Observed Data

Inner tube specifications:

Tube length = 7' 4''
Nominal diameter =1''
Schedule no. 40

Table 01 Observed data for study of double pipe heat exchanger

Observation Steam Water temperature Water flowrate Condensate flowrate
no. pressure, P (oC)
(psig)
Inlet, T1 Outlet, T2 Volume Time (s) Mass (kg) Time (s)
(L)
1 5
25 54.00 10 114.02 0.650
2
25 42.00 10 28.99 1.100
3
25 39.00 10 25.00 1.200
4
25 37.00 10 24.88 1.250
1 10
25 42.00 10 39.06 1.000
2
25 39.50 10 31.35 1.100
120
3
25 39.00 10 26.53 1.230
4
25 39.00 10 23.81 1.300
1 15
25 46.50 10 43.86 1.150
2
25 42.00 10 30.03 1.280
3
25 40.00 10 25.91 1.370
4
25 40.50 10 12.55 1.260
Sample Calculation
Length of the pipe, L= 7 ft 4 inch = 7.33 ft. = 2.235 m
For nominal size 1 inch and schedule no. 40,
Outer diameter, DO = 1.315 inch = 0.0329 m
Inner diameter, Di = 1.049 inch = 0.0266 m
(Reference: J. P. Holman. ‘Heat Transfer’. McGraw – Hill. 10th Edition. Table A-11, page 665)
Outside surface area, AO = πDOL
= 3.1416 × 0.0329 × 2.235
= 0.231 m2
2
π Di
Water flow area, Ai = = 5.557 × 10-4 m2
4

For observation no. 02 at 5 psig pressure

Water inlet temperature, T1 = 25 oC
Water outlet temperature, T2 = 42 oC
Temperature difference, T2-T1 = (42-25) oC = 17 oC = 17 K
Mean temperature, Tm =¿) °C
= 33.5 oC

At, 33.5 oC mean temperature,

Specific Heat of capacity, Cpm = 4174 J.Kg-1K-1

Density of water, ρm = 994.10 Kgm-3

Thermal conductivity, km = .624 Wm-1.K-1

Dynamic viscosity, μm = 0.000722 Pa.s

(Reference: J. P. Holman. ‘Heat Transfer’. McGraw – Hill. 10th Edition. Table A-9, page 662)

Collected volume of water = 10 L

Time of collection = 28.99 s

.01× 994.10
Mass flow rate of water, Mw = = 0.343 Kg/s
28.99
Collected mass of condensate = 1.1 Kg

Time of collection = 120 s

1.1
Mass flow rate of condensate, Mc = = 0.0092 kg/s
120
Rate of heat taken up by water, Qw = MwCpm(T2-T1)
= 0.343 × 4174 × 17
= 24332.30 W
At 5 psig steam pressure,

Saturation temperature of steam, TS = 108.37 0C

Latent heat of vaporization, λS = 2234.38 kJkg-1

Rate of heat given up by steam, Qs = Mcλs

= 0.0092 × 2234.38 × 1000
= 20481.82 W

Qw +Qs
Mean rate of heat flow, Qm =
2

24332.30+20481.82
=
2

= 22407.06 W

Calculation of experimental overall heat transfer coefficient, UOE

Temperature difference at inlet, ∆T1 = TS – T1 = (108.37-25) 0C = 83.37 0C

Temperature difference at outlet, ∆T2 = TS – T2 = (108.37-42) 0C = 66.37 0C

Logarithmic mean temperature difference,

83.37−66.37
=
ln ¿ ¿ ¿ ¿
= 74.54 oC
Qm
Experimental overall heat transfer coefficient, UOE =
A o ∆ T lm
 22407.06
=
0.231× 74.547

= 1281.679 W.m-2.K-1

Calculation of velocity (v), Reynolds number (Re) and Prandtl Number (Pr)

T s+T m
Tube wall temperature, Tw =
2

108.37+33.5
= 2

= 70.935 oC

Mw
Velocity, v =
ρm A i

0.343
= −4
994.10 ×5.557 ×10

= 0.62 m/s

Di v ρ m
Reynolds Number, Re =
μm

0.0266 ×0.62 × 994.10

=
0.00072

= 22690.29

μ m C pm
Prandtl Number, Pr =
km
0.00072× 4174
= = 4.82
0.624

Calculation of water side heat transfer coefficient (hi) and Nusselt Number (Nu)
For turbulent flow, according to Dittus-Boelter equation,

hi =
 1
0.8 3
= 0.023 ×0.624 × 22690.29 × 4.82
0.0266
= 2780.81 Wm-2K-1

hi D i
Nusselt Number, Nu =
km

2780.81× 0.0266
= = 118.68
0.624

Calculation of steam side heat transfer coefficient (h O) and theoretical overall heat transfer
coefficient (UOT)

