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`UTC-2015.001
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`GE v. UTC
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`Trial IPR2016-01301
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`UTC-2015.001
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`GE v. UTC
`Trial IPR2016-01301
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`

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`% Higher Education
`
`HEAT TRANSFER TENTH EDITION
`
`PliblishedhyMcGraw—HilLahusinessunitof'lhe McGraw—Hill Companies, Inc, 1221
`Avenue offlieAmeriuS, NewYodgNYlOOZO. CopyliglflOZOlObyTthcGraw-IIiHCompameslnc.
`Allrightsreserved
`2002, 1997,3111! 1990_Nopanoffliispublicationmaybereproduced
`mdisnihmedmmyfmmmbymymemorstmedinadatabasemreuievalsysm,
`withmnthepriorwrittenconsentofThe McGraw—Hill Companies, Inc, induding,butnot limited to,
`mmymkmoflluekcumicsmgemummissimmhmdcastfmdismelwnmg.
`
`Some ancillaries, includingelectmnic andprintcomponents, maynothe availabletocustomers
`outside the United States.
`
`'Ihisbookisplintedonacid—fi'eepaper.
`
`1234567890VN'H/VNH09
`
`ISBN 978—0—07—352936—3
`MI-IlD 0—07—352936—2
`
`Global Publisher. Raghotharnan Srinivasan
`Senior Sponsoring Editor. Bill Stenquist
`Director ofDevelopment: Kristine Iibbefis
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`Cover Designer: Studio Montage, St. Louis, Missouri
`Cover Image: Intwfmrnetcrphato ofairflow across a hated cylinder; digitally enhanced by the author:
`Compositor: S4Carlisl¢ Publishing Services
`Typeface: 10.5/12 limes Roman
`Pn'mer: R. R. Donnelley, Jflmon City, MO
`
`library of Congress Cataloging-in—Puhlication Data
`
`Holman, J. P. (Jack Philip)
`Heat uansfer / Jack P. Holman—10d: ed
`
`p. un—(Mchaw—Hill series in mechanical engineering)
`Includes index
`
`ISBN 978—0-07—352936—3—ISBN 0—07—352936—2 (hard copy : all; paper)
`I. Heat-Timmission I. Title.
`
`QC320.H64 2010
`621.402’2—dc22
`
`wwwmhhecom
`
`2008033196
`
`UTC-2015.002
`
`

`

`10
`
`1-3 Convection Heat Transfer
`
`1-3 CONVECTION HEAT TRANSFER
`It is well known that a hot plate of metal will cool faster when placed in front of a fan than
`when exposed to still air. We say that the heat is convected away, and we call the process
`convection heat transfer. The term convection provides the reader with an intuitive notion
`concerning the heat-transfer process; however, this intuitive notion must be expanded to
`enable one to arrive at anything like an adequate analytical treatment of the problem. For
`example, we know that the velocity at which the air blows over the hot plate obviously
`influences the heat-transfer rate. But does it influence the cooling in a linear way; i.e., if
`the velocity is doubled, will the heat-transfer rate double? We should suspect that the heat-
`transfer rate might be different if we cooled the plate with water instead of air, but, again,
`how much difference would there be? These questions may be answered with the aid of
`some rather basic analyses presented in later chapters. For now, we sketch the physical
`mechanism of convection heat transfer and show its relation to the conduction process.
`Consider the heated plate shown in Figure 1-7. The temperature of the plate is Tw, and
`the temperature of the fluid is T∞. The velocity of the flow will appear as shown, being
`reduced to zero at the plate as a result of viscous action. Since the velocity of the fluid layer
`at the wall will be zero, the heat must be transferred only by conduction at that point. Thus
`we might compute the heat transfer, using Equation (1-1), with the thermal conductivity
`of the fluid and the fluid temperature gradient at the wall. Why, then, if the heat flows by
`conduction in this layer, do we speak of convection heat transfer and need to consider the
`velocity of the fluid? The answer is that the temperature gradient is dependent on the rate at
`which the fluid carries the heat away; a high velocity produces a large temperature gradient,
`and so on. Thus the temperature gradient at the wall depends on the flow field, and we must
`develop in our later analysis an expression relating the two quantities. Nevertheless, it must
`be remembered that the physical mechanism of heat transfer at the wall is a conduction
`process.
`To express the overall effect of convection, we use Newton’s law of cooling:
`q= hA (Tw − T∞)
`[1-8]
`Here the heat-transfer rate is related to the overall temperature difference between the
`wall and fluid and the surface area A. The quantity h is called the convection heat-transfer
`coefficient, and Equation (1-8) is the defining equation.An analytical calculation of h may be
`made for some systems. For complex situations it must be determined experimentally. The
`heat-transfer coefficient is sometimes called the film conductance because of its relation
`to the conduction process in the thin stationary layer of fluid at the wall surface. From
`Equation (1-8) we note that the units of h are in watts per square meter per Celsius degree
`when the heat flow is in watts.
`In view of the foregoing discussion, one may anticipate that convection heat transfer
`will have a dependence on the viscosity of the fluid in addition to its dependence on the
`
`Figure 1-7 Convection heat transfer from a plate.
`
`Flow
`
`Free stream
`
`u
`
`T
`
`u
`
`q
`
`Tw
`
`Wall
`
`UTC-2015.003
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`

