(19) internal convection
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INTERNAL FORCED CONVECTION
Associate Professor
IIT Delhi
E-mail: rabal@mech.iitd.ac.in
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Internal Forced
Convection
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cA ccm x)dAV(r,AV.mFor a circular pipe of radius
R
dAxrV
R0
22
0
c
A
m rdrxrVR
2
RAV c ),(
,
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Bulk MeanThe value of the mean temperature Tm isdetermined from the requirement that the
conservation of energy principle be satisfied.
That is, the energy transported by the fluid
throu h a cross section in actual flow must be
equal to the energy that would be transportedthrough the same cross section if the fluid
were at a constant temperature Tm.
at mean
temperature
mpTCm.
or a c rcu ar p pe w t constant property
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For flow in a circular tube,the Re is defined as
Hydraulic
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The region from the tube inlet to the point at which the boundary
entrance region, and the length of this region is called the
hydrodynamic entry length Lh.
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The region of flow over which the thermal boundary layer
develops and reaches the tube center is called the thermalentrance region, and the length of this region is called the
thermal entry length Lt.
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The friction factor is constant for the fully developed region why?
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Temperature Profile
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developed region is constant
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Since
In fully developed region, both heat transfer coefficient and
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developed region may vary with x in the flow direction.
That is, unlike the velocity profile, the temperature
profile can be different at different cross sections of the
tube in the develo ed re ion and it usuall is.
However, the dimensionless temperature profile defined
region when the temperature or heat flux at the tube
surface remains constant
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Pr (= /) >1
ar at ono t e r ct on
factorandtheconvection
heattransfercoefficientin
theflowdirectionforflow
inatube(Pr>1).
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Entry length
For Re = 20, the hydrodynamic
Thehydrodynamicentrylength
isusuallytakentobethe
distancefromthetubeentrance
en ry eng s a ou e s ze o
the diameter, but increaseslinearly with the velocity. In the
w eret e r ct oncoe c ent
reacheswithinabout2percent
ofthefullydevelopedvalue
limiting case of Re = 2300, the
hydrodynamic entry length is
.Kays and Crawford (1993),
Shah and Bhatti (1987)
For turbulent flow, hydrodynamic and thermal entry lengths are
almost similar and is independent of Pr
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,
as expected, and its dependence on the Reynolds number isweaker. It is 11D at Re =10,000, and increases to 43D at Re
=105. In ractice it is enerall a reed that the entrance effects
are confined within a tube length of 10 diameters, and the
hydrodynamic and thermal entry lengths are approximately taken
to beLh,turbulent Lt, turbulent10D
Bhatti and Shah (1987) and Zhi-qing (1982)
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Distribution of Nusselt No. for
Turbulent flow
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