Film temperature, Tf = TS – 0.75(TS-TW)

= 108.37 – 0.75 × (108.37 – 70.935) = 80.293 oC

At 80.293 0C film temperature,

Density of water, ρf = 971.02 Kg/m3

Thermal conductivity, kf = 0.67W/m.K

Dynamic viscosity, μf = 0.000344 Pa.s

( )
k 3 ρ2f gλ s 1/ 4
f
D 0 (T s−T w ) μf
Nusselt equation for film type condensation, ho = 0.725
= 0.725 ×

( )
1 /4
0.673 ×971.02 2 × 9.81× 2234.38× 1000
0.0329 × ( 108.37−70.935 ) ×0.000344
= 7946.85 Wm-2K-1

( )
−1
1 D x D
+ o + W o
ho D1 h 1 k M Dlm
Theoretical overall heat transfer coefficient, UOT =
The term for conduction can be neglected, then it can be presented as
1
UOT = 1 Do
+
h o D i hi
 1
= 1 0.0329
+
7946.85 0.0266 ×2780.81
= 1734.019 Wm-2K-1

Calculation of dirt factor, Rd

From the graph of Wilson plot i.e. 1/U vs (1/v) 0.8

For 5 psig steam pressure in figure 08

The intercept for dirty tube (experimental overall heat transfer coefficient) = 0.0005 m 2K/W
The intercept for clean tube (theoretical overall heat transfer coefficient) = 0.0002 m 2K/W
Dirt factor, Rd = 0.0005 – 0.0002 = 0.0003 m2K/W

For 10 psig steam pressure in figure 09

The intercept for dirty tube (experimental overall heat transfer coefficient) = 0.0003 m 2K/W
The intercept for clean tube (theoretical overall heat transfer coefficient) = 0.0002 m 2K/W
Dirt factor, Rd = 0.0003 – 0.0002 = 0.0001 m2K/W

For 15 psig steam pressure in figure 10

The intercept for dirty tube (experimental overall heat transfer coefficient) = 0.0004 m 2K/W
The intercept for clean tube (theoretical overall heat transfer coefficient) = 0.0001 m 2K/W
Dirt factor, Rd = 0.0004 – 0.0001 = 0.0003 m2K/W

Determination of applicability of Dittus-Boelter equation

1. For 5 psig steam pressure

Slope of ‘ln (Nu) vs. ln (Re)’ graph = ln ⁡¿ ¿ = 0.85

Slope of ‘ln (hi) vs. ln (v)’ graph = ln ¿ ¿ = 0.74
 2. For 10 psig steam pressure

(137 ¿¿ 93¿)
Slope of ‘ln (Nu) vs. ln (Re)’ graph = ln ¿ ¿ = 0.83
ln¿ ¿ ¿ ¿
(3203¿ ¿2190.12¿)
Slope of ‘ln (hi) vs. ln (v)’ graph = ln ¿¿ = 0.74
ln ¿ ¿ ¿ ¿

3. For 15 psig steam pressure

(231.02¿¿ 86.89 ¿)
ln ¿
Slope of ‘ln (Nu) vs. ln (Re)’ graph = 51927.22 = 0.81
ln
15692.7 ¿
(5407.12¿¿ 2045.49¿)
Slope of ‘ln (hi) vs. ln(v)’ graph = ln ¿ ¿ = 0.91
ln ¿ ¿ ¿ ¿

Graphical Representation
 Nusselt number vs Reynolds number for 5 psig
1000
Nusselt number,Nu

f(x) = 0.00476517495330359 x + 10.7923733801259

100 R² = 0.999843505724429

10
1000 10000 100000

Reynolds number,Re

Figure 2 Plot of ‘Nu vs Re’ for 5 psig steam pressure.

 Nusselt number vs Reynolds number for 10 psig
1000
Nusselt number,Nu

f(x) = 0.00437941051042289 x + 20.1665916274049

100 R² = 0.999373961908592

10
10000 Reynolds number,Re 100000

Figure 3 Plot of ‘Nu vs Re’ for 10 psig steam pressure.

 Nusselt number vs Reynolds number for 15 psig
1000

f(x) = 0.00391921204508322 x + 28.4202268084873

R² = 0.998382724182196
Nusselt number,Nu

100

10
10000 Reynolds number,Re 100000

Figure 4 Plot of ‘Nu vs Re’ for 15 psig steam pressure.

