP12
MP11
MP10
MP9
MP8
MP7
Fig.4 Flow pattern of U shaped fin-tube
Δt = ψ （ P, R)Δtm Δtm =
170 150 130 110 90 70 50
(3)
ln((tw,in − ta ,out ) /(tw,out − ta ,in ))
τmin tw,in −ta,in
R=
(4)
τmax τmin
(5)
Where
τmax = max[(tw,in −tw,out ),(ta,out −ta,in )]
(6)
τmin = min[(tw,in −tw,out ),(ta,out −ta,in )]
(7)
ψ （ P, R) is the factor of logarithm mean temperature difference Δtm (LMTD). Substituting inlet air temperature, outlet air temperature, inlet water temperature and outlet water temperature for the P and R calculation equation (4) and (5), we can obtain the values of P and R under different heating conditions, as shown in Tab.2. Tab.2 Values of P and R under different heating conditions Gw ( kgh-1) 170 150 130 110 90 70 50
Tab.1 Outlet water temperatures and outlet air temperatures Gw ( kgh-1)
(tw,in − ta ,out ) − (tw,out − ta ,in )
P=
A. Outlet Water Temperatures and Outlet Air Temperatures The outlet water temperatures and outlet air temperatures are shown in Tab.1, when inlet water temperature is from 45 to 60 and water flow rate is from 50 kg/h to 170 kg/h. tw,in =50℃ tw,out ta,out (℃) (℃) 44.45 28.24 43.99 27.79 43.23 27.47 42.66 26.91 40.87 26.66 39.10 26.30 35.68 25.39
（2）
Where
EXPERIMENTAL DATA PROCESSING
tw,in=55℃ tw,out ta,out (℃) (℃) 48.55 29.90 48.00 29.44 47.18 28.99 46.35 28.37 44.15 28.02 42.06 27.57 38.35 26.66
ta,in
ta,in
The mean temperature difference calculation equation is following [10]:
Fig.3 Layout of outlet air temperature measurement points (MP)
tw,in=60℃ tw,out ta,out (℃) (℃) 52.59 31.38 52.01 30.82 51.16 30.30 50.08 29.93 48.14 29.26 45.89 28.62 41.56 27.60
tw,out
（1）
MP1
ta,out tw,in
tw,out
Where Q is the heat dissipation of forced convector, W. cw is the specific heat of hot water, 4.2×103Jkg-1.k-1. Gw is the water flow rate, kgh-1. tw,in is the inlet water temperature and tw,out is the outlet water temperature, ℃. Water flow rate Gw is measured by weighing scale (measurement precision is 0.5%), inlet water temperature tw,in, outlet water temperature tw,out, and indoor air temperature ta are all measured by standard platinum thermometer (measurement error is ±0.1℃). Outlet air temperature ta,out measurement layout is shown in Figure 3, where the outlet is divided into 12 rectangles with equal area, and the center of rectangle is the measurement point. Twelve thermocouples (measurement error is ±0.1℃) are placed at the 12 measurement points to measure air temperature. At the same time, inlet air temperature ta,in is often measured by one thermocouple which lies in the center of the air inlet. Generally, all measurements are carried out when fan is under high rotation speed, and the energy balance between air side and water side was within 5%.
III.
ta,out
tw,in
tw,in=60℃ P R 0.17 1.95 0.19 1.73 0.21 1.50 0.23 1.29 0.28 1.01 0.27 1.21 0.25 1.74
tw,in=55℃ P R 0.17 1.95 0.19 1.73 0.21 1.50 0.23 1.30 0.29 1.02 0.28 1.22 0.25 1.73
tw,in =50℃ P R 0.17 1.95 0.19 1.73 0.21 1.51 0.23 1.30 0.28 1.02 0.28 1.20 0.25 1.74
tw,in =45℃ P R 0.18 1.93 0.19 1.75 0.21 1.50 0.23 1.31 0.28 1.03 0.27 1.20 0.25 1.73
Table 2 shows that, the values of P and R changes only a little under constant water flow rate. Looking up （ P, R ) : the reference [10], we can obtain the values of ψ （ P, R)Δtm ≈ Δtm , ψ （ 0.17 ~ 0.29,1.01~1.95) ≈ 0.99 , so Δt = ψ thus the flow pattern of U shaped fin-tube can be considered as counter flow. Since the ratio of maximum to minimum for difference between mean water air temperatures is less than 1.7, the Δtm can changed to be the algorithms mean temperature difference Δta , as follow:
tw,in =45℃ tw,out ta,out (℃) (℃) 39.82 26.57 39.68 26.46 39.23 25.90 38.87 25.45 37.21 25.14 35.90 24.77 32.96 24.04
Note: indoor air temperature ta is kept being about 18℃, and inlet air temperature ta,in is kept being about 17℃ too. At the same time, air
707 706
（8）
It is considered that the indoor air temperature is one of the most important parameters for heating system designer and user, so in this paper, indoor air temperature ta is used instead of average of air temperature (ta ,in + ta ,out ) / 2 , as follow:
Δ t a′ = I V.
t w ,in + t w ,out 2
-1
2
t +t − a,in a,out 2
Gw=170kg/h Gw=150kg/h Gw=130kg/h Gw=110kg/h Gw=90kg/h Gw=70kg/h Gw=50kg/h
400
-2
tw,in +tw,out
heat transfer coefficient K( wm K )
Δtm ≈Δta =
− ta
（9）
300
20
RESULTS AND DISCUSSION
26
28
30
32
34
36
38
40
'
Effect of Mean Temperature Difference and Water Flow Rate on Heat Transfer Coefficient Heat transfer equation and heat transfer coefficient calculation equation of forced convector are following:
K=
24
mean temperature difference △ ta( ℃ )
A.