`

`C H A P T E R 1
`
`Introduction
`
`11
`
`thermal properties of the fluid (thermal conductivity, specific heat, density). This is expected
`because viscosity influences the velocity profile and, correspondingly, the energy-transfer
`rate in the region near the wall.
`If a heated plate were exposed to ambient room air without an external source of motion,
`a movement of the air would be experienced as a result of the density gradients near the
`plate. We call this natural, or free, convection as opposed to forced convection, which
`is experienced in the case of the fan blowing air over a plate. Boiling and condensation
`phenomena are also grouped under the general subject of convection heat transfer. The
`approximate ranges of convection heat-transfer coefficients are indicated in Table 1-3.
`
`Convection Energy Balance on a Flow Channel
`The energy transfer expressed by Equation (1-8) is used for evaluating the convection loss
`for flow over an external surface. Of equal importance is the convection gain or loss resulting
`from a fluid flowing inside a channel or tube as shown in Figure 1-8. In this case, the heated
`wall at Tw loses heat to the cooler fluid, which consequently rises in temperature as it flows
`
`Table 1-3 Approximate values of convection heat-transfer coefficients.
`
`Mode
`Across 2.5-cm air gap evacuated to a pressure
`of 10−6 atm and subjected
`to T = 100◦C− 30◦C
`Free convection, T = 30◦C
`Vertical plate 0.3 m [1 ft] high in air
`Horizontal cylinder, 5-cm diameter, in air
`Horizontal cylinder, 2-cm diameter,
`in water
`Heat transfer across 1.5-cm vertical air
`gap with T = 60◦C
`Fine wire in air, d = 0.02 mm, T = 55◦C
`Forced convection
`Airflow at 2 m/s over 0.2-m square plate
`Airflow at 35 m/s over 0.75-m square plate
`Airflow at Mach number = 3, p= 1/20 atm,
`T∞ =−40◦C, across 0.2-m square plate
`Air at 2 atm flowing in 2.5-cm-diameter
`tube at 10 m/s
`Water at 0.5 kg/s flowing in 2.5-cm-diameter
`tube
`Airflow across 5-cm-diameter cylinder
`with velocity of 50 m/s
`Liquid bismuth at 4.5 kg/s and 420◦C
`in 5.0-cm-diameter tube
`Airflow at 50 m/s across fine wire,
`d = 0.04 mm
`Boiling water
`In a pool or container
`Flowing in a tube
`Condensation of water vapor, 1 atm
`Vertical surfaces
`Outside horizontal tubes
`Dropwise condensation
`
`h
`
`W/m2 · ◦C
`
`Btu/h· ft2 · ◦F
`
`0.087
`
`4.5
`6.5
`
`890
`
`2.64
`490
`
`12
`75
`
`56
`
`65
`
`3500
`
`180
`
`3410
`
`3850
`
`0.015
`
`0.79
`1.14
`
`157
`
`0.46
`86
`
`2.1
`13.2
`
`9.9
`
`11.4
`
`616
`
`32
`
`600
`
`678
`
`2500–35,000
`5000–100,000
`
`4000–11,300
`9500–25,000
`170,000–290,000
`
`440–6200
`880–17,600
`
`700–2000
`1700–4400
`30,000–50,000
`
`UTC-2015.004
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`