 Water side heat transfer coefficient vs velocity for 5 psig
10000

f(x) = 3726.78531827362 x + 413.748051904959

R² = 0.998120763301641
Water side heat transfer coefficient, hi (Wm-2K-1)

1000

100
0.1 1
Velocity, v (m/s)

Figure 5 Plot of ‘hi vs velocity’ for 5 psig steam pressure.

10000 Water side heat transfer coefficient vs velocity for 10 psig
Water side heat transfer coefficient, hi (Wm-2K-1)

f(x) = 3446.44166994602 x + 606.498168814323

R² = 0.999994290805288

1000
Velocity, v (m/s)

Figure 6 Plot of ‘hi vs velocity’ for 10 psig steam pressure.

 Water side heat transfer coefficient vs velocity for 15 psig
10000
Water side heat transfer coefficient, hi (Wm-2K-1)

f(x) = 3276.53992190476 x + 728.899669314337

R² = 0.999832088510586

1000
0.1 1 10
Velocity, v (m/s)

Figure 7 Plot of ‘hi vs velocity’ for 15 psig steam pressure.

 Wilson plot,(1/U) vs. (1/v)0.8 for 5 psig
0.0016
f(x) = 0.000277013295573811 x + 0.000173339891679615
f(x)
R² ==0.999947662896516
0.000198682899741445 x + 0.000531092130684107
0.0014 R² = 0.985308697968831

0.0012

0.001

Theoretical
0.0008
Linear (Theoretical)
Experimental
1/U (m2K/W)

0.0006 Linear (Experimental)

0.0004

0.0002

0
0 1 2 3 4 5 6

(1/v)0.8 (m/s)0.8

Figure 8 Plot of (1/U) vs. (1/v) 0.8 for 5 psig steam pressure.
 Wilson plot,(1/U) vs. (1/v)0.8 for 10 psig
0.0012

f(x) = 0.000393783310880784 x + 0.000331193287215238

0.001 R² = 0.94054043630326

0.0008

f(x) = 0.00029541464814056 x + 0.000150209040806537

Theoretical
R² = 0.999520036473528
0.0006 Linear (Theoretical)
Experimental
Linear (Experimental)
1/U (m2K/W)

0.0004

0.0002

0
0 1 2

1/v)0.8 (m/s)0.8

Figure 9 Plot of (1/U) vs. (1/v)0.8 for 10 psig steam pressure.

 Wilson plot,(1/U) vs. (1/v)0.8 for15 psig
0.0012

0.001
f(x) = 0.000313766616301996 x + 0.000363593553461963
R² = 0.908564926988083

0.0008
1/U (m2K/W)

f(x) = 0.000293545328450403 x + 0.000144635206527331

R² = 0.998566180307341
0.0006 Theoretical
Linear (Theoretical)
Experimental
Linear (Experimental)
0.0004

0.0002

0
0 1 2 3

1/v)0.8 (m/s)0.8

Figure 10 Plot of (1/U) vs. (1/v)0.8 for 15 psig steam pressure.

Calculated Data

Table 02 Water properties at average water temperature

Observation Temperature Average Specific Density, ρ Viscosity, Thermal
no difference of water heat, Cpm (kgm-3) μ conductivity,
inlet and temperature (Jkg-1.K-1) (Pa.s) Km (Wm-1K-1)
outlet water (OC)
∆T
(OC)

1 29.0 39.50 4174 992.10 0.00064 0.632

2 17.0 33.50 4174 994.10 0.00072 0.624

3 14.0 32.00 4174 994.90 0.00074 0.622

4 12.0 31.00 4174 995.20 0.00079 0.621

5 17.0 33.50 4174 994.10 0.00072 0.624

6 14.5 32.25 4174 994.70 0.00074 0.623

7 14.0 32.00 4174 994.90 0.00074 0.622

8 14.0 32.00 4174 994.90 0.00074 0.622

9 21.5 35.75 4174 993.80 0.00069 0.627

10 17.0 33.50 4174 994.57 0.00072 0.624

11 15.0 32.50 4174 994.89 0.00073 0.623

12 15.5 32.75 4174 994.73 0.00072 0.624

Table 03 Calculated data for saturation temperature, latent heat of condensation, mass flow rate
of water and condensate, heat given by steam and heat taken by water.
Obs. no Steam Saturation Latent heat of Mass Mass Heat Heat taken
pressure temperature condensation, flow flow given up up by
(psig) of steam λ (kJ/kg) rate of rate of by steam, water, Qw
Qc (W)
(OC) water, condens
(W)
MW ate, MC
(kg/s) (kg/s)

