Heat Transfer

Published on March 2017 | Categories: Documents | Downloads: 68 | Comments: 0 | Views: 614
of 10
Download PDF   Embed   Report

Comments

Content

ME 351 Mechanical Labroatory-1
Group 7

Experiments:
1. Heat Transfer in Laminar Flow
2. Heat Transfer in Turbulent Flow

Rohit Nanavati (13110099)
Sarabjeet Singh(13110108)
Jugal Shah(13110111)
Sharad Tiwari(13110115)

Heat Transfer in Laminar Flow
Objective:
To determine the overall heat transfer coefficient making use of logarithmic mean
temperature difference. From overall heat transfer coefficient, determine the individual film
heat transfer coefficient and verify the Seider-Tate equation for laminar flow heat transfer.
Apparatus:
1. Stainless steel double pipe heat exchanger with facility to measure inlet and outlet

temperature of hot fluid with accuracy of 0.1◦C. The inlet and outlet temperature of cold
fluid is measured with liquid in glass thermometer of 1◦C accuracy.
2. A stainless steel insulated tank with a heater. Pin n heat exchanger.
3. Hot fluid circulation pump with speed variation mechanism. Bare pipe without ns.
4. Cold fluid circulation pumps with speed variation mechanism. Steam generator to

generate steam at constant pressure. The steam generator is also provided with
temperature indicator and a dead weight safety valve.
5. An insulated stainless steel tank with bottom discharge to measure the flow rate of hot

fluid.
Theory:
In a heat exchanger, heat is transferred from hot fluid to cold fluid through metal wall, which
generally separates these two fluids. Heat transfer through metal wall is always by conduction
while on both sides of metal wall it is generally by convection. Generally resistance offered to
heat transfer by the metal wall is negligible as compared to resistance offered by convection.
The wall temperature is always between local temperatures of the two fluids. The actual value
depends upon individual heat transfer coefficient on either side.
At low Reynolds’s number (Re < 2100), the flow pattern is laminar and the fluid flows in an
ordered manner along generally parallel "Filament like" streams which do not mix. It follows
that in this type of flow that the heat transferred to and through the fluid is essentially by
conduction.
When heat is transferred through resistances in series, the total resistance to heat transfer is
the sum of individual resistances in series. Thus, for heat exchanger, one can write,
1/UiAi = 1/hiAi + x/KAlm + 1/hoAo

OR
1/Ui = 1/h1 + ∆xAi/KAlm + Ai/hoAo
Once the heat exchanger material and its geometry are fixed, then the metal wall resistance
x/KAlm becomes constant. Similarly, if the flow rate of cold fluid is fixed and its mean
temperature does not differ much for different flow rates of hot fluid, then the resistance by
the outside will remain almost constant. Thus, the overall heat transfer coefficient will depend
upon the value of inside heat transfer coefficient alone. If flow through inner tube is in the
turbulent flow regime, then Sieder-Tate equation can be used to predict the inside lm heat
transfer coefficient.
Nu = 1.86*Re1/3*Pr1/3
If the bulk mean temperature does not differ much for different flow rates, then all the physical
properties will remain nearly the same and equation (3) can be re-written as:
Nu = constant × (velocity)1/3

Substituting equation (4) in equation (2), one can write it as:
1/Ui = C1 / U1/3 + C2

Thus, the graph of 1/Ui vs 1 / U1/3 (which is known as Wilson plot) should be a straight line with
a slope equal to constant1 and intercept equal to constant2. From this graph, inside lm heat
transfer coefficient can be calculated which can be used to verify Sieder-Tate equation.
Observations
1. Inside diameter of inner tube (d1)
2. Outside diameter of inner tube (d2)

=
=

1.0 cm.
1.27 cm.

3. Inside diameter of outer tube (D1)

=

2.20cms.

4. Length of heat exchanger (L)

=

85 cms.