`

`12
`
`1-4 Radiation Heat Transfer
`
`Figure 1-8 | Convection in a channel.
`
`T_
`
`.
`
`q
`
`\
`
`Te
`1
`1
`.
`m“-
`
`
`from inlet conditions at T; to exit conditions at T,. Using the symbol 1' to designate enthalpy
`(to avoid confusion with h, the convection coeflicient). the energy balance on the fluid is
`
`q=m(ie —ii)
`
`where Iii is the fluid mass flow rate. For many single-phase liquids and gases operating over
`reasonable temperature ranges Ai = cpAT and we have
`
`which may be equated to a convection relation like Equation (1-8)
`
`q =Ith(72 —
`
`‘1 =mcp(Te —
`
`= hA(Tw,avg — Tfluid, avg)
`
`[1‘8"]
`
`In this case, the fluid temperatures Te, 7}, and Tania are called bulk or enelgv average
`temperatures. A is the surface area of the flow channel in contact with the fluid. We shall
`have more to say about the notions of computing convection heat transfer for external and
`internal flows in Chapters 5 and 6. For now, we simply want to alert the reader to the
`distinction between the two types of flows.
`We must be careful to distinguish between the surface area for convection that is
`employed in convection Equation (1-8) and the cross-sectional area that is used to calculate
`the flow rate from
`
`ti: = pu Ac
`
`where Ac = 7212/4 for flow in a circular tube. The surface area for convection in this case
`would be ML, where L is the tube length. The surface area for convection is always the
`area of the heated surface in contact with the fluid.
`
`1—4 | RADIATION HEAT TRANSFER
`
`In contrast to the mechanisms ofconduction and convection, where energy transfer through a
`material medium is involved, heat may also be transferred through regions where a perfect
`vacuum exists. The mechanism in this case is electromagnetic radiation. We shall limit
`our discussion to electromagnetic radiation that is propagated as a result of a temperature
`difl'erence; this is called thermal radiation.
`
`Thermodynamic considerations show“ that an ideal thermal radiator, or blackboafv, will
`emit energy at a rate proportional to the fourth power of the absolute temperature of the
`body and directly proportional to its surface area. Thus
`
`qm=aA14
`
`[1-91
`
`'See, for example, J. P. Holmm Thermodynamics. 4th ed New Yuk McGraw-Hill, 1988, p. 705.
`
`UTC-2015.005
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`

`

`C H A P T E R 1
`
`Introduction
`
`25
`
`Consult whatever sources are needed, and devise suitable measures for energy con-
`sumption and cost using the SI system of units. How would you price such items as
`Energy content of various types of coal
`Energy content of gasoline
`Energy content of natural gas
`Energy “content” of electricity
`After devising the SI system of cost measures, construct a table of conversion factors
`like that given in the front inside cover of this book, to convert from SI to English
`and from English to SI.
`1-43 Using information developed in Problem 1-42, investigate the energy cost saving that
`results from the installation of a layer of glass wool 15 cm thick on a steel building
`12 by 12 m in size and 5 m high. Assume the building is subjected to a temperature
`difference of 30◦C and the floor of the building does not participate in the heat lost.
`Assume that the outer surface of the building loses heat by convection to a surrounding
`temperature of −10◦C with a convection coefficient h= 13 W/m2 · ◦C.
`1-44 A boy-scout counselor gives the following advice to his scout troop regarding camp-
`ing out in cold weather. “Be careful when setting up your cot/bunk—you may have
`provided for plenty of blankets to cover the top of your body, but don’t forget that
`you can lose heat from the bottom through the thin layer of the cot/bunk. Provide a
`layer of insulation for your bottom side also.” Investigate the validity of this state-
`ment by making suitable assumptions regarding exterior body temperature, thermal
`conductivity of blankets and cot/bunk materials, and the like.
`
`REFERENCES
`1. Glaser, P. E., I. A. Black, and P. Doherty. Multilayer Insulation, Mech. Eng., August 1965, p. 23.
`2. Barron, R. Cryogenic Systems. New York: McGraw-Hill, 1967.
`3. Dewitt, W. D., N. C. Gibbon, and R. L. Reid. “Multifoil Type Thermal Insulation,” IEEE Trans.
`Aerosp. Electron. Syst., vol. 4, no. 5, suppl. pp. 263–71, 1968.
`
`UTC-2015.006
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