Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 80
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1, A. Bar-Cohen andA. D. Kraus, eds., Hemisphere Publishing, New York.Morega, A. M., Bejan, A., and Lee, S. W. (1995). Free Stream Cooling of Parallel Plates, Int.J. Heat Mass Transfer, 38(3), 519–531.Nakayama, W., and Park, S.-H. (1996). Conjugate Heat Transfer from a Single SurfaceMounted Block to Forced Convective Air Flow in a Channel, J.
Heat Transfer, 118, 301–309.Nakayama, W., Matsushima, H., and Goel, P. (1988). Forced Convective Heat Transfer fromArrays of Finned Packages, in Cooling Technology for Electronic Equipment, W. Aung,ed., Hemisphere Publishing, New York, pp. 195–210.BOOKCOMP, Inc. — John Wiley & Sons / Page 523 / 2nd Proofs / Heat Transfer Handbook / Bejan[523], (85)Lines: 3757 to 3792———9.0pt PgVar———Short PagePgEnds: TEX[523], (85)524123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSOosthuizen, P.
H., and Naylor, D. (1999). Convective Heat Transfer Analysis, WCB/McGrawHill, New York, Chap. 6.Ortega, A. (1996). Conjugate Heat Transfer in Forced Air Cooling of Electronic Components,in Air Cooling Technology for Electronic Equipment, S. J. Kim and S. W. Lee, eds., CRCPress, Boca Raton, FL, pp. 103–171.Ortega, A., Wirth, U., and Kim, S. J. (1994). Conjugate Forced Convection from a DiscreteHeat Source on a Plane Conducting Surface: A Benchmark Experiment, in Heat Transferin Electronic Systems, ASME-HTD-292, ASME, New York, pp. 25–36.Pohlhausen, E.
(1921). Der Wärmeaustausch zwishen festen Körpern und Flüssigkeiten mitkleiner Reibung und kleiner Wärmeleitung, Z. Angew. Math. Mech., 1, 115–121.Roeller, P. T., and Webb, B. (1992). A Composite Correlation for Heat Transfer from IsolatedTwo- and Three Dimensional Protrusions in Channels, Int. J. Heat Mass Transfer, 35(4),987–990.Roeller, P. T., Stevens, J., and Webb, B. (1991). Heat Transfer and Turbulent Flow Characteristics of Isolated Three-Dimensional Protrusions in Channels, J. Heat Transfer, 113, 597–603.Smith, A. G., and Spalding, D.
B. (1958). Heat Transfer in a Laminar Boundary Layer withConstant Fluid Properties and Constant Wall Temperature, J. R. Aeronaut. Soc., 62, 60–64.Whitaker, S. (1972). Forced Convection Heat Transfer Correlations for Flow in Pipes, Past FlatPlates, Single Cylinders, Single Spheres and for Flow in Packed Beds and Tube Bundles,AIChE J., 18, 361–371.Wirtz, R. A., and Dykshoorn, P.
(1984). Heat Transfer from Arrays of Flat Packs in ChannelFlow, Proc. 4th International Electronics Packaging Society Conferences, New York, pp.318–326.Wirtz, R. A., Sohal, R., and Wang, H. (1997). Thermal Performance of Pin-Fin Fan-SinkAssemblies, J. Electron. Packag., 119, 26–31.Womac, D. J., Ramadhyani, S., and Incropera, F. P. (1993). Correlating Equations for Impingement Cooling of Small Heat Sources with Single Circular Liquid Jets, J.
Heat Transfer, 115,106–115.Zhukauskas, A. (1972). Heat Transfer from Tubes in Cross Flow, in Advances in Heat Transfer,J. P. Hartnett and T. F. Irvine, eds., Vol. 8, Academic Press, New York.Zhukauskas, A. (1987). Convective Heat Transfer in Cross Flow, in Convective Heat Transfer,S. Kakaç, R. K. Shah, and W. Aung, eds., Wiley, New York.BOOKCOMP, Inc.
— John Wiley & Sons / Page 524 / 2nd Proofs / Heat Transfer Handbook / Bejan[Last Page][524], (86)Lines: 3792 to 3820———161.04701pt PgVar———Normal PagePgEnds: TEX[524], (86)123456789101112131415161718192021222324252627282930313233343536373839404142434445CHAPTER 7Natural ConvectionYOGESH JALURIAMechanical and Aerospace Engineering DepartmentRutgers UniversityNew Brunswick, New Jersey[First Page]7.17.2IntroductionBasic mechanisms and governing equations7.2.1 Governing equations7.2.2 Common approximations7.2.3 Dimensionless parameters7.3 Laminar natural convection flow over flat surfaces7.3.1 Vertical surfaces7.3.2 Inclined and horizontal surfaces7.4 External laminar natural convection flow in other circumstances7.4.1 Horizontal cylinder and sphere7.4.2 Vertical cylinder7.4.3 Transients7.4.4 Plumes, wakes, and other free boundary flows7.5 Internal natural convection7.5.1 Rectangular enclosures7.5.2 Other configurations7.6 Turbulent flow7.6.1 Transition from laminar flow to turbulent flow7.6.2 Turbulence7.7 Empirical correlations7.7.1 Vertical flat surfaces7.7.2 Inclined and horizontal flat surfaces7.7.3 Cylinders and spheres7.7.4 Enclosures7.8 SummaryNomenclatureReferences7.1[525], (1)Lines: 0 to 83———-0.65392pt PgVar———Normal PagePgEnds: TEX[525], (1)INTRODUCTIONThe convective mode of heat transfer involves fluid flow along with conduction, ordiffusion, and is generally divided into two basic processes.
