Solar Utility Technologies Lecture Notes PDF

Solar utility technologies Lecture #3 Radiative heat transfer Assoc. prof. dr. Ciril Arkar Laboratory for Sustainable Technologies in Buildings - LOTZ Chair of...

Solar utility technologies Lecture #3 Radiative heat transfer Assoc. prof. dr. Ciril Arkar Laboratory for Sustainable Technologies in Buildings - LOTZ Chair of Thermal and Environmental Engineering UL, FS, LOTZ © Faculty of Mechanical Engineering, University of Ljubljana Electromagnetic radiation Thermal radiation Radiation is electromagnetic energy that is propagated trough space at the speed of light. Spectrum of EM radiation is divided into wavelength bands, limits are not sharply defined For solar energy applications only thermal radiation is important: emitted by bodies due to their temperature Emitted radiation is usually distributed over a range of wavelengths Thermal radiation: Solar radiation outside the atmosphere most energy from 0,25 to 3 m; at the ground 0,3-2,5 m Solar energy applications: UV+ near IR 0,29-25 m; this includes Visible spectrum: light, to which human eye responds 0,38-0,78 m In solar energy applications a photon is considered as the energy carrier – a particle with zero mass and zero charge, with energy: 𝐸 =ℎ∙𝜈 ℎ is Planck‘s constant 6,6256 10-34 Js; 𝜈 is frequency of EM rad. 𝑐 𝜆 is vawelength, 𝑐 is speed of light in the medium 𝜆= 𝜈 UL, FS, LOTZ © Thermal radiation The blackbody By definition, a blackbody is a perfect absorber of radiation. All incident radiation, no matter what wavelengths or direction, will be absorbed Ideal concept, does not exist in nature… black carbon can absorb ≈99% Blackbody is also a perfect emitter of thermal radiation. The wavelength distribution of thermal radiation emitted by a blackbody is defined by Planck‘s law: spectral emissive power (in W/m2m) is 2 ∙ 𝜋 ∙ ℎ ∙ 𝑐02 𝐶1 𝐸𝜆𝑏 𝜆, 𝑇 = = ℎ ∙ 𝑐0 𝐶2 5 𝜆 ∙ exp −1 𝜆5 ∙ exp −1 𝜆 ∙ 𝑘𝐵 ∙ 𝑇 𝜆∙𝑇 Wien‘s displacement law: describes the relation between blackbody temperature and wavelength with max spectral emissive power T absolute temperature (K) h Planck‘s constant 6,6256 10-34 J s 𝜆𝑚𝑎𝑥 ∙ 𝑇 = 𝐶3 = 2898 𝜇𝑚 𝐾 kB Boltzmann's constant 1,381 10-23 J/K c0 speed of light in vacuum 2,998 108 m/s C1 1st radiation constant 3,742 108 W m4/m2 C2 2nd radiation constant 1,439 104 m K UL, FS, LOTZ © C3 3rd radiation constant 2898 m K Thermal radiation The blackbody In engineering practice, the total emissive power (in W/m2) is of more interest. By integrating Plank‘s law eq. we get Stefan-Boltzmann‘s law: ∞ 𝐸𝑏 = න 𝐸𝜆𝑏 𝜆, 𝑇 ∙ 𝑑𝜆 = 𝜎 ∙ 𝑇 4 0 where 𝜎 is the Stefan-Boltzmann constant - equal to 5,67·10−8 W∕m2 K4 Absorbed or emitted power in a certain wavelength interval can be obtained from blackbody radiation tables. 𝐹0−𝜆 represents the share of thermal radiation energy emitted from blackbody with absolute temperature T in the wavelength range from 0 to . 𝐸0−𝜆 = 𝐹0−𝜆 ∙ 𝜎 ∙ 𝑇 4 𝐸𝜆1 −𝜆2 = 𝐹𝜆1 −𝜆2 ∙ 𝜎 ∙ 𝑇 4 𝐹𝜆1 −𝜆2 = 𝐹0−𝜆2 − 𝐹0−𝜆1 UL, FS, LOTZ © Thermal radiation The blackbody radiation tables ·T (m K) F0- (-) ·T (m K) F0- (-) ·T (m K) F0- (-) Absorbed or emitted power in a certain wavelength interval can 200 0,000000 4.200 0,516014 8.500 0,874608 be obtained from blackbody radiation tables. 𝐹0−𝜆 represents 400 0,000000 4.400 0,548796 9.000 0,890029 600 0,000000 4.600 0,579280 9.500 0,903085 the share of thermal radiation energy emitted from blackbody 800 0,000016 4.800 0,607559 10.000 0,914199 with absolute temperature T in the wavelength range from 0 to . 