This document discusses internal forced convection, including flow inside pipes and tubes. It covers general thermal analysis, laminar flow, and turbulent flow. Key points include the differences between pipes and tubes, hydrodynamic and thermal entry lengths, constant surface heat flux versus constant surface temperature, exit temperature calculations, and relationships for Nusselt number in developing versus fully developed laminar and turbulent flow. Examples are provided to demonstrate calculating exit temperature, heat transfer rate, and determining the required heater power or pipe length.

1. CH2043
Heat Transfer Processes and Equipment
CC01, CC02, CC03, CC04
Wan Zaireen Nisa Yahya and Shafirah Samsuri 2022
English Program
Ho Chi Minh City University of Technology

2. CHAPTER 3: CONVECTIVE HEAT TRANSFER
Part 3: Internal Forced Convection
▪ Flow Inside Pipes or Tubes
▪ Thermal Analysis
▪ Laminar Flow in Tubes
▪ Turbulent Flow in Tubes

3. 3
• Overview
Convective Heat Transfer
Heat Convection Problems
Flow Outside Object
Geometry
Flat Plate Single Tube Tube Banks
Re#
Turbulent
Laminar
Vmax
Re#
Tube Pitch
QS const TS const
Laminar
Re#
Turbulent
Re#
Laminar
Developing
Laminar
Flow Inside Object

4. 4
• Definitions
Flow Inside Pipes or Tubes
Pipes Tubes
A pressure-tight circular hollow
section of a piping system used to
transport liquids or gases.
A long hollow cylinder used for
moving liquids or gases.
Pipes Tubes
Shape Round, cylindrical. Square, rectangular, and round.
Size Specified in NPS (nominal pipe size) Specified in mm OD (outside diameter)
Thickness Specified in schedule number Specified in mm or BWG (Birmingham
wire gauge)
Applications Transport of liquids or gasses where it is
important to know the capacity.
Specialty applications, e.g. medical
devices that require a precise outside
diameter to indicate stability.

5. 5
• The Entrance Regions
Flow Inside Pipes or Tubes
▪ The Entry Lengths
Nu, and thus h
values are much
higher in the
entrance region.

6. 6
• The Reynolds Number
Flow Inside Pipes or Tubes
▪ Generally the hydraulic diameter Dh is: Dh =
4𝐴𝑐
𝑝

7. 7
• Thermal conditions at the surface of Tubes or Pipes
Thermal Analysis
i. constant surface heat flux (qs = const)
ii. constant surface temperature (Ts= const)

8. 8
• Constant Surface Heat Flux (qs = const)
Thermal Analysis
Mean fluid temperature at the tube exit:
In the case of qs = constant, the rate of heat transfer:
Surface temperature (Tm is the mean temperature of
the fluid at that location):

9. 9
• Constant Surface Temperature (Ts = constant)
Thermal Analysis
The average temperature difference Tavg = (Ts – Tm)avg
is expressed as:
Rate of heat transfer to or from a fluid flowing in a tube:
i.e., logarithmic mean temperature difference (LMTD)
TLM

10. 10
• Constant Surface Temperature (Ts = constant)
Thermal Analysis
The average temperature difference Tavg = (Ts – Tm)avg
is expressed as:
Rate of heat transfer to or from a fluid flowing in a tube:
i.e., logarithmic mean temperature difference (LMTD)
Then,

11. 11
• Exit Temperature
Thermal Analysis

12. 12
Example 1: Heating of Water in a Tube by Steam
Water enters a 2.5 cm internal diameter thin copper tube of a heat exchanger
at 15ºC at a rate of 0.3 kg/s, and is heated by steam condensing outside at
120ºC. If the average heat transfer coefficient is 800 W/m2∙K, determine the
length of the tube required in order to heat the water to 115ºC.
Solutions
Flow across cylinders and spheres
Rate of heat transfer:
Properties of water Tm = (Ti + Te)/2 = (15 ºC + 115 ºC) /2 = 65 ºC → Cp = 4187 J/kg.K.
( )
W
125600
C)
15
C
K)(115
4817J/kg
(0.3kg/s)( o
o
.
.
=
−

=
−
= i
e
p T
T
c
m
Q
Given: Heat transfer rate of water in pipe, determine the length of the pipe.

14. Δ𝑇𝑙𝑚 =
(120 − 115) − (120 − 15)
ln[ (120 − 115)/(120 − 15)]
= 32.85oC
14
Example 1: Heating of Water in a Tube by Steam
For constant surface temperature
Flow across cylinders and spheres
Surface area of heat transfer:
and h = 800 W/m2∙K
where
For a 2.5 cm internal diameter thin-walled tube, →
#answer

15. 15
• Constant Surface Heat Flux (qs = constant)
Laminar Flow in Tubes
▪ Circular tube, laminar (qs = const):
▪ Circular tube, laminar (Ts = const):
• Constant Surface Temperature (Ts = constant)

16. 16
• Laminar Flow in Circular Tube
Laminar Flow in Tubes
▪ For fully developed laminar flow in a circular tube subjected to constant
surface heat flux or constant surface temperature, the Nusselt number is
a constant.
▪ There is no dependence on the Reynolds or the Prandtl numbers.
▪ The thermal conductivity k for use in the Nu relations should be
evaluated at the bulk mean fluid temperature.

