1、NASA 5P-164_OcOoOTHERMALRADIATIONHEATTRANSFERProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-vNASA SP-164THERMALRADIATIONHEATTRANSFERVolume IThe Blackbody, Electromagnetic Theory,and Material PropertiesRobert Siegel and John R. HowellLewis Research C
2、enterCleveland, OhioScientific and Technical Inormation DivisionOFFICE OF TECHNOLOGY UTILIZATION 1968NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONWashington, D.C.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PREFACESeveral years ago it was realized
3、 that thermal radiation was becomingof increasing importance in aerospace research and design. This im-portance arose from several areas: high temperatures associated withincreased engine efficiencies, high-velocity flight which is accompaniedby elevated temperatures from frictional heating, and the
4、 operation ofdevices beyond the Earths atmosphere where convection vanishes andradiation becomes the only external mode of heat transfer. As a result,a course in thermal radiation was initiated at the NASA Lewis ResearchCenter as part of an internal advanced study program.The course was divided into
5、 three main sections. The first dealt withthe radiation properties of opaque materials including a discussion ofthe blackbody, electromagnetic theory, and measured properties. Thesecond discussed radiation exchange in enclosures both with and with-out convection and conduction. The third section tre
6、ated radiation inpartially transmitting materials-chiefly gases.When the course was originated, there was not available any singleradiation textbook that covered the desired span of material. As a resultthe authors began writing a set of notes; the present publication is anoutgrowth of the notes dea
7、ling with the first of the three main sections.During the past few years, a few radiation textbooks have appeared inthe literature; hence, the need for a single reference has been partiallysatisfied. The objectives here are more extensive than the content of astandard textbook intended for a one-sem
8、ester course. Many parts ofthe present discussion have been made quite detailed so that they willserve as a source of reference for some of the more subtle points inradiation theory. The detailed treatment has resulted in some of the sec-tions being rather long, but the intent was to be thorough rat
9、her than totry to conserve space. The sections have been subdivided so that specificportions can be located for easy reference.This volume is divided into five chapters. The introduction discussesthe conditions where thermal radiation is of importance and indicatessome of the inherent differences an
10、d complexities of radiation problemsas compared with convection and conduction.Chapter 2 deals with the blackbody, which is defined as a perfectabsorber. It is important to understand the behavior of a blackbody beforeconsidering real materials, as the blackbody provides an ideal perform-ance with w
11、hich real material performance can be compared. First theblackbody is discussed qualitatively with its properties being deducedUlProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THERMAL RADIATION HEAT TRANSFERfrom the original definition of a perfect
12、absorber. A quantitative elabora-tion, including a numerical tabulation, then provides the blackbodyemission as a function of wavelength and temperature.The third chapter is completely devoted to the definitions of emis-sivity, absorptivity, and reflectivity. These properties are used to com-pare th
13、e radiative performance of real materials with the ideal (blackbody)behavior. A functional notation has been introduced that includes primesuperscripts to denote directional quantities and by which ambiguitiesin the various hemispherical and directional quantities are avoided. Anextensive examinatio
14、n of the property definitions is made in order todemonstrate when it is valid to use various reciprocity relations andequalities, such as Kirchhoffs laws relating emissivity and absorptivity.The restrictions on these relations are summarized in tables for con-venient reference.The use of classical e
15、lectromagnetic theory for the prediction ofradiative properties is the subject of chapter 4. The electromagnetictheory discussed deals with ideal surfaces and hence does not accountfor the many factors (e.g., contamination and roughness) that influencethe behavior of real surfaces. In spite of this
16、shortcoming, the theorydoes provide a valuable basis for many observed trends and serves torelate optical and electrical properties to radiative properties.The final chapter illustrates the radiative performance of real materialsby showing a number of examples of property variations with wavelengtha
17、nd temperature.Each chapter contains numerical examples to acquaint the reader withthe use of the analytical relations. It is hoped that these examples willhelp bridge the gap between theory and practical application.ivProvided by IHSNot for ResaleNo reproduction or networking permitted without lice
