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