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5
CHAPTER 5
Forced Convection: Internal Flows
ADRIAN BEJAN
Department of Mechanical Engineering and Materials Science
Duke University
Durham, North Carolina
5.1
Introduction
5.2
Laminar ﬂow and pressure drop
5.2.1
Flow entrance region
5.2.2
Fully developed ﬂow region
5.2.3
Hydraulic diameter and pressure drop
5.3
Heat transfer in fully developed ﬂow
5.3.1
Mean temperature
5.3.2
Thermally fully developed ﬂow
5.4
Heat transfer in developing ﬂow
5.4.1
Thermal entrance region
5.4.2
Thermally developing Hagen–Poiseuille ﬂow
5.4.3
Thermally and hydraulically developing ﬂow
5.5
Optimal channel sizes for laminar ﬂow
5.6
Turbulent duct ﬂow
5.6.1
Timeaveraged equations
5.6.2
Fully developed ﬂow
5.6.3
Heat transfer in fully developed ﬂow
5.7
Total heat transfer rate
5.7.1
Isothermal wall
5.7.2
Wall heated uniformly
5.8
Optimal channel sizes for turbulent ﬂow
5.9
Summary of forced convection relationships
Nomenclature
References
5.1 INTRODUCTION
An
internal ﬂow
is a ﬂow con±guration where the ﬂowing material is surrounded by
solid walls. Streams that ﬂow through ducts are primary examples of internal ﬂows.
Heat exchangers are conglomerates of internal ﬂows. This class of ﬂuid ﬂow and
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FORCED CONVECTION: INTERNAL FLOWS
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convection phenomena distinguishes itself from the class of an external ﬂow, which
is treated in Chapters 6 (forcedconvection external) and 7 (natural convection). In an
external ﬂow conFguration, a solid object is surrounded by the ﬂow.
There are two basic questions for the engineer who contemplates using an internal
ﬂow conFguration. One is the heat transfer rate, or the thermal resistance between the
stream and the conFning walls. The other is the friction between the stream and the
walls. The ﬂuid friction part of the problem is the same as calculation of the pressure
drop experienced by the stream over a Fnite length in the ﬂow direction. The ﬂuid
friction question is the more basic, because friction is present as soon as there is ﬂow,
that is, even in the absence of heat transfer. This is why we begin this chapter with the
calculation of velocity and pressure drop in duct ﬂow. The heat transfer question is
supplementary, as the duct ﬂow will convect energy if a temperature difference exits
between its inlet and the wall.
To calculate the heat transfer rate and the temperature distribution through the
ﬂow, one must know the ﬂow, or the velocity distribution. When the variation of
temperature over the ﬂow Feld is sufFciently weak so that the ﬂuid density and
viscosity are adequately represented by two constants, calculation of the velocity Feld
and pressure drop is independent of that of the temperature Feld. This is the case in
all the conFgurations and results reviewed in this chapter. When this approximation
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 Spring '10
 mikey
 Convection, Heat Transfer, Log mean temperature difference, Bejan

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