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1. CME 341 Heat Transfer
CONVECTION
Fall 2020
Dr. Hadil Abu Khalifeh

2. 2.4 Forced Convection in Pipes andDucts
•Many correlations for calculating heat-transfer coefficients in this
type of flow have been proposed
•Correlations are given for each of the three flow regimes: turbulent,
transition, and laminar.
•The physical situation described by the correlations is depicted in
Figure 2.4. Fluid enters the pipe at an average temperature Tb1 and
leaves at an average temperature Tb2.
•(Tb stands for bulk temperature. It is the fluid temperature averaged
over the flow area.)
•The pipe wall temperature is Tw1 at the entrance and Tw2 at the exit.
•The fluid is either heated or cooled as it flows through the pipe,
depending on whether the wall temperature is greater or less than
the fluid temperature.
FIGURE 2.4 Heat transfer in pipeflow.

3. With respect to heat transfer in circular pipes, fully developed turbulent flow is achieved at a Reynolds
number of approximately 104. For this flow regime (Re ≥ 104),the following correlation is widely used:
…………………(2.35)
…………………(2.36)
Equation (2.34) is valid for fluids with Prandtl numbers between 0.5 and 17,000, and for pipes with L/D >10.
However, for short pipes with 10 < L/D < 60, the right-hand side of the equation is often multiplied by the
factor [1 + (D/L)2/3] to correct for entrance and exit effects. The correlation is generally accurate to within ±
20% to ±40%.
…………………(2.34)
Equation (2.34) is generally attributed to Seider and Tate

5. It is most accurate for fluids with low to moderate Prandtl numbers (0.5 Pr 100), which includes all gases
and low-viscosity process liquids such as water, organic solvents, light hydrocarbons, etc. It is less accurate
for highly viscous liquids, which have correspondingly large Prandtl numbers.
For laminar flow in circular pipes (Re < 2100), the Seider-Tate correlation takes the form:
…………………(2.37)
This equation is valid for 0.5 <Pr < 17,000 and (Re Pr D/L)1/3 (µ/µw)0.14 > 2, and is generally accurate towithin
± 25%. Fluid properties are evaluated at Tb,ave except for μw, which is evaluated atTw,ave.
For (RePrD/L)1/3 (µ/µw)0.14 < 2, the Nusselt number should be set to 3.66,which is the theoretical value for
laminar flow in an infinitely long pipe with constant walltemperature.
For flow in the transition region (2100 < Re < 104), the Hausen correlation is recommended
…………………(2.38)

6. An alternative equation for the transition and turbulent regimes has been proposed by Gnielinski
…………………(2.39)
Where, f is the Darcy friction factor, which can be computed from the following explicit
approximation of the Colebrook equation
…………………(2.40)
Equation (2.39) is valid for 2100 < Re < 106 and 0.6 < Pr < 2000. It is generally accurate to within ± 20%.
For flow in ducts and conduits with non-circular cross-sections, Equations (2.34) and (2.38)–(2.40), can
be used if the diameter is replaced everywhere by the equivalent diameter, De, where
De = 4 hydraulic radius = 4 flow area/wetted perimeter …………………(2.41)
This approximation generally gives reliable results for turbulent flow. However, it is not
recommended for laminar flow.

7. The most frequently encountered case of laminar flow in non-circular ducts
is flow in the annulus of a double-pipe heat exchanger. For laminar annular
flow, the following equation given by Gnielinski is recommended:
…………………(2.42)
Schematic of a co-currentdouble pipe heat exchanger
The Nusselt number in Equation (2.42)is based on the equivalent diameter, De.
All of the above correlations give average values of the heat-transfer coefficient over the entire length,
L, of the pipe. Hence, the total rate of heat transfer between the fluid and the pipe wall can be
calculated from Equation (2.1), which takes the following form:
…………………(2.43)

8. In equation (2.43) , A is the total heat-transfer surface area (πDL for a circular pipe) and ∆Tln is an average
temperature difference between the fluid and the pipe wall. A logarithmic average is used; it is termed the
logarithmic mean temperature difference (LMTD) and is defined by:
…………………(2.44)
Where
Like any mean value, the LMTD lies between the extreme values, ∆T1 and ∆T2. Hence, when ∆T1 and ∆T2
are not greatly different, the LMTD will be approximately equal to the arithmetic mean temperature
difference, by virtue of the fact that they both lie between ∆T1 and ∆T2. The arithmetic mean temperature
difference, ∆Tave, is given by:
…………………(2.45)
The difference between ∆Tln and ∆Tave is small when the flow is laminar and RePrD/L >10

9. Example2.5
Carbon dioxide at 300 K and 1 atm is to be pumped through a 5 cm ID pipe at a rate of 50 kg/h. The pipe
wall will be maintained at a temperature of 450 K in order to raise the carbon dioxide temperature to 400 K.
What length of pipe will be required?
q = hA ∆Tln =hπDL ∆Tln
Solution
In order to solve the equation for the length, L, wemust
first determine q, h, and ∆Tln . The required physical
properties of CO2 are obtained from Table A.10.
i)
Since Re > 104, the flow is turbulent, and Equation (2.34) is applicable.
ii)

