4 m2 0151 kgs1008 jkg c 80c exp 713c then the

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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 re-evaluate 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 Single-Phase 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 Single-Phase 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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