1、I,NASA SP-164_ oi_ Ia Io THERMAL_ RADIATION! HEAT_, i_ TRANSFERProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA $P-16A.THERMALRADIATIONHEATTRANSFERVolume IIRadiation ExchangeBetween Surfaces and in EnclosuresJohn R. Howell and Robert SiegelLewis
2、Research CenterCleveland, OhioScie_ui_c and Technical Informalion DivisionOFFICE OF TECHNOLOGYUTILIZATION 1969NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONWashington, D.C.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-For S_e by the Superintendent o
3、f Documents,U.S. Government Printing Office, Washington, D.C. 20402Price $1.50Library of Congre_ Catalog Card Number 67-62877Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-!tCHAPTgR1f. 2CONTENTSPAGEINTROD UCTOR Y COMMENTS II.I ENCLOSURE THEORY 1I.I.
4、I Ideal Enclosures . 21.1.2 Nonideal Enclosures 31.2 ENERGY TRANSFER BY COMBINED MODES . 41.3 NOTATION 41.4 CONCLUDING REMARKS 5REFERENCES . 5EXCHANGE OF RADIANT ENERGY BETWEENBLACK ISOTHERMAL SURFACES . 72.1 INTRODUCTION 72.2 SYMBOLS 82.3 RADIATIVE EXCHANGE BETWEEN TWO DIFFERENTIALAREA ELEMENTS . 8
5、2.4 RADIATIVE GEOMETRIC CONFIGURATION FACTORS ANDENERGY EXCHANGE BETWEEN TWO SURFACES . 122.4.1 Configuration Factor for Energy Exchange Between Differ-ential Elements 132.4.1.1 Reciprocity for differentialelement configuration factors. 142.4.1.2 Some sample configuration factors between differentia
6、lelements .142.4.2 Configuration Factor Between a DifferentialElement and aFinite Area 192.4.2.1 Reciprocity for configuration factor between differentialand finiteareas 212.4.2.2 Radiation interchange between differentia and finiteareas 212.4.2.3 Some sample configuration factors involving a differ
7、entialand a finite area . 972.4.3 Configuration Factor for Two Finite Areas . 262.4.3.1 Reciprocity for configuration factor between finiteareas . 272.4.3.2 Radiation exchange between finite areas . 282.4.4 Summary of Configuration Factor and Energy ExchangeRelations 302.5 METHODS FOR EVALUATING CON
8、FIGURATION FACTORS 302.5.1 Configuration Factor Algebra for Pairs of Surfaces . 302.5.2 Configuration Factor, in Enclosures 392.5.3 Mathematical Techniques for the EvaJuation of ConfigurationFactors . 422.5.3.1 Hottels crossed-string method 43o111Provided by IHSNot for ResaleNo reproduction or netwo
9、rking permitted without license from IHS-,-,-CHAPTER34THERMAL RADIATION HEAT TRANSFERPAGE2.5.3.2 Contour integration . _ 462.5.3.2.1 Configuration factor between a differential and afinite area 472.5.3.2.2 Configuration factor between finite areas . 522.5.3.3 Differentiation of known factors 552.6 C
10、OMPILATION OF REFERENCES FOB KNOWN CONFIG-URATION FACTORS 592.7 RADIATION EXCHANGE IN A BLACK ENCLOSURE 592.8 CONCLUDING REMARKS 64REFERENCES . 65RADIATION EXCHANGE IN AN ENCLOSURECOMPOSED OF DIFFUSE.GRAY SURFACES 673.1 INTRODUCTION 673.1.1 Restrictions in the Analysis . 673.1.2 Summary of Restricti
11、ons 683.2 SYMBOLS 693.3 RADIATION BETWEEN FINITE AREAS 703.3.1 Net Radiation Method 703.3.1.1 System of equations relating surface heating Q andsurface temperature T . 773.3.1.2 Solution method in terms of outgoing radiative flux qo 793.3.2 Matrix Inversion . 813.4 RADIATION BETWEEN INFINITESIMAL AR
12、EAS . 833.4.1 Generalized Net Radiation Method for Infinitesimal Areas. 833.4.1.1 Relations between surface temperature T and surfaceheating q. 863.4.1.2 Solution method in terms of outgoing radiative flux q0. 883.4.1.3 Special case when imposed heating q is specified for allsurfaces 893.4.2 Methods
13、 for Solving Integral Equations . 973.4.2.1 Numerical integration yielding simultaneous equations. 973.4.2.2 Use of approximate separable kernel . 993.4.2.3 Approximate solution by variational method 1023.4.2.4 Approximate solution by Taylor series expansion 1033.4.2.5 Exact solution of integral equ
14、ation for radiation from aspherical cavity 1043.5 CONCLUDING REMARKS 107REFERENCES . 107RADIATION IN ENCLOSURES HAVING SOMESPECULARLY REFLECTING SURFACES lo94.1 INTRODUCTION 1094.2 SYMBOLS 1094.3 RADIATION BETWEEN PAIRS OF SURFACES WITH SPEC-ULAR REFLECTIONS 1104.3.1 Some Simple Cases . 1104.3.2 Ene
15、rgy Exchange Between Specular Surfaces . “ 1154.3.2.1 Ray tracing and the construction of images . 1154.3.2.2 Energy exchange between simple specular surfaces 1174.3.3 Configuration Factor Reciprocity for Specular Surfaces 123ivProvided by IHSNot for ResaleNo reproduction or networking permitted wit
16、hout license from IHS-,-,-CHAPTER56CONTENTSPAGF4.4 NET RADIATION METHOD IN ENCLOSURES HAVINGSPECULAR AND DIFFUSE SURFACES 1294.4.1 Enclosures With Plane Surfaces 1294.4.2 Curved Specular Reflecting Surfaces 1394.5 CONCLUDING REMARKS 142REFERENCES . 144THE EXCHANGE OF THERMAL RADIATION BE-TWEEN NONDI
17、FFUSE NONGRAY SURFACES 1475.1 INTRODUCTION 1475.2 SYMBOLS 1485.3 ENCLOSURE THEORY FOR DIFFUSE SURFACES WITHSPECTRALLY DEPENDENT PROPERTIES . 1495.4 THE BAND ENERGY APPROXIMATION . 1565.4.1 Multiple Bands . 1575.4.2 The Semigra? Approximations . 1605.5 DIRECTIONAL-GRAY SURFACES 1625.6 SURFACES WITH D