5. Inner heat transfer area of heat exchanger (A)

=

0.0267m2

6. Zero error of hot fluid digital thermometers

=

0◦C

7. Volume of measuring tank between bottom and middle mark =
(V1)
8. Specific heat of the oil, Cp = 0.625 kcal/kg °C = 2625
Ns/m2

.000880m3

9. Specific gravity of oil = 0.835
10. Viscosity of oil, μ = 4 * 10-3 Pa s

Observation Table
Observation

Inlet

Outlet

Inlet

Outlet

Time
Required to
Fill fixed
volume(sec)

Number

Temp of

Temp of

Temp of

Temp of

1
2
3
4
5
6
7

Hot Fluid
(°C)
64.5
66.9
68
69
69.9
70.9
72.6

Hot Fluid
(°C)
63.6
65.8
66.9
67.9
68.8
69.8
71.3

Cold Fluid
(°C)
29.8
29.8
29.9
29.9
30
30
29.9

Cold Fluid
(°C)
30.2
30.2
30.3
30.3
30.4
30.4
30.4

20.18
16.67
14.78
14.08
12.89
11.6
11.5

A: Table of Calculated Results

volumetric
Flow rate
cc/sec

Amount of
Heat
Transfer
Q

Velocity of
Hot fluid
u

LMTD
Delta T

Overall heat transfer coefficient
U (Kcal/hr m2◦C)

43.60753221
52.78944211
59.53991881

73.73488603
109.0959808
123.0466847

0.522245895
0.632208888
0.71305292

34.04586352
36.34484123
37.34497938

81.14468629
112.4650035
123.4494385

62.5
68.26997673
75.86206897
76.52173913

129.1640625
141.0884407
156.7784483
186.8947826

0.748502994
0.817604512
0.908527772
0.916428014

38.34511032
39.14521026
40.14532958
41.79353987

126.2069091
135.0405598
146.3196859
167.5480767

B: Table of Calculated Results
Velocity_cubrt_inverse

resistance inverse

1.241771406
1.165144531
1.11933327
1.101375689
1.069429698
1.032493352
1.029517851

0.012323666
0.008891655
0.008100482
0.007923496
0.007405183
0.00683435
0.005968436

Inside film
heat transfer
46.89625164
55.891979
58.47788259
59.08944415
60.95634691
63.15383811
66.8072462

Nusselt
number
0.55828871
0.665380702
0.696165269
0.703445764
0.725670797
0.751831406
0.79532436

Reynolds number
1090.188305
1319.736053
1488.49797
1562.5
1706.749418
1896.551724
1913.043478

Axis Title

Chart Title
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0

y = 0.0153x - 0.009
R² = 0.9975

Series1
Linear (Series1)

1.02

1.04

1.06

1.08

1.1

Axis Title

1.12

1.14

1.16

1.18

y = 3855.5x - 1128.5
R² = 0.9244

Chart Title
10000

Axis Title

1000

100

Series1
Linear (Series1)

10

1
0.1

1

Axis Title

Result & Conclusion:
1. The Graph for the 1/U Vs 1/V

1/3

is approximately a linear graph and hence it satisfies Seider

Tate equation for laminar and parallel flow heat exchanger.
2. Graetz number (Gz) Vs Nusselt number(Nu) Graph are showing approximately linear trend
and hence they also possess a linear relationship with respect to each other.

Heat Transfer in Turbulent Flow
Aim
To determine the overall heat transfer coefficient making use of logarithmic mean temperature
difference. From overall heat transfer coefficient, determine the individual lm heat transfer
coefficients and verify the Dittus-Boelter equation for turbulent flow heat transfer.
Apparatus

1. Stainless steel double pipe heat exchanger with facility to measure inlet and outlet

temperature of hot fluid with accuracy of 0.1◦C. The inlet and outlet temperatures of cold
fluid are measured with liquid in glass thermometer of 1◦C accuracy.
2. A stainless steel insulated tank with a heater.
3. Hot fluid circulation pump with speed variation mechanism.
4. Cold fluid circulation pumps with speed variation mechanism.
5. An insulated stainless steel tank with bottom discharge to measure the flow rate of hot

fluid.