10. iii)
The rate of heat transfer, q, is obtained from an energy balance on the CO2.
iv)
v)
Checking the length to diameter ratio,

12. Example 2.6
1000 lbm/h of oil at 100F enters a 1-in. ID heated copper tube. The tube is 12 ft long and its inner surface
is maintained at 215F. Determine the outlet temperature of the oil. The following physical property data
are available for the oil:
Solution
Since the temperature dependencies of the fluid properties are not given, the properties will be assumed constant.In
this case, the heat-transfer coefficient is independent of the outlet temperature, and can be computed at the outset.
In order to obtain a first approximation for the outlet temperature, Tb2, we assume ∆Tln Ξ ∆Tave: Then,

13. Solving forTb2,
To obtain a second approximation for Tb2, we next calculatethe LMTD:
Then

14. Example 2.8
Carbon dioxide at 300 K and 1 atm is to be pumped through a duct with a 10 cm x 10 cm square cross-section at a rate of
250 kg/h. The walls of the duct will be at a temperature of 450 K. What distance will the CO2 travelthrough the duct before
its temperature reaches 400K?
Solution
The required physical properties are tabulated in Example 2.5. The equivalent diameteris calculated from Equation (2.41):
i)
Note that the Reynolds number is not equal to for non-circular ducts. Rather thecontinuity
equation is used to express the Reynolds number in terms of mass flow rate.
Perimeter=10+10 +10+10 cm
De = 4 hydraulicradius
= 4 flow area/perimeter

15. ii)
iii)
iv)

16. 2.5 Forced Convection in External Flow
es ve
l
Many problems of engineering interest involve heat transfer to fluids flowing over objects such as
pipes, tanks, buildings or other structures. In this section, correlations for several such systems are
presented in order to illustrate the method of calculation.
Many other correlations can be found in heat-transfer textbooks.
Flow over a flat plate is illustrated in Figure 2.5. The undisturbed fluid velocity and temperature
upstream of the plate are VN and TN, r pecti y.The surface temperature of the plate is Ts and L is
the length of the plate in the direction of flow. The fluid may flow
over one or both sides of the plate. The heat-transfer coefficient is obtained from the following
correlations :
(2.47)
(2.48)
FIGURE 2.5 Forced convectionin flow over a flat plate
where

17. Equation (2.47) is valid for Prandtl numbers greater than about 0.6. Equation (2.48) is
applicable for Prandtl numbers between 0.6 and 60, and Reynolds numbers up to 108.
In these equations all fluid properties are evaluated at the film temperature, Tf, defined by:
(2.49)
The heat-transfer coefficients computed from Equations (2.47) and (2.48) are average values for theentire
plate. Hence, the rate of heat transfer between the plate and the fluid is given by:
(2.50)
where A is the total surface area contacted by thefluid.
For flow perpendicular to a circular cylinder of diameter D, the average heat-transfer coefficient canbe
obtained from the correlation
(2.51)
where

18. Tѳ.
The correlation is valid for Re Pr > 0.2, and all fluid properties are evaluated at the film temperature, Tf.
The rate of heat transfer is given by Equation (2.50) with A = π DL, where L is the length of the cylinder.
For flow over a sphere of diameter D, the following correlation is recommended
(2.52)
where
All fluid properties, except μs, are evaluated at the free-stream temperature, The viscosity, µs, is evaluated at
the surface temperature, Ts. Equation (2.52) is valid for Reynolds numbers between 3.5 and 80,000, and
Prandtl numbers between 0.7 and 380.
For a gas flowing perpendicular to a cylinder having a square cross-section (such as an air duct), the following
equation is applicable
(2.53)
The Nusselt and Reynolds numbers are calculated as for a circular cylinder but with the diameter, D, replaced by
the length of a side of the square cross-section.All fluid properties are evaluated at the film temperature. Equation
(2.53) is valid for Reynolds numbers in the range 5000 to 105. In general, one should not expect the accuracy of
computed values to be better than 25% to 30% when using these equations.

19. Example 2.9
Air at 20 oC is blown over a 6 cm OD pipe that has a surface temperature of 140 oC. The free-stream air
velocity is 10 m/s. What is the rate of heat transfer per meter of pipe?
Solution
For forced convection from a circular cylinder, Equation (2.51) is applicable. The film temperature is:

21. Example 2.10
A duct carries hot waste gas from a process unit to a pollution control device. The ductcross-section is
4 ft X 4 ft and it has a surface temperature of 140 o C. Ambient air at 20 o C blows across the duct with
a wind speed of 10 m/s. Estimate the rate of heat loss per meter of duct length.
Solution
The film temperature is the same as in the previous example:
Therefore, the same values are used for the properties of air. The Reynolds number is based on the lengthof
the side of the duct cross-section. Hence, we set:

22. The Reynolds number is outside the range of Equation (2.53). However, the equation will be usedanyway
since no alternative is available. Thus,
The surface area of the duct per meter of lengthis:
Finally, the rate of heat loss is: