Principles of Heat Transfer -Kreith 7th

Arquivado no curso de Engenharia Elétrica na UNIFEB

(Parte 2 de 6)

Chapter 8 Heat Exchangers 484

8.1 Introduction 485 8.2Basic Types of Heat Exchangers485 8.3Overall Heat Transfer Coefficient494 8.4Log Mean Temperature Difference498 8.5Heat Exchanger Effectiveness506 8.6*Heat Transfer Enhancement516 8.7*Microscale Heat Exchangers524

Contents xi 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xi

8.8 Closing Remarks 525

References 527 Problems 529 Design Problems539

Chapter9Heat Transfer by Radiation540

9.1 Thermal Radiation 541 9.2 Blackbody Radiation 543 9.3 Radiation Properties 5 9.4The Radiation Shape Factor571 9.5Enclosures with Black Surfaces581 9.6Enclosures with Gray Surfaces585 9.7* Matrix Inversion 591 9.8*Radiation Properties of Gases and Vapors602 9.9Radiation Combined with Convection and Conduction610 9.10 Closing Remarks 614

References 615 Problems 616 Design Problems623

Chapter10Heat Transfer with Phase Change624

10.1Introduction to Boiling625 10.2Pool Boiling625 10.3Boiling in Forced Convection647 10.4 Condensation 660 10.5* Condenser Design 670 10.6*Heat Pipes672 10.7*Freezing and Melting683

References 688 Problems 691 Design Problems696

Appendix 1The International System of UnitsA3

Appendix 2Data TablesA6

Properties of SolidsA7 Thermodynamic Properties of LiquidsA14 Heat Transfer FluidsA23 xii Contents 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xii

Liquid MetalsA24 Thermodynamic Properties of GasesA26 Miscellaneous Properties and Error FunctionA37 Correlation Equations for Physical PropertiesA45

Appendix 3Tridiagonal Matrix Computer ProgramsA50 Solution of a Tridiagonal System of EquationsA50

Appendix 4Computer Codes for Heat TransferA56 Appendix 5The Heat Transfer LiteratureA57 Index I1

Contents xiii 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xiii

International

System of English System Symbol Quantity Units of Units avelocity of soundm/sft/s a acceleration m/s2 ft/s2

Aarea; Accross-sectional area; Ap, m2ft2 projected area of a body normal to the direction of flow; Aq, area through which rate of heat flow is q; As, surface area; Ao, outside surface area; Ai, inside surface area bbreadth or widthmft cspecific heat; cp, specific heat at J/kg KBtu/lbm°F constant pressure; c , specific heat at constant volume

C constant C thermal capacity J/K Btu/°F

Chourly heat capacity rate in Chapter 8; W/KBtu/h °F

Cc, hourly heat capacity rate of colder fluid in a heat exchanger; Ch, hourly heat capacity rate of warmer fluid in a heat exchanger

CDtotal drag coefficient

Cfskin friction coefficient; Cfx, local value of

Cfat distance xfrom leading edge; , average value of Cfdefined by Eq. (4.31) d, Ddiameter; DH, hydraulic diameter; Do, mft outside diameter; Di, inside diameter ebase of natural or Napierian logarithm einternal energy per unit massJ/kgBtu/lbm E internal energy J Btu

Eemissive power of a radiating body; Eb, W/m2Btu/h ft2 emissive power of blackbody

Cqf

(Continued) xv

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International

System of English System Symbol Quantity Units of Units

E monochromatic emissive power per W/m2 mBtu/h ft2micron micron at wavelength heat exchanger effectiveness defined by Eq. (8.2) fDarcy friction factor for flow through a pipe or a duct, defined by Eq. (6.13) ffriction coefficient for flow over banks of tubes defined by Eq. (7.37)

F force N lbf FTtemperature factor defined by Eq. (9.119)

F1–2geometric shape factor for radiation from one blackbody to another

1–2geometric shape and emissivity factor for radiation from one graybody to another gacceleration due to gravitym/s2ft/s2 gcdimensional conversion factor1.0 kg m/N s232.2 ft lbm/lbfs2

Gmass flow rate per unit kg/m2slbm/h ft2 area (G U )

Girradiation incident on unit surface W/m2Btu/h ft2 in unit time henthalpy per unit massJ/kgBtu/lbm hclocal convection heat transfer coefficientW/m2KBtu/h ft2°F combined heat transfer coefficient W/m2KBtu/h ft2°F

; hb, heat transfer coefficient of a boiling liquid, defined by Eq. (10.1);

, average convection heat transfer coefficient; , average heat transfer coefficient for radiation hfglatent heat of condensation J/kgBtu/lbm or evaporation iangle between sun direction raddeg and surface normal i electric current amp amp Iintensity of radiationW/srBtu/h sr

I intensity per unit wavelengthW/sr mBtu/h sr micron J radiosity W/m2 Btu/h ft2 hqr hqc hq = hqc + hqr hq xvi Nomenclature 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xvi

International

System of English System Symbol Quantity Units of Units kthermal conductivity; ks, thermal W/m KBtu/h ft °F conductivity of a solid; kf, thermal conductivity of a fluid

Kthermal conductance; Kk, thermal W/KBtu/h °F conductance for conduction heat transfer; Kc, thermal conductance for convection heat transfer; Kr, thermal conductance for radiation heat transfer llength, generalmft or in.

