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Heat exchanger
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Experimental Setup
Figure 1: Schematic Diagram for a Double pipe Heat Exchanger
Observed Data
Room temperature=28 ℃
Mass of empty bucket= 1.1 kg
Steam
Pressure
P psig
Number of
observation
Water Temperature ℃ Water Condensate
Inlet T1 Outlet T2 Volume
(L)
Time
(s)
Wight
with
bucket
(kg)
Time
(s)
5
01
29.5
50 5
20
1.4
20
02 45 6 1.4
03 43 8 1.45
04 40 11 1.3
10
01 53 6 1.3
02 44 8 1.4
03 40 11 1.3
04 38.5 12 1.4
15
01 44 10 1.6
02 40 12 1.5
03 38.5 13 1.43
04 39 13 1.3
Calculated Data
Length of the pipe, L= 7 ft 4 inch = 7.33 ft. = 2.234184 m.
Outer diameter of the pipe, Do=1.315 inch. = 0.0334 m.
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-11 pp 612]
Outside surface area, Ao = πDoL = 0.2344 m2.
Table 2: Calculated Data for Condensate
Steam
Pressure
P psig
Number of
Observation
Saturation
Temperature
Ts (℃)
Latent Heat
of
Condensation
𝜆s (kJ/kg)
Weight of
Condensate
(kg)
Mass Flow
rate of
condensate
Mc (kg/s)
Wall
Temperature
Tw (℃)
Film
Temperature
Tf (℃)
5
01
108.33
2234.35
0.2 0.01 74.04 82.6125
02 0.3 0.015 72.79 81.675
03 0.35 0.0175 72.29 81.3
04 0.2 0.01 71.54 80.7375
10
01
115.556
2215.61
0.2 0.01 78.403 87.69125
02 0.3 0.015 76.153 86.00375
03 0.2 0.01 75.153 85.25375
04 0.3 0.015 74.778 84.9725
15
01
121.11
2199.24
0.5 0.025 78.93 89.475
02 0.4 0.02 77.93 88.725
03 0.33 0.0165 77.555 88.44375
04 0.2 0.01 77.68 88.5375
Table 3: Calculated Data for Physical Properties at mean temperature
Steam
Pressure
P psig
Number of
Observation
Mean
Temperatue
Tm ℃
Density
ρm
(kg/m3)
Viscosity
𝜇m (kg/m.s)
Thermal
conductivity
km (W/m.oC)
Prandtl
number
5
01 39.75 992.375 0.00066 0.632488 4.38959
02 37.25 993.1625 0.00069 0.629338 4.63209
03 36.25 993.5125 0.00071 0.628078 4.72909
04 34.75 994.0375 0.000727 0.626188 4.87459
10
01 41.25 991.675 0.00063 0.634378 4.24409
02 36.75 993.1375 0.000697 0.628708 4.639367
03 34.75 994.0375 0.000727 0.626188 4.851567
04 34 994.3 0.000738 0.625243 4.931142
15
01 36.75 993.1375 0.000697 0.628708 4.639367
02 34.75 994.0375 0.000727 0.626188 4.851567
03 34 994.3 0.000738 0.625243 4.931142
04 34.25 994.2125 0.00074 0.625558 4.904617
Table 4: Calculated Data at Tm for water flowing for cooling
Steam
Pressure
P psig
Volume
of water
(m3)
Weight
of
Water
(kg)
Mass
Flow
Rate Mc
(kg/s)
Velocity
v (m/s)
Mass
Velocity
(kg/m2s)
Reynolds’
s number
Nre
Nusselt’s
Number
Water side
heat
transfer
coeffic-
ients,
hi
(W/m2.oC)
5
0.005 4.9619 0.24809 0.446429 444.6125 17989.48 90.88034 2144.802
0.006 5.959 0.29795 0.535714 533.9583 20668.11 103.2052 2423.543
0.008 7.9481 0.39741 0.714286 712.1953 26786.86 127.7905 2994.864
0.011 10.934 0.54672 0.982143 979.7861 35978.43 163.2838 3815.16
10
0.006 5.9501 0.2975 0.535714 533.1586 22592.87 107.9544 2555.368
0.008 7.9451 0.39726 0.714286 711.9265 27261.81 128.8574 3022.896
0.011 10.934 0.54672 0.982143 979.7861 35978.43 163.052 3809.746
0.012 11.932 0.59658 1.071429 1069.14 38664.22 173.564 4049.239
15
0.01 9.9314 0.49657 0.892857 889.9082 34077.26 154.0413 3613.693
0.012 11.928 0.59642 1.071429 1068.858 39249.19 174.8063 4084.387
0.013 12.926 0.6463 1.160714 1158.235 41886.24 185.0415 4317.011
0.013 12.925 0.64624 1.160714 1158.133 41793.39 184.4147 4304.554
