ME 144: Heat Transfer Introduction to Radiation (v 1.0) J. M. Meyers

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1 ME 144: Heat Transfer Introduction to Radiation (v 1.0)

2 Initial Concepts Heat transfer by conduction and convection requires the presence of a temperature gradient in some form of matter. Heat transfer by thermal radiation requires no matter. It is an extremely important process, and in the physical sense it is perhaps the most interesting of the heat transfer modes. It is relevant to many industrial heating, cooling, and drying processes, as well as to energy conversion methods that involve fossil fuel combustion and solar radiation Very important in high speed aerodynamics and reentry aerothermodynamics 2

3 Initial Concepts Considerasolidthatisinitiallyatahighertemperature thanthatofitssurroundings, but around which there exists a vacuum The presence of the vacuum precludes energy loss from the surface of the solid by conduction or convection This cooling is associated with a reduction in the internal energy stored by the solid and is a direct consequence of the emission of thermal radiation from the surface. In turn, the surface will intercept and absorb radiation originating from the surroundings. However, if > the net heat transfer rate by radiation, is from the surface, and the surfacewillcooluntil reaches. 3

4 Initial Concepts All forms of matter emit radiation. For gases and for semitransparent solids, such as glass and salt crystals at elevated temperatures, emission is a volumetric phenomenon we concentrate on situations for which radiation can be treated as a surface phenomenon. In most solids and liquids, radiation emitted from interior molecules is strongly absorbed by adjoining molecules. Accordingly, radiation that is emitted from a solid or a liquid originates from molecules that are within a distance of approximately 4

5 Initial Concepts We know that radiation originates due to emission by matter and that its subsequent transport does not require the presence of any matter. One theory views radiation as the propagation of a collection of particles termed photons or quanta. Alternatively, radiation may be viewed as the propagation of electromagnetic waves. Regardless, we will use the standard wave properties of frequency and wavelength when dealing with radiation exchanges. These two properties are related by = wavelength speed of light in a vacuum [ m/s] frequency 5

6 Initial Concepts ELECTROMAGNETIC SPECTRUM A region containing a portion of the UV and all of the visible and infrared (IR) is termed thermal radiation because it is both caused by and affects the thermal state or temperature of matter for this reason, thermal radiation is pertinent to heat transfer. 6

7 Initial Concepts Thermal radiation emitted by a surface encompasses a range of wavelengths The magnitude of the radiation varies with wavelength, and the term spectralis used to refer to the nature of this dependence. This spectral distribution will vary with the nature and temperature of the emitting surface A surface may emit preferentially in certain directions, creating a directional distribution of the emitted radiation. 7

8 Radiation Heat Fluxes Various types of heat fluxes are pertinent to the analysis of radiation heat transfer Emissive power, 4 [W/m 6 ], rate at which radiation is emitted from a surface per unit surface area, over all wavelengths and in all directions. Recall our treatment of radiation emission: 4 =

9 Radiation Heat Fluxes Irradiation, : [W/m 6 ], rate at which radiation is incident upon the surface per unit surface area, over all wavelengths and from all directions. All of the irradiation must be reflected, absorbed, or transmitted, it follows that ;+=+> = 1 A medium that experiences no transmission is termed opaque, in which case: ;+= = 1 9

10 Radiation Heat Fluxes Radiosity, J (W/m2), of a surface accounts for all the radiant energy leaving the surface. For an opaque surface, it includes emission and the reflected portion of the irradiation,? = = 4 +;: 10

11 Radiation Heat Fluxes Net radiative fluxfrom a surface, (W/m2), is the difference between the outgoing and incoming radiation " =? : Combining previous relations: " = 4+;: : = 78 9 =: 11

12 Radiation Heat Fluxes 12

13 Radiation Intensity Radiation leaving a surface can propagate in all directions thus its directional distribution is important. Radiation incident upon a surface may come from different directions and the manner in which the surface responds to this radiation depends on the direction. These directional effects are quite important in determining the net radiative heat transfer rate and may be treated by introducing the concept of radiation intensity. Due to its nature, mathematical treatment of radiation heat transfer involves the extensive use of the spherical coordinate system. 13

14 Radiation Intensity Mathematical Definitions The differential solid angle CD is defined by a region between the rays of a sphere and is measuredastheratiooftheareace onthespheretothesphere sradiussquared: CD = CE F 6 The unit of the solid angle is the steradian (sr), analogous to radians for plane angles. 14

15 Radiation Intensity Mathematical Definitions 15

16 Radiation Intensity Radiation Intensity and Its Relation to Emission 16

17 Radiation Intensity Radiation Intensity and Its Relation to Emission The total, hemispherical emissive power, 4 (W/m 2 ), is the rate at which radiation is emitted per unit area at all possible wavelengths and in all possible directions. Although the directional distribution of surface emission varies according to the nature of the surface, there is a special case that provides a reasonable approximation for many surfaces. A diffuse emitter is a surface for which the intensity of the emitted radiation is independent of direction, in which case G H,,I,J = G H, (,): 17