Llength along a heat flow path or mft or in. characteristic length of a body

Lflatent heat of solidificationJ/kgBtu/lbm mass flow ratekg/slbm/s or lbm/h

M mass kg lbm m molecular weight gm/gm-mole lbm/lb-mole Nnumber in general; number of tubes, etc.

pstatic pressure; pc, critical pressure; pA, N/m2psi, lbf/ft2, or atm partial pressure of component A

P wetted perimeter m ft qrate of heat flow; qk, rate of heat flow by WBtu/h conduction; qr, rate of heat flow by radiation; qc, rate of heat flow by convection; qb, rate of heat flow by nucleate boiling rate of heat generation per unit volumeW/m3Btu/h ft3 q heat fluxW/m2Btu/h ft2 Qquantity of heatJBtu volumetric rate of fluid flowm3/sft3/h rradius; rH, hydraulic radius; ri, mft or in. inner radius; ro, outer radius

Rthermal resistance; Rc, thermal resistance K/Wh °F/Btu to convection heat transfer; Rk, thermal resistance to conduction heat transfer;

Rr, thermal resistance to radiation heat transfer

Re electrical resistance ohm ohm

Nomenclature xvii

(Continued)

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International

System of English System Symbol Quantity Units of Units rperfect gas constant8.314 J/K kg-mole1545 ft lbf/lb-mole °F Sshape factor for conduction heat flow

S spacing m ft

SLdistance between centerlines of tubes in adjacent longitudinal rowsmft

STdistance between centerlines of tubes in adjacent transverse rowsmft t thickness m ft

Ttemperature; Tb, temperature of bulk K or °CR or °F of fluid; Tf, mean film temperature;

Ts, surface temperature; T , temperature of fluid far removed from heat source or sink; Tm, mean bulk temperature of fluid flowing in a duct; Tsv, temperature of saturated vapor; Tsl, temperature of a saturated liquid; Tfr, freezing temperature;

Tl, liquid temperature; Tas, adiabatic wall temperature uinternal energy per unit massJ/kgBtu/lbm utime average velocity in xdirection; u , instantaneous fluctuating xcomponent of velocity; , average velocitym/sft/s or ft/h

Uoverall heat transfer coefficientW/m2KBtu/h ft2°F

U free-stream velocity m/s ft/s specific volume m3/kg ft3/lbm time average velocity in ydirection; , m/sft/s or ft/h instantaneous fluctuating ycomponent of velocity

V volume m3 ft3 wtime average velocity in zdirection; w , m/sft/s instantaneous fluctuating zcomponent of velocity wwidthmft or in. rate of work outputWBtu/h xdistance from the leading edge; xc, mft distance from the leading edge where flow becomes turbulent xviii Nomenclature 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xviii

International

System of English System Symbol Quantity Units of Units x coordinate m ft x quality y coordinate m ft ydistance from a solid boundary measured in direction normal to surfacemft z coordinate m ft

Zratio of hourly heat capacity rates in heat exchangers

Greek Letters absorptivity for radiation; , monochromatic absorptivity thermal diffusivity k/ cm2/sft2/s temperature coefficient 1/K1/R of volume expansion ktemperature coefficient 1/K1/R of thermal conductivity specific heat ratio, cp/c body force per unit massN/kglbf/lbm cmass rate of flow of condensate per unit breadth for a vertical tubekg/s mlbm/h ft boundary-layer thickness; h, mft hydrodynamic boundary-layer thickness; th, thermal boundary-layer thickness difference between values packed bed void fraction emissivity for radiation; , monochromatic emissivity

Hthermal eddy diffusivitym2/sft2/s

Mmomentum eddy diffusivitym2/sft2/s ratio of thermal to hydrodynamic boundary-layer thickness, th/ h

Nomenclature xix

(Continued)

