(19) Internal Convection

8/13/2019 (19) Internal Convection

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INTERNAL FORCED CONVECTION

Associate Professor

IIT Delhi

E-mail: [email protected]


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Internal Forced

Convection

P.Talukdar/Mech-IITD 2


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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


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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