Table 5: Calculated physical properties for condensate at film temperature
Steam
Pressure
P psig
Number of
Observation
Density
ρf
(kg/m3)
Viscosity
µf (kg/ms)
Thermal
conductivity
km (W/m.oC)
Condensation
heat transfer
coefficients,
ho (W/m2.oC)
5
01 969.9503 0.000387 0.673382 7940.977
02 970.5418 0.000393 0.672538 7834.615
03 970.7785 0.000395 0.672201 7793.283
04 971.1334 0.000399 0.671695 7732.522
10
01 966.7558 0.000366 0.674892 7872.231
02 967.8181 0.000377 0.674284 7699.565
03 968.2903 0.000382 0.674014 7626.602
04 968.4673 0.000384 0.673913 7599.802
15
01 965.633 0.000363 0.675868 7632.1
02 966.1051 0.000368 0.675463 7560.809
03 966.2821 0.00037 0.675311 7534.595
04 966.2231 0.000369 0.675362 7543.302
Table 6: Calculated Data for Experimental Heat Transfer Coefficient
Steam
Pressure
P psig
Number of
Observation
Rate of
heat
taken-up
by water,
Qw(kW)
Rate of heat
given-up by
steam,
Qc (kW)
Mean
rate of
heat
transfer,
Qm(kW)
Percent
Heat
Loss
(%)
Log mean
temperature
difference,
Tlm(oC)
Experimental
overall heat
transfer
Coefficient,
UOE
(W/m2 o
C)
5
01 21.22864 22.34347 21.786 4.989521 68.06627 1365.492
02 19.27639 33.51521 26.396 42.48464 70.79744 1590.595
03 22.39337 39.10107 30.747 42.72951 71.8688 1825.189
04 23.96112 22.34347 23.152 7.23994 73.45497 1344.669
10
01 29.18172 22.15612 25.669 31.7095 73.68247 1486.229
02 24.04306 33.23418 28.639 27.65561 78.58317 1554.766
03 23.96112 22.15612 23.059 8.14676 80.69217 1219.114
04 22.41112 33.23418 27.823 32.56604 81.47317 1456.889
15
01 30.05383 54.98105 42.517 45.33784 84.1519 2155.488
02 26.13941 43.98484 35.062 40.57178 86.25351 1734.219
03 24.27872 36.28749 30.283 33.09343 87.03246 1484.436
04 25.62528 21.99242 23.809 16.5187 86.77335 1170.562
Table 7: Calculated Data for theoretical heat transfer
Steam
Pressure
P psig
Number of
Observation
Theoretical
Overall heat transfer
coefficients,
UOT (W/m2.oC)
OTU
1
OEU
1
8.0
1
MV
5
01 1469.512 0.0007 0.00073 1.900883
02 1590.879 0.0006 0.00063 1.642897
03 1816.379 0.0006 0.00055 1.305147
04 2084.369 0.0005 0.00074 1.01162
10
01 1648.296 0.0006 0.00067 1.642897
02 1821.456 0.0005 0.00064 1.305147
03 2074.99 0.0005 0.00082 1.01162
04 2141.934 0.0005 0.00069 0.943597
15
01 2015.819 0.0005 0.00046 1.091771
02 2148.591 0.0005 0.00058 0.943597
03 2209.025 0.0005 0.00067 0.885068
04 2206.505 0.0005 0.00085 0.885068
Graphical Representation
1. Nusselt Number (NNu) vs. Reynold Number (NRe) on a logarithmic plot
Graph 1: Nusselt Number vs. Reynold Number at 5 psig steam pressure
Figure 2: Graphical Representation for NNu vs. NRe at 5 psig steam pressure
Graph 2: Nusselt Number vs. Reynold Number at 10 psig steam pressure
Figure 3: Graphical Representation for NNu vs. NRe at 10 psig steam pressure
10
100
1000
10000 100000
NN
u
NRe
Nusselt Number vs. Reynold Number at 5 psig steam pressure
10
100
1000
10000 100000
NN
u
NRe
Nusselt Number vs. Reynold Number at 10 psig steam pressure
Graph 3: Nusselt Number vs. Reynold Number at 15 psig steam pressure
Figure 4: Graphical Representation for NNu vs. NRe at 15 psig steam pressure
2. Water side heat transfer coefficient, hi vs. velocity on a logarithmic plot
Graph 1: Waterside heat transfer coefficient vs. inner pipe velocity at 5 psig steam pressure
Figure 5: Graphical Representation for hi vs. v at 5 psig steam pressure
10
100
1000