If the motion of the525BOOKCOMP, Inc. — John Wiley & Sons / Page 525 / 2nd Proofs / Heat Transfer Handbook / Bejan526123456789101112131415161718192021222324252627282930313233343536373839404142434445NATURAL CONVECTIONfluid arises from an external agent, for instance, a fan, a blower, the wind, or themotion of the heated object itself, which imparts the pressure to drive the flow, theprocess is termed forced convection. If, on the other hand, no such externally inducedflow exists and the flow arises “naturally” from the effect of a density difference,resulting from a temperature or concentration difference in a body force field suchas gravity, the process is termed natural convection. The density difference gives riseto buoyancy forces due to which the flow is generated.
A heated body cooling inambient air generates such a flow in the region surrounding it. The buoyant flowarising from heat or material rejection to the atmosphere, heating and cooling ofrooms and buildings, recirculating flow driven by temperature and salinity differencesin oceans, and flows generated by fires are other examples of natural convection.There has been growing interest in buoyancy-induced flows and the associated heatand mass transfer over the past three decades, because of the importance of theseflows in many different areas, such as cooling of electronic equipment, pollution,materials processing, energy systems, and safety in thermal processes. Several books,reviews, and conference proceedings may be consulted for detailed presentations onthis subject.
See, for instance, the books by Turner (1973), Jaluria (1980), Kakaç etal. (1985), and Gebhart et al. (1988).The main difference between natural and forced convection lies in the mechanismby which flow is generated. In forced convection, externally imposed flow is generallyknown, whereas in natural convection it results from an interaction of the densitydifference with the gravitational (or some other body force) field and is thereforeinevitably linked with and dependent on the temperature and/or concentration fields.Thus, the motion that arises is not known at the onset and has to be determined froma consideration of the heat and mass transfer process which are coupled with fluidflow mechanisms.
Also, velocities and the pressure differences in natural convectionare usually much smaller than those in forced convection.The preceding differences between natural and forced convection make the analytical and experimental study of processes involving natural convection much morecomplicated than those involving forced convection. Special techniques and methodshave therefore been devised to study the former, with a view to providing informationon the flow and on the heat and mass transfer rates.To understand the physical nature of natural convection transport, let us considerthe heat transfer from a heated vertical surface placed in an extensive quiescentmedium at a uniform temperature, as shown in Fig.
7.1. If the plate surface temperature Tw is greater than the ambient temperature T∞ , the fluid adjacent to thevertical surface gets heated, becomes lighter (assuming that it expands on heating),and rises. Fluid from the neighboring areas moves in, due to the generated pressuredifferences, to take the place of this rising fluid. Most fluids expand on heating, resulting in a decrease in density as the temperature increases, a notable exception beingwater between 0 and 4°C.
If the vertical surface is initially at temperature T∞ , andthen, at a given instant, heat is turned on, say through an electric current, the flowundergoes a transient before the flow shown is achieved. It is the analysis and studyof this time-dependent as well as steady flow that yields the desired information on theheat transfer rates, flow and temperature fields, and other relevant process variables.BOOKCOMP, Inc. — John Wiley & Sons / Page 526 / 2nd Proofs / Heat Transfer Handbook / Bejan[526], (2)Lines: 83 to 95———0.0pt PgVar———Normal PagePgEnds: TEX[526], (2)INTRODUCTION123456789101112131415161718192021222324252627282930313233343536373839404142434445527yVelocityboundary layerFlowxT⬁ , ⬁EntrainmentTwT⬁ , ⬁TwEntrainment[527], (3)xLines: 95 to 105Body force(gravity field)Tw > T⬁———FlowTw < T⬁y(a)(b)The flow adjacent to a cooled surface is downward, as shown in Fig. 7.1b, providedthat the fluid density decreases with an increase in temperature.Heat transfer from the vertical surface may be expressed in terms of the commonlyused Newton’s law of cooling, which gives the relationship between the heat transferrate q and the temperature difference between the surface and the ambient as(7.1)where h̄ is the average convective heat transfer coefficient and A is the total area of thevertical surface.
The coefficient h̄ depends on the flow configuration, fluid properties,dimensions of the heated surface, and generally also on the temperature difference,because of which the dependence of q on Tw −T∞ is not linear. Since the fluid motionbecomes zero at the surface due to the no-slip condition, which is generally assumedto apply, the heat transfer from the heated surface to the fluid in its immediate vicinityis by conduction.
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