1 5 108.37 2234.3 0.087 0.005 12102.89 10532.33

2 0.343 0.009 20481.82 24332.30

3 0.398 0.010 22343.8 23255.19

4 0.400 0.010 23274.79 20035.20

1 10 115.25 2215.5 0.254 0.008 18462.92 18058.07

2 0.317 0.009 20309.21 19204.51

3 0.375 0.011 22709.39 21918.01

4 0.417 0.011 24001.79 24417.95

1 15 120.93 2199.6 0.226 0.009 21079.31 20334.09

2 0.331 0.010 23462.19 23500.70

3 0.384 0.011 25111.87 24043.96

4 0.792 0.010 23095.59 51291.76

Table 04 Calculated data for Mean rate of heat, experimental overall heat transfer coefficient, Wall
temperature, velocity and Reynolds number.
 Obs. Steam Mean LMTD Experiment Wall Velocity Reynolds
no pressure rate of (OC) al overall temperature, ,v no. Re
(psig) heat, QM heat transfer TW (m/s)
coefficient, (OC)
(W)
UOE
(W/m2.K)

1 5

11317.61 67.84 711.36 73.93 0.157 6482

2

22407.06 74.54 1281.67 70.93 0.618 22690

3

22799.49 76.15 1276.58 70.18 0.717 25527

4

21654.99 77.21 1195.87 69.68 0.721 25125

1 10

18260.49 81.45 955.92 74.37 0.459 16839

2

19756.85 82.78 1017.59 73.75 0.572 20460

3

22313.70 83.05 1145.61 73.625 0.676 24059

4

24209.87 83.05 1242.97 73.62 0.753 26803

1 15

20706.69 84.72 1042.12 78.34 0.409 15692

2

23481.44 87.15 1148.85 77.21 0.597 21914

3

24577.91 88.21 1187.99 76.71 0.692 24893

4

37193.67 87.95 1803.21 76.84 1.429 51927

Table 05 Calculated data for Prandtl no., Water side heat transfer coefficient, Nusselt no., Film
temperature and water density, viscosity, thermal conductivity at film temperature.
Obs. Steam Prandtl Water side Nusselt Film Water Water Thermal
no pressure no. heat transfer no. Temperature, Densit viscosity conductivity
(psig) Pr coefficient, Nu Tf y at Tf, at Tf, μf at Tf, kf
(OC) ρf (Pa.s) (W/m.K)
hi
(kg/m3)
(W/m2.K)

1 5 4.23 989.18 41.70 82.54 969.55 0.000335 0.671

2 4.82 2780.81 118.68 80.29 971.02 0.000344 0.670

3 4.99 3080.84 131.90 79.73 971.38 0.000347 0.669

4 5.11 3058.73 131.25 79.35 971.63 0.000348 0.669

1 10 4.83 2190.12 93.50 84.59 968.20 0.000327 0.672

2 4.96 2577.43 110.30 84.12 968.50 0.000329 0.672

3 4.99 2938.29 125.80 84.03 968.60 0.000329 0.672

4 4.99 3203.47 137.15 84.03 968.56 0.000329 0.672

1 15 4.59 2045.49 86.895 88.98 965.20 0.000310 0.675

2 4.83 2703.93 115.43 88.14 965.70 0.000313 0.675

3 4.94 3010.92 128.79 87.76 966.01 0.000315 0.674

4 4.88 5407.12 231.02 87.86 965.90 0.000314 0.674

Table 06 calculated data for Steam side heat transfer coefficient, theoretical overall heat transfer
coefficient, experimental 1/U, theoretical 1/U, and (1/v) 0.8.

Obs. Steam Steam side heat Theoretical overall Experimental Theoretical (1/v)0.8
no pressure transfer heat transfer 1/U 1/U (m/s)0.8
(psig) coefficient, hO coefficient, UOT (m2.K/W) (m2.K/W)
(W/m2.K) (W/m2.K)

1 5 8177.74 719.55 0.001405 0.00139 4.39

2 7946.85 1734.01 0.000780 0.00057 1.46

3 7891.20 1873.80 0.000783 0.00053 1.30

4 7855.79 1861.54 0.000836 0.00053 1.29

1 10 7871.66 1429.60 0.001046 0.00069 1.86

2 7830.57 1628.29 0.000982 0.00061 1.56

3 7821.84 1803.29 0.000872 0.00055 1.36

4 7821.68 1925.95 0.000804 0.00051 1.25

1 15 7889.58 1351.92 0.000959 0.00070 2.04

2 7816.57 1690.30 0.000870 0.00059 1.50

3 7785.18 1835.36 0.000841 0.00054 1.34

4 7795.49 2776.62 0.000554 0.00036 0.75