ME 476 Solar Energy UNIT TWO THERMAL RADIATION

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1 ME 476 Solar Energy UNIT TWO THERMAL RADIATION

2 Unit Outline 2 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

3 Electromagnetic Radiation 3 The electromagnetic energy emitted by matter as a result of the changes in the electronic configurations of the atoms or molecules. Electromagnetic radiation energy is transported by waves These waves have a frequency ( ) and wavelength ( ).

4 Electromagnetic Radiation 4 Frequency and wavelength Are related by: where, C = C 0 / n C: the speed of propagation of a wave in the medium C 0 = m/s, the speed of light in a vacuum n, the index of refraction of that medium Examples: n =1 (air and most gases) n = 1.5 (glass) n = 1.33 (water)

5 Electromagnetic Radiation 5 Radiation differs from conduction and convection It does not require the presence of a material medium Radiation transfer occurs in all types of matter (solid, liquid, or gas)

6 Electromagnetic Radiation 6 Electromagnetic radiation can be viewed as the propagation of a collection of discrete packets of energy called photons or quanta. In this view, each photon of frequency (n) is considered to have an energy of: where h is called Planck s constant h = x J.s This means that the energy of a photon is inversely proportional to its wavelength

7 Unit Outline 7 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

8 Thermal Radiation 8 Thermal radiation is the part of electromagnetic radiation that primarily creates a heating effect. Thermal radiation is emitted as a result of energy transitions of molecules, atoms, and electrons of a substance. Temperature is a measure of the strength of these activities at the microscopic level Therefore, thermal radiation emission increases with increasing temperature

9 Thermal Radiation 9 Thermal radiation mainly covers: Infrared radiation Visible light Ultraviolet radiation Thermal radiation is continuously emitted by all matter whose temperature is above absolute zero.

10 Unit Outline 10 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

11 Blackbody Radiation 11 A blackbody is a body that absorbs all the incident radiation regardless of wavelength and direction AND emits the maximum amount radiation at a given temperature. It is an idealized body to serve as a standard against which the radiative properties of real surfaces may be compared.

12 Blackbody Radiation 12 The amount of radiation emitted by a blackbody is given by Planck s Law: where, k = x J/K (Boltzmann s Constant) Planck s Law shows that the energy emitted from a blackbody does not depend on direction. Blackbody radiation is diffuse.

13 Blackbody Radiation 13 From Planck s Law, we can find the wavelength at which the maximum radiation is emitted by a blackbody This is done by taking the derivative of E b and setting it to zero The result is called Wien s displacement law:

14 Blackbody Radiation 14 Locus of maximum power T = mm.k

15 Blackbody Radiation 15 Integrating Planck s Law yields Stefan-Boltzmann s Equation: where, s = 5.67 x 10-8 W/m 2.K 4 (Stefan-Boltzmann Constant)

16 Unit Outline 16 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

17 Radiation Emitted from a Real Surface 17 A real surface does not emit as much energy as a blackbody. A real surface does not emit energy uniformly in all directions. The amount of energy emitted by a real surface is quantified by emittance. Emittance is the ratio of radiation emitted by a real surface to the radiation emitted by a blackbody at the same temperature. When the energy emitted in all directions and at all wavelengths is integrated, the result is the total hemispherical emittance Emittance ranges from 0 to 1.

18 Unit Outline 18 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

19 Irradiance 19 Irradiance is the rate at which radiant energy is incident on a surface per unit area of that surface (W/m 2 ). Some references refer to irradiance as incident radiation It is usually denoted with (G). Irradiance can be either: Absorbed Reflected Transmitted (if the medium is transparent)

20 Irradiance 20 The ratio of absorbed irradiance to total irradiance is called absorptance (a) The ratio of reflected irradiance to total irradiance is called reflectance (r) The ratio of transmitted irradiance to total irradiance is called transmittance (t ) Irradiance

21 Irradiance 21 Absorptance: α = Absorbed radiation Irradiance = G abs G, 0 α 1 Reflectance: ρ = Reflected radiation Irradiance = G ref G, 0 ρ 1 Transmittance: τ = Transmitted radiation Irradiance = G tr G, 0 τ 1 G abs + G ref + G tr = G a + r + t = 1 a + r = 1 (for opaque surfaces)

22 Unit Outline 22 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

23 Kirchhoff s Law 23 The total hemispherical emittance of a surface at temperature T is equal to its total hemispherical absorptance for radiation coming from a blackbody at the same temperature. e(t) = a(t)

24 Unit Outline 24 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

25 Diffuse and Gray Surface 25 A gray surface is a surface whose e and a are independent of wavelength. If the surface is diffuse and gray: e = a In this case, the source of irradiation does not have to be a blackbody and the source s temperature does not have to be equal to the surface temperature

26 Unit Outline 26 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

27 View Factor 27 The view factor (F ij ) is the fraction of the radiation leaving surface i that strikes surface j directly The view factor ranges between 0 and 1. F ij

28 View Factor 28 EXAMPLE The view factor F 12 = 1 since all the radiation leaving Surface 1 hits Surface 2. F 21 < 1, since not all the radiation leaving Surface 2 will hit Surface 1. Some of the radiation leaving one part of Surface 2 will hit another part on Surface 2 itself.

29 View Factor 29 View factor between two aligned parallel rectangles of equal size

30 View Factor 30 View factor between two coaxial parallel disks

31 View Factor 31 View factors for two concentric cylinders of finite length

32 View Factor Relations 32 The Reciprocity Relation

33 View Factor Relations 33 The Summation Rule

34 Unit Outline 34 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

35 Radiation Exchange Between Two Black Bodies 35 If Surface 1 and Surface 2 are blackbodies, the net radiation heat transfer from Surface 1 to Surface 2 is: The reciprocity relation asserts that: A 1 F 1 2 = A 2 F 2 1 Also: E b = s T 4 Therefore,

36 Unit Outline 36 Electromagnetic radiation Thermal radiation Blackbody radiation Radiation emitted from a real surface Irradiance Kirchhoff s Law Diffuse and gray surface View factor Radiation exchange between black bodies Radiation from a diffuse, gray surface

37 Radiosity 37 Radiation from a diffuse gray surface differs from radiation from a black body in two ways: The radiation emitted is e E b (instead of E b ) The reflected radiation is r G (instead of 0) The total radiation energy leaving a surface per unit time and per unit area is called radiosity (J).

38 Radiosity 38 J i = ε i E b + ρ i G i But r i + a i = 1 For a diffuse gray surface, a i = e i Therefore: r i + e i = 1 r i = 1 e i J i = ε i E b + 1 ε i G i G i = J i ε i E b 1 ε i

39 39 Net Rate of Radiation Heat Transfer from a Diffuse Gray Surface = A i J i G i = A i J i J i ε i E b 1 ε i = A i ε i 1 ε i E bi J i

40 Radiation Heat Transfer in Two-Surface Enclosures 40 This is true for any two diffuse gray surfaces. Example: Radiation from a horizontal solar collector to the sky at night The sky can be considered a blackbody at a temperature below ambient

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