18 Radiation Intensity Radiation Intensity and Its Relation to Irradiance The intensity of the incident radiation may be related to the irradiation, which encompasses radiation incident from all directions. The spectral irradiation :(W/m 2 Mm) is defined as the rate at which radiation of wavelength is incident on a surface, per unit area of the surface and per unit wavelength interval C about : Eq

19 Blackbody Radiation 1. A blackbody absorbs all incident radiation, regardless of wavelength and direction. 2. For a prescribed temperature and wavelength, no surface can emit more energy than a blackbody 3. Although the radiation emitted by a blackbody is a function of wavelength and temperature, it is independent of direction. That is, the blackbody is a diffuse emitter. As the perfect absorber and emitter, the blackbody serves as a standard against which the radiative properties of actual surfaces may be compared. 19

20 Blackbody Radiation PLANCK DISTRIBUTION Black body emission can be described by the well known Planck distribution: G H,N, = 2h P 6 Q exp h P /S T 1 h = VW9 J s S T = V6W J/K P = m/s Planck constant Boltzmann constant Speed of light 4 H,N, = \G H,N, = ]^ Q exp ] 6 / 1 First Radiation Constant: Second Radiation Constant: ]^ = 2\h P 6 = W μm 9 /m 6 ] 6 = h P S T = μm K 20

21 Blackbody Radiation PLANCK DISTRIBUTION Log scale 21

22 Blackbody Radiation Several important features should be noted: PLANCK DISTRIBUTION 1. The emitted radiation varies continuously with wavelength 2. At any wavelength the magnitude of the emitted radiation increases with increasing Temperature 3. The spectral region in which the radiation is concentrated depends on temperature, with comparatively more radiation appearing at shorter wavelengths as the temperature increases. 4. Asignificantfractionoftheradiationemittedbythesun,whichmaybeapproximatedasa blackbody at 5800 K, is in the visible region of the spectrum. In contrast, for T < 800 K, emission is predominantly in the infrared region of the spectrum and is not visible to the eye. 22

23 Blackbody Radiation WIEN S LAW The blackbody spectral distribution has a maximum and that the corresponding wavelength max depends on temperature The nature of this dependence may be obtained by differentiating Planck s Law with respect to and setting the result equal to zero, which leads to: bc = ] W Wien s Law Where the third radiation constant is ] W = 2898 μm K According to this result, the maximum spectral emissive power is displaced to shorter wavelengths with increasing temperature This emission is in the middle of the visible spectrum ( bc 0.5 μm) for solar radiation, since thesunemitsapproximatelyasablackbodyat5800k. A tungsten filament lamp operating at 2900 K ( bc = 1 μm) emits white light, although most oftheemissionremainsintheirregion 23

24 Blackbody Radiation WIEN S LAW IR thermography temperatures 24

25 Blackbody Radiation STEPHAN-BOLTZMAN LAW Determining the total, hemispherical emissive power, using Planck s Law yields the Stephan- Boltzman Law Performing the integration, it may be shown that where the Stefan-Boltzmann constant, which depends on C 1 and C 2, has the numerical value: This Stefan-Boltzmann law enables calculation of the amount of radiation emitted in all directions and over all wavelengths simply from knowledge of the temperature of the blackbody. 25

26 Band Emission To account for spectral effects, it is often necessary to know the fraction of the total emission from a blackbody that is in a certain wavelength interval or band 26

27 Emission From Real Surfaces 7, = 4, 4 N, 27

28 Absorption, Reflection, and Transmission by Real Surfaces ABSORPTIVITY The absorptivity is a property that determines the fraction of the irradiation absorbed by a surface. 28

29 Absorption, Reflection, and Transmission by Real Surfaces REFLECTIVITY The reflectivity is a property that determines the fraction of the incident radiation reflected by a surface. Surfaces may be idealized as diffuse or specular, according to the manner in which they reflect radiation diffuse specular 29

30 Absorption, Reflection, and Transmission by Real Surfaces TRANSMISSIVITY Deals with the of the response of a semitransparent material to incident radiation 30

31 Absorption, Reflection, and Transmission by Real Surfaces 31

32 Absorption, Reflection, and Transmission by Real Surfaces 32

33 Environmental Radiation 33

34 Environmental Radiation 34

35 Environmental Radiation OUR SUN 35

36 Environmental Radiation 36

37 Environmental Radiation NASA Glenn Research Center 37

38 Some Practical Radiation Studies 38

39 Some Practical Radiation Studies A. M. Brandis, et al., Validation of CO 4th Positive Radiation for Mars Entry, NASA Ames Research Center, AIAA

40 Some Practical Radiation Studies A. M. Brandis, et al., Validation of CO 4th Positive Radiation for Mars Entry, NASA Ames Research Center, AIAA

41 Radiation Exchange Between Surfaces (Chpt. 13) 41

42 Radiation Exchange Between Surfaces (Chpt. 13) 42

43 Radiation Exchange Between Surfaces (Chpt. 13) 43

44 References Bergman, Lavine, Incropera, and Dewitt, Fundamentals of Heat and Mass Transfer, 7 th Ed., Wiley, 2011 Chapman, Heat Transfer, 3 rd Ed., MacMillan, 1974 Y. A. Çengeland A. J. Ghajar, Heat and Mass Transfer, 5 th Ed., Wiley,

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