10000 100000
NN
u
NRe
Nusselt Number vs. Reynold Number at 15 psig steam pressure
1000
10000
0.1 1Wat
er s
ide
hea
t tr
ansf
er c
oef
ficie
nt
hi
Velocity v (m/s)
Water side heat transfer coefficient, hi vs. velocity v at 5 psig
steam pressure
Graph 2: Waterside heat transfer coefficient vs. inner pipe velocity at 10 psig steam pressure
Figure 6: Graphical Representation for hi vs. v at 10 psig steam pressure
Graph 3: Waterside heat transfer coefficient vs. inner pipe velocity at 15 psig steam pressure
Figure 7: Graphical Representation for hi vs. v at 15 psig steam pressure
1000
10000
0.1 1 10
Wat
er s
ide
hea
t tr
ansf
er c
oef
ficie
nt
hi
Velocity v (m/s)
Water side heat transfer coefficient, hi vs. velocity v at 10 psig
steam pressure
1000
10000
0.1 1 10
Wat
er s
ide
hea
t tr
ansf
er c
oef
ficie
nt
hi
Velocity v (m/s)
Water side heat transfer coefficient, hi vs. velocity v at 15 psig
steam pressure
3. Wilson Plot showing (1/U) vs. (1/v) 0.8
Graph 1: Theoretical and experimental values of (1/U) vs. (1/v) 0.8
for 5 psig steam pressure
Figure 8: Graphical Representation of (1/U) vs. (1/v) for 5 psig steam pressure
Graph 2: Theoretical and experimental values of (1/U) vs. (1/v) 0.8
for 10 psig steam pressure
Figure 9: Graphical Representation of (1/U) vs. (1/v) for 10 psig steam pressure
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.5 1 1.5 2
(1/U
)
(1/v)
(1/U) vs. (1/V)0.8 for 5 psig steam pressure
Experimental
Theoretical
dirt factor=(0.00065-0.00036)=0.00029
Graph 3: Theoretical and experimental values of (1/U) vs. (1/v) 0.8
for 15 psig steam pressure
Figure 10: Graphical Representation of (1/U) vs. (1/v) for 15 psig steam pressure
Sample Calculation
For observation number 8 at 10 psig steam pressure
Weight of empty bucket for collecting condensate,W1 = 1.1kg
Volume of water, WB = 12 L
Density at 34°C, ρm = 994.3 kg/m3
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Weight of water for cooling Ww= V× 𝜌m=((12× 10−3) × 994.3) kg =11.932 kg
Mass flow rate of water, MW = WW/tw = (11.932 ÷20) kg/s = 0.5966 kg/s
Weight of (bucket+condensate), WS = 1.4 kg
Weight of condensate collected, WC = WS– W1 = (1.4-1.1) kg = 0.3 kg
Mass flow rate of condensate, MC = WC/tc = (0.3 ÷ 20) kg/s = 0.015 kg/s
Mean temperature of water, Tm = (T1+ T2)/2 = (29.5 + 38.5)/2 =34oC
From literature data,
*Saturation temperature of steam at 5 psig pressure, Ts = 108.39°C
*Heat of vaporization at 5 psig pressure, λs= 2215.61 kJ/Kg
*At mean temperature heat capacity of water, Cp = 4174 J/Kg°C
*[ J M Smith, H C Van Ness, M M Abbott. (2001) ‘Chemical Engineering Thermodynamics’, McGraw - Hill, 7th
Ed, Table F1, pp-715]
Rate of heat taken by water, QW = MW × Cp× (T2-T1)
= 0.5966 × 4174 × (34-29.5) J/s
= 22.411 kJ/s
Rate of heat given by steam, QC = MC × λs = (0.015 × 2215.61) kJ/s =33.2342 kJ/s
Mean rate of heat flow,
Qm = 2
CW QQ =
2
2342.33411.22 = 27.823 kJ/s
Temperature difference at inlet,
ΔT1 = Ts - T1 = (115.21 – 29.5)oC = 85.71
oC
Temperature difference at outlet,
ΔT2 = Ts - T2 = (115.21 – 38.5) oC = 76.71
oC
Log mean temperature difference,
ΔTLMTD =
2
1
21
lnT
T
TT
=
71.76
71.85ln
71.7671.85 oC = 81.4732
oC
For 1 in. nominal diameter & schedule 40 steel tube,
The outside surface per linear feet, Ao = 0.344 ft2/ft
Inside diameter (ID) of the pipe, Di = 1.049 in. = 0.02665 m.