17. 17

18. 18
• Developing Laminar Flow in the Entrance Region
Laminar Flow in Tubes
▪ For a circular tube of length L subjected to constant surface
temperature, the average Nusselt number for the thermal entrance
region (Lt):
▪ The average Nusselt number is larger at the entrance region,
and it approaches asymptotically to the fully developed value of 3.66 as
L → ∞.

19. 19
• Fully developed turbulent flow in a smooth tube
Turbulent Flow in Tubes

20. Example: Heating of Water by Resistance Heaters in a Tube
Water is to be heated from 15°C to 65°C as it flows through a 3-cm-internal diameter 5-
m-long tube. The tube is equipped with an electric resistance heater that provides
uniform heating throughout the surface of the tube. The outer surface of the heater is
well insulated, so that in steady operation all the heat generated in the heater is
transferred to the water in the tube. If the system is to provide hot water at a rate of
10 L/min, determine the power rating of the resistance heater. Also, estimate the inner
surface temperature of the pipe at the exit.

21. 21
Example 2: Flow of Oil in a Pipeline through an Icy Lake
Consider the flow of oil at 20ºC in a 30-cm diameter pipeline at an average
velocity of 2 m/s. A 200 m long section of the horizontal pipeline passes
through icy waters of a lake at 0ºC. Measurements indicate that the surface
temperature of the pipe is very nearly 0ºC. Disregarding the thermal resistance
of the pipe materials, determine:
a. The temperature of the oil when the pipe leaves the lake.
b. The rate of heat transfer from the oil.
Solutions
Laminar Flow in Tubes
Assume Tm = 20ºC. Then Properties of oil;
𝜌= 888.1 kg/m3, 𝜈 = 9.429 x 10-4 m2/s, Pr= 10863,
k = 0.145 W/m∙K, cp = 1880 J/kg•K.

22. 22
Example 2: Flow of Oil in a Pipeline through an Icy Lake
Calculate the Reynolds number and check the thermal entry length:
Laminar Flow in Tubes
∴ At length of pipe = 200 m, the flow is in the thermally developing region.
r)
636(lamina
m/s
10
9.429
0.3m
2m/s
ν
D
V
Re 4
avg
=


=
= −
200m)
103600m(
0.3m
10863
636
0.05
0.05RePrD
Lt

=



=
=
Then for thermally developing region, the correlation of Nusselt number is;

23. 23
Example 2: Flow of Oil in a Pipeline through an Icy Lake
The Nusselt number:
Laminar Flow in Tubes
Then the heat transfer coefficient:
K
W/m
0.3m
K
0.145W/m
37.3
D
Nuk
h 2

=


=
= 02
.
18

24. 24
Example 2: Flow of Oil in a Pipeline through an Icy Lake
a. The temperature of the oil when the pipe leaves the lake.
Laminar Flow in Tubes
where,
)
71
.
19
)
1880
6
.
125
5
.
188
02
.
18
exp(
)
20
0
(
0
0
C
20
to
(near
C
T
0
e
=


−
−
−
=
2
s 188.5m
200m
0.3m
π
πDL
A =


=
=
125.6kg/s
2m/s
]m
π(0.3)
4
1
[
888.1kg/m
m 2
2
3
.
=


=
= avg
cV
A

then,

25. 25
Example 2: Flow of Oil in a Pipeline through an Icy Lake
b. The rate of heat transfer from the oil
Laminar Flow in Tubes
where,
then,
.
lm
s T
hA
Q 
=
Δ𝑇𝑙𝑚 =
(19.74 − 0) − (20 − 0)
ln[ (19.74 − 0)/(20 − 0)]
= 19.87℃
Q = 16.3W/m2
⋅ K × 188.5m2
× (19.87o
C)
= 61052 W

26. 26

27. Summary
Internal Force Convection
• Flow Inside Pipes or Tubes
• General Thermal Analysis
• Laminar Flow in Tubes
• Turbulent Flow in Tubes
• Characteristics of pipes vs. tubes
• Hydrodynamic and thermal entry lengths
• qs constant vs. Ts constant
• Exit temperature, Te
• Nu, developing vs. fully developed flow
27

28. Summary
Internal flow is
characterized by the fluid
being completely
confined by the inner
surfaces of the tube.
The Reynolds number
for internal flow and
the hydraulic diameter
The entry lengths
Q
Laminar
For fully developed laminar flow in a
circular pipe
For developing laminar flow in the entrance region with constant surface temperature
For fully developed
turbulent flow with
smooth surfaces