18、nse from IHS-,-,-CHAPTER13CONTENTSPAGERADIATION FROM A BLACKBODY 92.1 SYMBOLS . 92.2 DEFINITION OF A BLACKBODY 112.3 PROPERTIES OF A BLACKBODY 112.3.1 Perfect Emitter . 112.3.2 Radiation Isotropy in a Black Enclosure . 122.3.3 Perfect Emitter in Each Direction . 132.3.4 Perfect Emitter at Every Wave
19、length 132.3.5 Total Radiation a Function Only of Temperature . 132.4 EMISSIVE CHARACTERISTICS OF A BLACKBODY 152.4.1 Definition of Blackbody Radiation Intensity . 152.4.2 Angular Independence of Intensity . 162.4.3 Blackbody Emissive Power-Definition and Cosine LawDependence 182.4.4 Hemispherical S
20、pectral Emissive Power of a Blackbody 192.4.5 Spectral Emissive Power Through a Finite Solid Angle . 202.4.6 Spectral Distribution of Emissive Power . 202.4.7 Approximations for Spectral Distribution 252.4.7.1 Wiens formula 262.4.7.2 Rayleigh-Jeans formula 262.4.8 Wiens Displacement Law . 262.4.9 To
21、tal Intensity and Emissive Power . 272.4.10 Behavior of Maximum Intensity With Temperature 292.4.11 Blackbody Radiation in a Wavelength Interval 292.4.12 Blackbody Emission in a Medium Other Than a Vacuum 352.5 EXPERIMENTAL PRODUCTION OF A BLACKBODY . 362.6 SUMMARY OF BLACKBODY PROPERTIES . 372.7 HI
22、STORICAL DEVELOPMENT . 43REFERENCES 45DEFINITIONS OF PROPERTIES FOR NON-BLACK SURFACES 473.1 INTRODUCTION 473.1.1 Nomenclature 523.1.2 Notation . 53INTRODUCTION . 11.1 IMPORTANCE OF THERMAL RADIATION . 11.2 SYMBOLS . 31.3 COMPLEXITIES INHERENT IN RADIATION PROBLEMS. 31.4 WAVE AGAINST QUANTUM MODEL 5
23、1.5 ELECTROMAGNETIC SPECTRUM 6Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THERMAL RADIATION HEAT TRANSFERCHAPTER PAGE3.2 SYMBOLS . 543.3 EMISSIVITY 553.3.1 Directional Spectral Emissivity _ ( _, fl, O, TA ) 553.3.2 Averaged Emissivities . 573.3.2
24、.1 Directional total emissivity e(fl, 0, TA) 573.3.2.2 Hemispherical spectral emissivity e_()t, TA) 593.3.2.3 Hemispherical total emissivity (TA) . 593.4 ABSORPTIVITY 643.4.1 Directional Spectral Absorptivity ax(X, fl, O, TA) 643.4.2 Kirchhoffs “Law . 653.4.3 Directional Total Absorptivity a(g, 0, T
25、A) 663.4.4 Kirchhoffs Law for Directional Total Properties 673.4.5 Hemispherical Spectral Absorptivity ct_(), TA) 673.4.6 Hemispherical Total Absorptivity a(TA) . 683.4.7 Summary of Kirchhoffs Law Relations . 713.5 REFLECTIVITY . 723.5.1 Spectral Reflectivities . 723.5.1.1 Bidirectional spectral ref
26、lectivity p_(_, fir, 0r, 8, 0) . 723.5.1.2 Reciprocity for bidirectional spectral reflectivity . 733.5.1.3 Directional spectral reflectivities 743.5.1.4 Reciprocity for directional spectral reflectivity 753.5.1.5 Hemispherical spectral reflectivity px(),) . 763.5.1.6 Limiting cases for spectral surf
27、aces . 773.5.1.6.1 Diffusely reflecting surfaces 773.5.1.6.2 Specularly reflecting surfaces 783.5.2 Total Reflectivities 803.5.2.1 Bidirectional total reflectivity p“(Jr, Or, f3, O). 803.5.2.2 Reciprocity 813.5.2.3 Directional total reflectivity p. 813.5.2.4 Reciprocity 823.5.2.5 Hemispherical total
28、 reflectivity p . 823.5.3 Summary of Restrictions on Reciprocity Relations BetweenReflectivities 833.6 RELATIONS AMONG REFLECTIVITY, ABSORPTIVITY,AND EMISSIVITY 843.7 CONCLUDING REMARKS 88REFERENCE . 884 PREDICTION OF RADIATIVE PROPERTIES BYCLASSICAL ELECTROMAGNETIC THEORY. 894.1 INTRODUCTION 894.2
29、SYMBOLS . 904.3 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICTHEORY . 914.4 RADIATIVE WAVE PROPAGATION . 924.4.1 Propagation in Perfect Dielectric Media 934.4.2 Propagation in Isotropic Media of Finite Conductivity . 984.4.3 Energy of an Electromagnetic Wave 100viProvided by IHSNot for ResaleNo reproduct
30、ion or networking permitted without license from IHS-,-,-CHAPTER5CONTENTSPAGE4.5 LAWS OF REFLECTION AND REFRACTION 1014.5.1 Incidence and Reflection of a Wave From Dielectric or Trans-parent Media (K Negligible Compared to, n) 1074.5.2 Incidence on an Absorbing Medium 1094.6 APPLICATION OF ELECTROMA
31、GNETIC THEORY RELA-TIONS TO RADIATIVE PROPERTY PREDICTIONS 1104.6.1 Radiative Properties of Dielectrics (K-_0) 1114.6.1.1 Reflectivity 1114.6.1.2 Emissivity 1134.6.2 Radiative Properties of the Metals . 1164.6.2.l Reflectivity and emissivity relations using opticalconstants . 1164.6.2.2 Relation bet
32、ween emissive and electrical properties 1224.6.3 Summary of Prediction Equations . 1284.7 EXTENSIONS OF THE THEORY OF RADIATIVE PROP-ERTIES . 130REFERENCES 130RADIATIVE PROPERTIES OF REAL MATE.RIALS . 1335.1 INTRODUCTION 1335.2 SYMBOLS . 1335.3 RADIATIVE PROPERTIES OF METALS . 1345.3.1 Directional V
33、ariations . 1355.3.2 Effect of Wavelength . 1365.3.3 Effect of Surface Temperature . 1375.3.4 Effect of Surface Roughness 1385.3.5 Effect of Surface Impurities 1415.4 RADIATIVE PROPERTIES OF OPAQUE NONMETALS 1465.4.1 Spectral Measurements 1485.4.2 Variation of Total Properties With Temperature 1505.