Outside diameter (OD) of the pipe, Do = 1.32 in. = 0.033528 m.
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-11 pp 612]
Tube length = 7 ft. 4 in. = 88 in. = 7.33 ft.
Outside area available for heat transfer, Ao = 0.344×7.33 ft2 = 0.2344 m
2.
Experimental overall heat transfer coefficient, UOE = 0.AT
Q
lm
m
= 2344.04732.81
1000823.72
W/m
2.oC
= 1456.89 W/m2.oC
Tube wall temperature on steam side,
Tw = 2
mS TT oC =
2
3421.115 oC = 74.778
oC
Properties at mean temperature, Tm= 34oC
Density of water, ρm = 994.3 kg/m3
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Viscosity of water, μm = 0.00074 kg/m.s
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Thermal conductivity of water, km = 0.62524W/m.oC
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Mass velocity of water, Gm = i
W
A
M =
0410576.5
0.5966
m/s = 1069.14 kg/m2s
Prandtl no. of water, Pr = 4.93114
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Reynolds no. of water,
Re = m
i mvD
=
04104.7
3.99407143.102665.0
= 38664.2
Water side heat transfer coefficient for turbulent flow
Using Dittus-Boelter equation, hi = 0.023 ×i
m
D
k×(Re)
0.8 ×(Pr)
1/3
= 0.023×02665.0
62524.0× (38664.2)
0.8× (4.93114)
1/3
= 4049.24W/m2.oC
Film temperature,
Tf = Ts-0.75 × (Ts-Tw)
= 115.21- 0.75× (115.21–74.778) oC
= 84.9725 ℃
Properties of condensate at film temperature, Tf = 79.36875oC
Density, ρf = 968.467 kg/m3
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Viscosity of condensate, μf = 0.00038 kg/m.s
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Thermal conductivity of condensate, kf = 0.67391 W/m.oC
[J. P. Holman. (1997) ‘Heat Transfer’. McGraw – Hill. 10th Ed. Table A-9 pp 609]
Steam side heat transfer coefficient using Nusselt equation for film type condensation,
ho =0.725× fWS
Sff
TTD
gk
)(
...
0
23
1/4
=0.725× 00038.0)778.7421.115(033528.0
2215611.8.9467.96867391.0 23
1/4
W/m2.oC
= 7599.8 W/m2.oC
Now, xw= mDD i .003439.0
2
02665.0033528.0
2
0
Carbon-steel metal’s thermal conductivity, KM = 43 W/m.oC
Log-mean diameter, Dlm =
i
i
D
D
DD
0
0
ln
= m.02996.0
02665.0
033528.0ln
02665.0033528.0
Theoretical overall heat transfer coefficient,
UOT = lmm
W
ii Dk
Dx
hD
D
h .
.
.
1 00
0
−1
= 1)02996.043
033528.0003439.0
24.049402665.0
033528.0
7599.8
1(
W/m
2.oC
= 2141.93 W/m2.oC
Now for Wilson plot,
0006864.0 1456.89
11
OEU m
2.oC/W
00046687.0 2141.93
11
OTUm
2.oC/W
9436.0)1.07143(
118.08.0
v (s/m)
0.8