18、IRECTIONALLY AND SPECTRALLYDEPENDENT PROPERTIES 1695.7 CONCLUDING REMARKS . 175REFERENCES . 175THE MONTE CARLO APPROACH TO RADIANTINTERCHANGE PROBLEMS . 1776.1 INTRODUCTION 1776.1.1 Definition of Monte Carlo 1776.1.2 History 1786.1.3 General References . 1786.2 SYMBOLS 1796-3 DETAILS OF THE METHOD 1
19、806.3.1 The Random Walk 1806.3.2. Choosing From Probability Distributions 1816.3.3 Random Numbers . 1876.3.3.1 Definition of random numbers 1876.3.3.2 How random numbers are generated . 1876.3.3.3 How the numbers are made sufficiently random 1886.3.4 Evaluation of Error 1886.4 APPLICATION TO THERMAL
20、 RADIATIVE TRANSFER 1906.4.1 Introduction . 1906.4.2 Model of the Radiative Exchange Process 1916.4.3 Sample Problem . 1916.4.4 Useful Functions . 1976.4.5 Literature on Application to Radiation Exchange BetweenSurfaces . 2046.4.5.1 Configuration factor computation 2046.4.5.2 Cavity properties . 207
21、6.4.5.3 Extension to directional and spectral surfaces . 2086.4.6 Statistical Dittlculties of Monte Carlo Technique . 2096.4.7 Closing Remarks . 209REFERENCES . 210Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CHM_ER7THERMAL RADIATION HEAT TRANSFER
22、PAGERADIATION IN THE PRESENCE OF OTHERMODES OF ENERGY TRANSFER 2t37.1 INTRODUCTION 2137.2 SYMBOLS 21s7.3 PROBLEMS INVOLVING COMBINED RADIATION ANDCONDUCTION . 2177.3.1 Uncoupled Problems 2177.3.2 Coupled Nonlinear Problems . 2187.4 RADIATION AND CONVECTION . 2277.5 RADIATION COMBINED WITH BOTH CONDU
23、CTION ANDCONVECTION . 2327.6 COMPUTER PROGRAMS FOR MULTIMODE ENERGYTRANSFER . 2377.7 CONCLUDING REMARKS 237REFERENCES . 238APPENDIXESA DIFFUSE CONFIGURATION FACTORS 241B ENCLOSURE ANALYSIS METHOD OF GEBHART 277C CONVERSION FACTORS 279INDEX . 2a3viProvided by IHSNot for ResaleNo reproduction or netwo
24、rking permitted without license from IHS-,-,-Chapter 1. Introductory CommentsThe study of radiation interchange between individual surface ele-ments in a system is required in a variety of engineering disciplinesincluding applied optics, illumination engineering, and heat transfer.Indeed, such studi
25、es have been conducted for many years as evidencedby the publication dates of references 1 and 2. More recently the studyof radiant interchange has been given impetus by technological advancesthat have resulted in systems where thermal radiation can be a verysignificant factor. Some examples are sat
26、ellite temperature control,energy leakage into cryogenic vacuum systems, high-temperature phe-nomena in hypersonic flight, and the heat transfer in nuclear propulsionsystems.1.1 ENCLOSURE THEORYIn this volume the theory will be developed for computing thermalradiation exchanges within enclosures. Fi
27、rst it must be understood whatis meant by an enclosure. Any surface can be considered as completelysurrounded by an envelope of other solid surfaces or open areas. Thisenvelope is the enclosure for the surface; thus an enclosure accountsfor all directions surrounding the surface. By considering the
28、radiationgoing from the surface to all parts of the enclosure, and the radiationarriving at the surface from all parts of the enclosure, it is assured thatall the radiative contributions are accounted for. In working a problem,a convenient enclosure will usually be evident from the physical con-figu
29、ration. An opening can be considered as a plane of zero reflectivity.It will also act as a source of radiation when radiation is entering theenclosure from the environment.All the enclosures considered here will be subject to the assumptionthat the medium in the space between the surfaces is perfect
30、ly trans-parent and thus does not participate in the radiative interchange. Foran enclosure filled with a radiating material such as a gas containingwater vapor, carbon dioxide, or smoke, the theory will be treated involume III of this series.Reference 3, which is volume I of this series, discusses
31、in detail theradiative properties of solid surfaces. It was demonstrated that for somematerials there are substantial variations of properties with wavelength,surface temperature, and direction. For radiation computations withinenclosures, the geometric effects governing how much radiation from ones
32、urface reaches another is a complication in addition to the variationsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THERMAL RADIATION HEAT TRANSFERof the surface properties. For simple geometries it may be possible toaccount in detail for property
33、variations without the problem becomingunduly complex. As the geometry becomes more involved, it is oftennecessary to invoke more idealizations of the surface properties in orderthat the problem can be solved with reasonable effort.The treatment presented here could begin with the most generalsituat