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International

System of English System Symbol Quantity Units of Units ffin efficiency timesh or s wavelength; max, wavelength mmicron at which monochromatic emissive power Eb is a maximum latent heat of vaporizationJ/kgBtu/lbm absolute viscosityN s/m2lbm/ft s kinematic viscosity, / m2/sft2/s rfrequency of radiation1/s1/s mass density, 1/ ; l, density kg/m3lbm/ft3 of liquid; , density of vapor reflectivity for radiation shearing stress; s, shearing N/m2lbf/ft2 stress at surface; w, shear at wall of a tube or a duct transmissivity for radiation Stefan–Boltzmann constant W/m2 K4 Btu/h ft2 R4 surface tension N/m lbf/ft angle rad rad angular velocity rad/s rad/s solid angle sr steradian Dimensionless Numbers

Nuxlocal Nusselt number at a distance x from leading edge, hcx/kf average Nusselt number for blot plate, average Nusselt number for cylinder, hqcD/kfNuD hqcL/kfNuL

Biot number =hqL/ks or hqro/ks x Nomenclature 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page x

Symbol Quantity

PePeclet number RePr

Miscellaneous a bagreater than b a basmaller than b proportional sign approximately equal sign infinity sign summation sign

Stanton number=hqc/rUqcp or Nu/RePr

Nomenclature xxi 67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page xxi

Seventh Edition

Principles of HEAT TRANSFER

67706_00_FM_pi-xi.qxd 5/14/10 9:32 AM Page 1

CHAPTER 1

Basic Modes of Heat Transfer

Concepts and Analyses to Be Learned

Heat is fundamentally transported, or “moved,” by a temperature gradient; it flowsor is transferredfrom a high temperature region to a low temperature one. An understanding of this process and its different mechanisms requires you to connect principles of thermodynamics and fluid flow with those of heat transfer. The latter has its own set of concepts and definitions, and the foundational principles among these are introduced in this chapter along with their mathematical descriptions and some typical engineering applications. A study of this chapter will teach you:

•How to apply the basic relationship between thermodynamics and heat transfer.

•How to model the concepts of different modes or mechanisms of heat transfer for practical engineering applications.

•How to use the analogy between heat and electric current flow, as well as thermal and electrical resistance, in engineering analysis.

•How to identify the difference between steady state and transient modes of heat transfer.

A typical solar power station with its arrays or field of heliostats and the solar power tower in the foreground; such a system involves all modes of heat transfer–radiation, conduction, and convection, including boiling and condensation.

Source: Photo courtesy of Abengoa Solar.

67706_01_ch01_p002-069.qxd 5/14/10 7:46 AM Page 2

1.1The Relation of Heat Transfer to Thermodynamics

Whenever a temperature gradient exists within a system, or whenever two systems at different temperatures are brought into contact. energy is transferred. The process by which the energy transport taltes place is known as heat transfer. The thing in transit, called heat, cannot be observed or measured directly. However, its effects can be identified and quantified through measurements and analysis. The flow of heat, like the performance of work, is a process by which the initial energy of a system is changed.

The branch of science that deals with the relation between heat and other forms of energy, including mechanical work in particular, is called thermodynamics. Itsprinciples, like all laws of nature, are based on observations and have been generalized into laws that are believed to hold for all processes occurring in nature because no exceptions have ever been found. For example, the first law of thermodynamics states that energy can be neither created nor destroyed but only changed from one form to another. It governs all energy transformations quantitatively, but places no restrictions on the direction of the transformation. It is known, however, from experience that no process is possible whose sole result is the net transfer of heat from a region of lower temperature to a region of higher temperature. This statement of experimental truth is known as the second law of thermodynamics.

All heat transfer processes involve the exchange and/or conversion of energy.

They must, therefore, obey the first as well as the second law of thermodynamics. Atfirst glance, one might therefore be tempted to assume that the principles of heat transfer can be derived from the basic laws of thermodynamics. This conclusion, however, would be erroneous, because classical thermodynamics is restricted primarily to the study of equilibrium states including mechanical, chemical, and thermal equilibriums, and is therefore, by itself, of little help in determining quantitavely the transformations that occur from a lack of equilibrium in engineering processes. Since heat flow is the result of temperature nonequilibriuin, its quantitative treatment must be based on other branches of science. The same reasoning applies to other types of transport processes such as mass transfer and diffusion.

Limitations of Classical ThermodynamicsClassical thermodynamics deals with the states of systems from a macroscopic view and makes no hypotheses about the structure of matter. To perform a thermodynamic analysis it is necessary to describe the state of a system in terms of gross characteristics, such as pressure, volume, and temperature, that can be measured directly and involve no special assumptions regarding the structure of matter. These variables (or thermodynamic properties) are of significance for the system as a whole only when they are uniform throughout it, that is, when the system is in equilibrium. Thus, classical thermodynamics is not concerned with the details of a process but rather with equilibrium states and the relations among them. The processes employed in a thermodynamic analysis are idealized processes devised to give information concerning equilibrium states.

(Parte 2 de 6)

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