34、4.3 Effect of Surface Roughness 1525.4.4 Semiconductors . 1555.5 SPECIAL SURFACES 1565.5.1 Modification of Spectral Characteristics . 1575.5.2 Modification of Directional Characteristics 1655.6 CONCLUDING REMARKS 167REFERENCES 168APPENDIX 17lINDEX 185viiProvided by IHSNot for ResaleNo reproduction o
35、r networking permitted without license from IHS-,-,-Chapter 1. IntroductionAll substances continuously emit electromagnetic radiation by virtueof the molecular and atomic agitation associated with the internal energyof the material. In the equilibrium state, this internal energy is in directproporti
36、on to the temperature of the substance. The emitted radiantenergy can range from radio waves, which can have wavelengths of miles,to cosmic rays with wavelengths of less than 10 -I centimeter (cm). Inthis volume, only radiation that is detected as heat or light will be con-sidered; this is termed th
37、ermal radiation, and it occupies an intermediatewavelength range. This range is defined explicitly in section 1.5.Although radiant energy constantly surrounds us, we are not veryaware of it because our bodies are able to detect only portions of it di-rectly. Other portions require detection by use o
38、f some intermediateinstrumentation. Our eyes are sensitive direct detectors of light, beingable to form images of objects, but are relatively insensitive to heat(infrared) radiation. Our skin is a direct detector for heat radiation butnot a good one. The skin is not aware of images of warm or cool s
39、urfacesaround us unless the heat radiation is large. We require indirect meanssuch as infrared-sensitive film in a camera to form images using heatradiation.Before discussing the nature of thermal radiation in detail, it is wellto consider why thermal radiation is so important in our moderntechnolog
40、y.1.i IMPORTANCE OF THERMAL RADIATIONOne of the factors that causes some of the important applications ofthermal radiation to arise is the dependence of radiant emission on tem-perature. For conduction and convection the transfer of energy betweentwo locations depends on the temperature difference o
41、f the locations toapproximately the first power2 The transfer of energy by thermal radia-tion, however, depends on the differences of the individual absolute tem-peratures of the bodies each raised to a power in the range of about 4 or 5.From this basic difference between radiation and the convectio
42、n andconduction energy exchange mechanisms, it is evident that the impor-tance of radiation becomes intensified at high absolute temperaturelevels. Consequently, radiation contributes substantially to the heatFor free convection or when variable property effects are included, the power of the temper
43、ature difference may be-come larger than unity but usually in convection and conduction does not approach 2.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 THERMAL RADIATION HEAT TRANSFERtransfer in furnaces and combustion chambers and in the energ
44、y emis-sion from a nuclear explosion. The laws of radiation govern the tempera-ture distribution within the Sun and the radiant emission from the Sunor from a source duplicating the Sun in a solar simulator. Some devicesfor space applications are designed to operate at high temperature levelsin orde
45、r to achieve high thermal efficiency. Hence, radiation must oftenbe considered when calculating thermal effects in devices such as arocket nozzle, a nuclear powerplant, or a gaseous core nuclear rocket.A second distinguishing feature of radiative transfer is that no mediumneed be present between two
46、 locations in order for radiant interchangeto occur. The radiative energy will pass perfectly through a vacuum.This is in contrast to convection and conduction where a physicalmedium must be present to carry the energy with the convective flowor to transport it by means of thermal conduction. When n
47、o mediumis present, radiation becomes the only significant mode of heat transfer.Some common instances are the heat leakage through the evacuatedwalls of a Dewar flask or thermos bottle, or the heat dissipation fromthe filament of a vacuum tube. A more recent application is the radiationused to reje
48、ct waste heat from a powerplant operating in space.Radiation can be of importance in some instances even though thetemperature levels are not elevated and other modes of heat transferare present. The following example is quoted from a Cleveland news-paper published in the spring of 1964. A florist “
49、noted the recurrenceof a phenomenon he has observed for two seasons since using plasticcoverings over flower flats. Water collecting in the plastic has formedice a quarter-inch thick at night when the official temperature readingwas well above freezing. Id like an answer to that, I supposed youcouldnt get ice without freezing temperatur