Q = KF Δ t
22
Fig.6 Effect of mean temperature difference on heat transfer coefficient
（10）
Q F Δt
(11)
-2 -1
average heat transfer coefficient Kp (Wm k )
Where Q is the heat transfer quantity which is equal to heat dissipation of forced convector, W. F is the heat transfer surface of forced convector, F=0.128m2. Δt is the mean temperature difference, ℃. K is the heat transfer coefficient of forced convector, Wm-2k-1 Substituting inlet water temperature, outlet water temperature and water flow rate for equation (1), we can obtain the heat dissipation or heat transfer quantity Q of forced convector under different heating conditions. Meanwhile, substituting the inlet air temperature, outlet air temperature, inlet water temperature and outlet water temperature for the mean temperature difference calculation equation (8) and (9), we can obtain the mean temperature differences Δta and Δta′ under different heating conditions. Finally, substituting these heat transfer quantities and mean temperature differences for heat transfer coefficient calculation equation (11), we can obtain the heat transfer coefficients of forced convector, as shown in Fig.5 and Fig.6.
Both Figure 5 and Figure 6 show that, heat transfer coefficients are almost independent of the mean temperature difference Δta and Δta′ under constant water flow rate, when inlet water temperature is from 45 to 60 and water flow rate from 50 kg/h to 170 kg/h. It is almost because that both inside and outside convective heat transfer coefficients change a little under constant air velocity and constant water flow rate. So we can obtain the average of these heat transfer coefficients KP under the same water flow rate by accumulating these values and dividing by sum, as shown in Fig.7. 400
mean temperature difference Δta′ mean temperature difference Δta 350
300
250
200 40
60
80
100
120
140
160
180
water flow rate Gw (kg/h) Gw=170kg/h Gw=150kg/h Gw=130kg/h Gw=110kg/h Gw=90kg/h Gw=70kg/h Gw=50kg/h
-2
-1
heat transfer coefficient K( Wm K )
500
400
Fig.7 Effect of water flow rate on average of heat transfer coefficient
Figure 7 shows that average of heat transfer coefficients KP have significant exponential relationship with water flow rate when water flow rate is from 50 kg/h to 170 kg/h, and quickly increases at the point of Gw =110kg/h. It is almost because that the water flow parameter Reynolds number is about 2300 when the water flow rate is 110kg/h, so the water flow pattern is in laminar region when the water flow rate is less than 110kg/h, and in transition or turbulence region when the water flow rate is more than 110kg/h. From reference (11), the heat transfer coefficient K can be in expression of a function of the mean temperature difference and water flow rate, as follow:
300
18
20
22
24
26
28
30
32
34
mean temperature difference △ t a( ℃ )
Fig.5 Effect of mean temperature difference on heat transfer coefficient
708 707
K = K (Δ t , Gw ) = aΔt b Gwc
This study was supported by the National key Technologies R&D Program in the 11th Five-Year Plan of China (Grant number 2006BAJ01A04).
Where a, b and c are the characteristic coefficients. Since heat transfer coefficient is almost independent of the mean temperature difference, the heat transfer coefficient K calculation equation (12) can be changed to a function only of the water flow rate, as follow:
⎧⎪a1G K (Δt , Gw ) = ⎪⎨ ⎪⎪a2Gwc2 ⎩ c1 w
50 ≤ G ≤ 110
REFERENCES [1]
（13）
110 ≤ G ≤ 170
B.
Heat dissipation characteristic equation Substituting the heat transfer coefficient K calculation equation (13) for heat transfer quantity calculation equation （ 10 ） ,we can obtain the heat dissipation characteristic equation, as follow:
⎧⎪ A1ΔtGwc1 Q = ⎪⎨ ⎪⎪ A2ΔtGwc2 ⎩
ACKNOWLEDGMENT
（12）
50kg/h ≤ G ≤ 110kg/h 110kg/h ≤ G ≤ 170kg/h
[2]
[3] [4] [5]
（14） [6]
Where A is the comprehensive characteristic coefficient, A=aF Substituting the heat dissipation Q, mean temperature difference Δt and water flow rate Gw for equation (14), we can obtain the values of comprehensive characteristic coefficient A and equation (14) calculation relative error, as shown in Tab.2.
[7]
[8]
Tab.2 Values of comprehensive characteristic coefficient A and
[9]
equation (14) calculation relative error Mean temperature difference
Δtl Δ ta
Characteristic coefficients A1=11.372 c1=0.273 A2=28.096 c2=0.083 A1=10.472 c1=0.258 A2=27.024 c2=0.059
equation determination coefficient R2 0.997 0.992 0.992 0.994
Maximum calculation relative error（%） 3.67 2.47 3.73 2.70
[10] [11]
Note: calculation relative error is the ratio of equation (14) calculation results to experiment data.
Table 2 shows that the calculation results of the heat dissipation calculation equation (14) are closed to experimental data, equation determination coefficients are all morn than 0.99, and maximum calculation relative errors are all less than 4%. V. CONCUSIONS After experimental study above, the conclusions can be got as follows: Heat transfer coefficients of forced convector with U shaped fin-tube are almost independent of the mean temperature difference under constant water flow rate, but it has significant exponential relationship with the water flow rate under variable water flow rate, when inlet water temperature is from 45 to 60 and water flow rate is from 50 kg/h to 170 kg/h. Calculation results of heat dissipation characteristic equation of forced convector are closed to experimental data.
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