Unformatted text preview: 0 80
Ts Ti
hAs Tln (13.5 W/m2 °C)(6.4 m2)( 15.2°C) Tln
·
Q 1313 W Therefore, air will lose heat at a rate of 1313 W as it flows through the duct in
the attic.
Discussion The average fluid temperature is (80
71.3)/2
75.7°C, which
is sufficiently close to 80°C at which we evaluated the properties of air. Therefore, it is not necessary to reevaluate the properties at this temperature and to
repeat the calculations. SUMMARY
Internal flow is characterized by the fluid being completely
confined by the inner surfaces of the tube. The mean velocity
and mean temperature for a circular tube of radius R are expressed as
m 2
R2 R (r, x)rdr and 0 Tm 2
2
mR R Trdr
0 dynamic entry length Lh. The region beyond the entrance
region in which the velocity profile is fully developed is the
hydrodynamically fully developed region. The length of the region of flow over which the thermal boundary layer develops
and reaches the tube center is the thermal entry length Lt. The
region in which the flow is both hydrodynamically and thermally developed is the fully developed flow region. The entry
lengths are given by The Reynolds number for internal flow and the hydraulic diameter are defined as
Re mD mD and Dh Lh, laminar 0.05 Re D
Lt, laminar 0.05 Re Pr D Pr Lh, laminar
Lh, turbulent Lt, turbulent 10D 4Ac
p The flow in a tube is laminar for Re
2300, turbulent for
Re 10,000, and transitional in between.
The length of the region from the tube inlet to the point at
which the boundary layer merges at the centerline is the hydro ·
For q s constant, the rate of heat transfer is expressed as
·
·
Q q·s As m Cp(Te Ti) cen58933_ch08.qxd 9/4/2002 11:29 AM Page 450 450
HEAT TRANSFER For Ts For fully developed turbulent flow with smooth surfaces,
we have constant, we have
·
·
Q hAs Tln m Cp(Te Ti)
·
Te Ts (Ts Ti)exp( hAs /m Cp)
Ti Te
Ti
Te
Tln
ln[(Ts Te)/(Ts Ti)] ln( Te / Ti) f
Nu
Nu The pressure drop and required pumping power for a volume
·
flow rate of V are
2 m
L
D2 P ·
Wpump and Nu ·
VP For fully developed laminar flow in a circular pipe, we have:
(r)
f
·
V 2 m 64
D 1 m ave Ac r2
R2 max 64
Re
PR2
R2
8L r2
R2 1 R4 P
8L ·
Circular tube, laminar (q s constant): Nu Circular tube, laminar (Ts constant): Nu R4 P
128 L
hD
k
hD
k 3.66 Nu Circular tube: Nu Parallel plates: Nu 0.065(D/L) Re Pr
1 0.04[(D/L) Re Pr]2/3
Re Pr D 1/3 b 0.14
1.86
s
L
0.03(Dh /L) Re Pr
7.54
1 0.016[(Dh /L) Re Pr]2/3
3.66 104 Re 106 0.7 Pr 160
Re 10,000
0.023 Re0.8 Prn with n 0.4 for heating and 0.3 for
cooling of fluid
( f/8)(Re 1000) Pr
0.5 Pr 2000
1 12.7( f/8)0.5 (Pr2/3 1) 3 103 Re 5 106
0.023 Re0.8 Pr1/3 constant:
constant: Nu
Nu 4.8
6.3 0.0156 Re0.85 Pr0.93
s
0.0167 Re0.85 Pr0.93
s For fully developed turbulent flow with rough surfaces, the
friction factor f is determined from the Moody chart or
1 4.36 2 The fluid properties are evaluated at the bulk mean fluid
temperature Tb
(Ti
Te)/2. For liquid metal flow in the
range of 104 Re 106 we have:
Ts
q·s For developing laminar flow in the entrance region with constant surface temperature, we have
Circular tube: Nu (0.790 ln Re 1.64)
0.125f Re Pr1/3 f 2.0 log /D
3.7 2.51
Re f 1.8 log 6.9
Re /D
3.7 1.11 For a concentric annulus, the hydraulic diameter is Dh
Do Di, and the Nusselt numbers are expressed as
Nui hi Dh
k and Nuo ho Dh
k where the values for the Nusselt numbers are given in
Table 8–4. REFERENCES AND SUGGESTED READING
1. M. S. Bhatti and R. K. Shah. “Turbulent and Transition
Flow Convective Heat Transfer in Ducts.” In Handbook
of SinglePhase Convective Heat Transfer, ed. S. Kakaç,
R. K. Shah, and W. Aung. New York: Wiley
Interscience, 1987. 2. A. P. Colburn. Transactions of the AIChE 26 (1933),
p. 174.
3. C. F. Colebrook. “Turbulent flow in Pipes, with Particular
Reference to the Transition between the Smooth and cen58933_ch08.qxd 9/4/2002 11:29 AM Page 451 451
CHAPTER 8 Rough Pipe Laws.” Journal of the Institute of Civil
Engineers London. 11 (1939), pp. 133–156. Surfaces.” In Augmentation of Convective Heat Transfer,
ed. A. E. Bergles and R. L. Webb. New York:
ASME, 1970. 4. R. G. Deissler. “Analysis of Turbulent Heat Transfer and
Flow in the Entrance Regions of Smooth Passages.” 1953.
Referred to in Handbook of SinglePhase Convective
Heat Transfer, ed. S. Kakaç, R. K. Shah, and W. Aung.
New York: Wiley Interscience, 1987. 21. B. S. Petukhov. “Heat Transfer and Friction in Turbulent
Pipe Flow with Variable Physical Properties.” In
Advances in Heat Transfer, ed. T. F. Irvine and J. P.
Hartnett, Vol. 6. New York: Academic Press, 1970. 5. D. F. Dipprey and D. H. Sabersky. “Heat and Momentum
Transfer in Smooth and Rough Tubes at Various Prandtl
Numbers.” International Journal of Heat Mass Transfer 6
(1963), pp. 329–353. 22. B. S. Petukhov and L. I. Roizen. “Generalized
Relationships for Heat Transfer in a Turbulent Flow of
a Gas in Tubes of Annular Section.” High Temperature
(USSR) 2 (1964), pp. 65–68. 6. F. W. Dittus and L. M. K. Boelter. University of
California Publications on Engineering 2 (1930), p. 433. 23. O. Reynolds. “On the Experimental Investigati...
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 Spring '10
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 Fluid Dynamics, Heat Transfer, TI, tube

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