Heat Transfer
Coefficients
Parker Williams
Tristan Grieves
Lucas Vacca
Outline

Apparatus/Procedure

Calculations

Results

Discussion of Results

Conclusions/Questions
Apparatus
Figure 1: The heat exchanger system used for conducting the experiment.
Calculations

Logarithmic-mean
temperature-difference (1.)

∆𝑇𝑙𝑛 =
(𝑇𝑤𝑖 −𝑇𝑓𝑖 )−(𝑇𝑤2 −𝑇𝑓2 )
ln
𝑇𝑤𝑖 −𝑇𝑓𝑖
𝑇𝑤2 −𝑇𝑓2

Heat transfer coefficient

h=
(𝑇𝑓2 −𝑇𝑓𝑖 )
𝑙𝑛(𝑇𝑤 −𝑇𝑓
∗
)
2𝑅
𝐿
∗
𝜌<𝑣>𝐶𝑝
4
(2.)
=
𝑚∗𝐶𝑝∗∆𝑇
𝐴∗𝑇𝑙𝑛

L = length of exchanger tube

Twi = water initial temperature

R = Radius of exchanger tube

Tw2 = water final temperature

𝜌 = Density of fluid

Tfi = steam initial temperature

m = mass flow of fluid

Tf2 = steam final temperature

A = cross sectional area
Calculations

Reynolds number (Re)


𝑅𝑒 =
(3.)

𝐷𝑉𝜌
𝜇
Nusselt number (Nu)

𝑁𝑢 =
(4.)
ℎ𝐷
𝑘

D = pipe diameter

h = heat transfer coefficient

V = fluid velocity

k = thermal conductivity of fluid

𝜌 = fluid density

𝜇 = fluid viscosity
Turbulent Nusselt Number (5.)

Prandtl number (Pr)

Pr =

(6.)
𝐶𝑝 ∗ 𝜇
𝑘
Cp = Specific heat capacity
Results
Heat Transfer Coefficient vs. Fluid Velocity
Heat Transfer Coefficicent (W/cm^2*K)
0.60
0.50
0.40
0.362 cm
0.798 cm
2.00 cm
0.30
0.20
0.10
0.00
0
50
100
150
200
Velocity (cm/s)
250
300
350
Figure 2: The relationship between heat transfer coefficients and fluid velocity
and pipe diameter.
Heat Transfer Coefficient vs. Log Mean Temperature
0.6
Heat Transfer Coefficient
0.5
0.4
0.362 cm
0.3
0.798 cm
2.00 cm
0.2
0.1
0
40
45
50
55
60
65
70
75
Log Mean Temperature
Figure 3: The relationship between heat transfer coefficient, log mean
temperature, and pipe diameter.
80
Nusselt Number vs. Reynolds Number
90
80
Nusselt Number
70
60
50
.362 cm
.798 cm
40
2.00 cm
.798 cm, T
30
20
10
0
0
5000
10000
15000
20000
25000
30000
Reynolds Number
Figure 4: Relationship between Nusselt number, Reynolds number, and diameter.
Table 1: Relation of Nusselt numbers using our chosen equation and
an equation representing turbulent flow (Mills).
Nu
Nu Turbulent errror
53.74
40.13
0.2533
61.49
60.67
0.0134
71.61
78.45
0.0954
Table 2: Representation of similar Reynolds numbers from different tubes
and the corresponding Nusselt numbers.
ID (cm) Re
0.362
0.798
2.00
Nu
4886
4878
4771
31.23
38.08
59.93
Conclusions

The heat transfer coefficient increases as radius decreases.

The heat transfer increases as the velocity of the water increases and
becomes more turbulent.

As the log mean temperature increases, the heat transfer coefficient
increases.

The convective heat transfer increases with increasing radius.

The Nusselt number increases with increasing turbulent flow.
References

Bird, Robert Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport
Phenomena. 2nd ed. New York: Wiley, 2002.

Crosby, E. J. "Experiment 7.a Heat-Transfer Coefficients in Circular
Tubes." Experiments in Transport Phenomena. New York: John Wiley & Sons,
1961. 88-107.

Mills, Anthony. F. Heat Transfer. CRC Press, 1992.