34、ion where properties vary with wavelength, temperature, anddirection, and where the radiation fluxes vary arbitrarily over the en-closure surfaces. All other situations would then be simplified specialcases. However, this would entail the uninitiated reader plunging intothe most complex treatment, w
35、hich would be very difficult to understand.Hence the development presented here will begin with the most simplesituation; successive complexities will then be added to build morecomprehensive treatments.1.1.1 Ideal EnclosuresThe greatest simplification is td assume that all the enclosure surfacesare
36、 black. In this instance there is no reflected radiation to be accountedfor. Also, all the emitted energy is diffuse; that is, the intensity leavinga given isothermal surface is independent of direction. The exchangetheory for a black enclosure is presented in chapter 2. The heat balancesinvolve the
37、 enclosure geometry, which governs how much radiationleaving a surface will reach another surface. The geometric effects areexpressed in terms of diffuse configuration factors; these factors are thefractions of radiation leaving a surface that reach another surface. Thefactors are derived on the bas
38、is that the directional distribution of radia-tion leaving a surface is diffuse and uniformly distributed, and theserestrictions should be kept in mind when the factors are applied innonblack enclosures.The computation of configuration factors involves integration overthe solid angles by which the s
39、urfaces can view each other. Since theseintegrations are often tedious, it is desirable to use certain useful rela-tions that exist between configuration factors. By using these relations,the desired factor can often be obtained from factors that are alreadyknown, and the integration will not have t
40、o be performed. These rela-tions, along with various shortcut methods that can be used to obtainconfiguration factors, are presented in detail in chapter 2. An appendixis also provided giving references where configuration factors can befound for approximately 150 different geometrical configuration
41、s.After analyzing the black enclosure, the next step of complexity isan enclosure with gray surfaces that emit and reflect diffusely. It is alsoassumed that both the emitted and reflected energies are uniform overProvided by IHSNot for ResaleNo reproduction or networking permitted without license fr
42、om IHS-,-,-INTRODUCTORY COMMENTSeach surface. For these conditions the diffuse configuration factors foundfor black surfaces still apply for the radiation leaving a surface. For graysurfaces, reflections between surfaces must be accounted for. This isdone in chapter 3 by using a method developed by
43、Poljak.Another type of ideal surface is a perfect mirror reflector. The emissionfrom this type of surface is approximated as being diffuse; hence, theemitted energy, is treated by using the diffuse configuration factors. Thereflected energy, however, is followed within the enclosure by using thechar
44、acteristics of a mirror where the angle of reflection is equal in mag-nitude to the angle of incidence. The method of tracing the reflectedradiation paths and deriving the necessary heat balances is treated inchapter 4.1.1.2 Nonideal EnclosuresIn some instances the black or diffuse-gray approximatio
45、ns are inade-quate and directional and/or spectral effects must be considered. Thenecessity of treating spectral effects was noticed quite early in the fieldof radiative transfer. In the remarkable paper (ref. 4) published in 1800by Sir William Herschel entitled “Investigation of the Powers of thePr
46、ismatic Colours to Heat and Illuminate Objects; with Remarks, thatprove the Different Refrangibility of Radiant Heat to which is added,an Inquiry into the Method of Viewing the Sun Advantageously, withTelescopes of large Apertures and High Magnifying Powers.“ appearsthe following statement: “In a va
47、riety of experiments I have occasionallymade, relating to the method of viewing the sun, with large telescopes,to the best advantage, I used various combinations of differently coloureddarkening glasses. What appeared remarkable was, that when I usedsome of them, felt a sensation of heat, though I h
48、ad but little light;while others gave me much light, with scarce any sensation of heat.Now, as in these different combinations, the suns image was also dif-ferently coloured, it occurred to me, that the prismatic rays might havethe power of heating bodies very unequally distributed amongthem “ This
49、paper was the first in which what is now called theinfrared region of the spectrum was defined and the energy radiated as“heat“ shown to be of different wavelengths than those for “light.“The quotation shows an awareness that in some instances spectraleffects must be included in the radiative analysis. The performance ofspectra