Theory
In a heat exchanger, heat is transferred from hot fluid to cold fluid through metal wall which
generally separates these two fluids. Heat transfer through metal wall is always by conduction
while on both sides of metal wall it is generally by convection. Generally resistance offered to
heat transfer by the metal wall is negligible as compared to resistance offered by convection.
The wall temperature is always between local temperatures of the two fluids. The actual value
depends upon individual lm heat transfer coefficient on either side. At higher Reynolds’s
number (Re >10,000), the ordered flow pattern of laminar flow regime is replaced by randomly
moving eddies thoroughly mixing the fluid and greatly assisting heat transfer. However, this
enhancement of lm heat transfer coefficient is accompanied by much higher pressure drop
which demands higher pumping power. Thus, although desirable, turbulent flow is usually
restricted to fluids of low viscosity. When heat is transferred through resistances in series, the
total resistance to heat transfer is the sum of individual resistances in series. Thus, for heat
exchanger, one can write,
(22.1)
Or
(22.2)
Once the heat exchanger material and its geometry is fixed, then the metal wall resistance
(∆x/KAlm) becomes constant. Similarly, if the flow rate of cold fluid is fixed and its mean
temperature does not differ much for different flow rates of hot fluid, then the resistance by
the outside lm will remain almost constant. Thus, the overall heat transfer coefficient will
depend upon the value of inside lm heat transfer coefficient alone. If flow through inner tube is
in the turbulent flow regime, then Ditturs-Boelter equation can be used to find out inside lm
heat transfer coefficient.
Nu = 0.023(Re)0.8(Pr)n (22.3)

If the bulk mean temperature does not differ much for different flow rates, then all the physical
properties will remain nearly the same and equation (3) can be re-written as:
Nu = constant × (velocity)0.8 (22.4)
Substituting the above equation in equation (2), we get:
constant

constant 2

(22.5)

Thus, the graph of 1/Ui vs 1/u0.8 (which is known as Wilson plot) should be a straight line with a
slope equal to constant1 and intercept equal to constant2. From this graph, inside lm heat
transfer coefficient can be calculated which can be used to verify Dittus-Boelter equation.

Observations:
1. Inside diameter of inner tube (d1) =

1.0cm.

2. Outside diameter of inner tube (d2) =

1.27cm.

3. Inside diameter of outer tube (D1) =

2.20cm.

4. Length of heat exchanger (L) =

85cm.

5. Inner heat transfer area of heat exchanger (A) = .0267m2.
6. Zero error of hot fluid digital thermometers =

0◦C

7.Specific heat of the oil, Cp = 0.625 kcal/(kg .K) = 2615 J/kg.K
8.Thermal conductivity of hot fluid, k = 0.609 W/(m.K)

Observation Table:

Observation

Inlet

Outlet

Inlet

Outlet

Number

Temp of

Temp of

Temp of

Temp of

1
2
3
4
5
6
7

Hot Fluid

Hot Fluid

Cold Fluid

Cold Fluid

(°C)
41.7
42.6
44.2
45.1
45.8
46.2
46.7

(°C)
37.3
38.8
39.2
41.6
42.5
43.3
44

(°C)
29.6
29.8
29.8
29.8
29.8
29.8
29.9

(°C)
30.6
31.2
31.4
31.75
31.9
32.2
32.3

volumetric Flow rate
cc/sec

Amount of Heat
Transfer Q

Velocity of
Hot fluid
u

LMTD
Delta T

Overall heat transfer
coefficient U (Kcal/hr
m2◦C)

0.0018
0.0024
0.003
0.004
0.005
0.006
0.0068

0.0148797
0.0171342
0.02818125
0.0263025
0.030999375
0.03269025
0.03449385

0.000018
0.000024
0.00003
0.00004
0.00005
0.00006
0.000068

9.135542117
9.975121211
10.7648864
12.37563696
13.11524077
13.5780377
14.09657362

0.06102549
0.06435719
0.098084917
0.079630766
0.08855806
0.090205425
0.09168104

Velocity_-0.8_inverse

resistance inverse

6248.589517
4963.991242
4152.436465
3298.769777
2759.459323

16.3865951
15.5382793
10.19524748
12.55796029
11.29202689

2384.948469
2157.708984

11.08580773
10.90738059

Chart Title

y = 0.0013x + 7.567
R² = 0.6859

18
16

Axis Title

14
12
10
8

Series1

6

Linear (Series1)

4
2
0
0

1000

2000

3000

4000

5000

6000

7000

Axis Title

Result & Conclusion:
 Above graph implies that the Dittus-Boelter Equation is valid (more or less) in this case.



Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close