1.000 0,000321 5.000 0,633747 10.500 0,923710 𝐹0−𝜆 is named blackbody function 1.200 0,002134 5.200 0,658970 11.000 0,931890 1.400 0,007790 5.400 0,680360 11.500 0,939959 1.600 0,019718 5.600 0,701046 12.000 0,945098 1.800 0,039341 5.800 0,720158 13.000 0,955139 Blackbody emmisive power in the wavelenght range from 0 to  2.000 0,066728 6.000 0,737818 14.000 0,962898 2.200 0,100888 6.200 0,754140 15.000 0,968933 𝐸0−𝜆 = 𝐹0−𝜆 ∙ 𝜎 ∙ 𝑇 4 2.400 0,140256 6.400 0,769234 16.000 0,973814 2.600 0,183120 6.600 0,783199 18.000 0,980860 2.800 0,227897 6.800 0,796129 20.000 0,985602 Blackbody emmisive power in the wavelenght range from 𝜆1 to 𝜆2 3.000 0,273232 7.000 0,808109 25.000 0,992215 3.200 0,318102 7.200 0,819217 30.000 0,995340 𝐸𝜆1 −𝜆2 = 𝐹𝜆1 −𝜆2 ∙ 𝜎 ∙ 𝑇 4 3.400 0,361735 7.400 0,829527 40.000 0,997967 3.600 0,403607 7.600 0,839102 50.000 0,998953 3.800 0,443382 7.800 0,848005 75.000 0,999713 The share of emmited power from blackbody in the wavelenght range 4.000 0,480877 8.000 0,856288 100.000 0,999905 from 𝜆1 to 𝜆2 𝐹𝜆1 −𝜆2 = 𝐹0−𝜆2 − 𝐹0−𝜆1 UL, FS, LOTZ © Thermal radiation The blackbody radiation tables ·T (m K) F0- (-) ·T (m K) F0- (-) ·T (m K) F0- (-) Two examples: 200 0,000000 4.200 0,516014 8.500 0,874608 Sun can be assumed as blackbody at 5780 K. 400 0,000000 4.400 0,548796 9.000 0,890029 600 0,000000 4.600 0,579280 9.500 0,903085 At which wavelength is the maximum 800 0,000016 4.800 0,607559 10.000 0,914199 1.000 0,000321 5.000 0,633747 10.500 0,923710 emissive power? 1.200 0,002134 5.200 0,658970 11.000 0,931890 1.400 0,007790 5.400 0,680360 11.500 0,939959 1.600 0,019718 5.600 0,701046 12.000 0,945098 1.800 0,039341 5.800 0,720158 13.000 0,955139 2.000 0,066728 6.000 0,737818 14.000 0,962898 2.200 0,100888 6.200 0,754140 15.000 0,968933 2.400 0,140256 6.400 0,769234 16.000 0,973814 2.600 0,183120 6.600 0,783199 18.000 0,980860 What is the share of solar energy in the visible spectral region 2.800 0,227897 6.800 0,796129 20.000 0,985602 3.000 0,273232 7.000 0,808109 25.000 0,992215 (0,38-0,78 m)? 3.200 0,318102 7.200 0,819217 30.000 0,995340 3.400 0,361735 7.400 0,829527 40.000 0,997967 𝜆1 ∙ 𝑇 = 𝐹0−𝜆1 = 3.600 0,403607 7.600 0,839102 50.000 0,998953 3.800 0,443382 7.800 0,848005 75.000 0,999713 4.000 0,480877 8.000 0,856288 100.000 0,999905 𝜆2 ∙ 𝑇 = 𝐹0−𝜆2 = 𝐹𝜆1 −𝜆2 = 𝐹0−𝜆2 − 𝐹0−𝜆1 = UL, FS, LOTZ © Thermal radiation Emission from real surfaces Blackbody has ideal surface behavior. Real surface spectral radiation emission differs from the Planck distribution. Also, the directional distribution may be other than diffuse. Real surface emits less power, what is represented with a surface radiative property known as emissivity 𝜀. It depends on temperature, wavelength, direction In engineering practice directional average surface properties are used. Spectral hemispherical emissivity is defined as: 𝐸𝜆 (𝜆, 𝑇) 𝜀𝜆 (𝜆, 𝑇) = 𝐸𝜆𝑏 (𝜆, 𝑇) Total hemispherical emissivity accounts for emission over all wavelengths and in all directions: ∞ 𝐸(𝑇) ‫𝜆( 𝜆𝜀 ׬‬, 𝑇) ∙ 𝐸𝜆𝑏 (𝜆, 𝑇) ∙ 𝑑𝜆 𝜀(𝑇) = 𝐸(𝑇) = 𝜀(𝑇) ∙ 𝜎 ∙ 𝑇 4 𝜀(𝑇) = 0 𝐸𝑏 (𝑇) 𝐸𝑏 (𝑇) UL, FS, LOTZ © Radiation characteristics Opaque real surfaces Surface property termed the emissivity 𝜀 is associated with thermal 𝐸 𝑇 𝑄𝑟𝑒𝑎𝑙 𝑄𝑔𝑟𝑒𝑦 𝜀 𝑇 = = = emission from a real surface. 𝐸𝑏 𝑇 𝑄𝑏𝑙𝑎𝑐𝑘 𝑄𝑏𝑙𝑎𝑐𝑘 To determine the net radiative heat flux, it is necessary to consider properties that determine the absorption and reflection. Absorptivity 𝛼 is a property of a surface and is defined as the fraction of the incident (solar) radiation that is absorbed by the surface. 𝐺 Stainless steel Total or spectral (hemispherical) absorptivity 𝐺𝑎𝑏𝑠 𝐺𝜆,𝑎𝑏𝑠 (𝜆) 𝐺𝑎𝑏𝑠 𝛼= 𝛼𝜆 (𝜆) = 𝐺 𝐺𝜆 (𝜆) Black paint Kirchhoff‘s law: in isothermal enclosure in steady-state conditions all bodies have the same temperature; net rate of energy transfer is zero. This leads to: emissivity of the surface is equal to its absorptivity 𝛼=𝜖 𝛼𝜆 = 𝜖𝜆 UL, FS, LOTZ © Radiation characteristics Opaque real surfaces Surface property termed the emissivity 𝜀 is associated with thermal 𝐸 𝑇 𝑄𝑟𝑒𝑎𝑙 𝑄𝑔𝑟𝑒𝑦 𝜀 𝑇 = = = emission from a real surface. 𝐸𝑏 𝑇 𝑄𝑏𝑙𝑎𝑐𝑘 𝑄𝑏𝑙𝑎𝑐𝑘 To determine the net radiative heat flux, it is necessary to consider properties that determine the absorption and reflection. Reflectivity 𝜌 is a property of a surface and is defined as the fraction of the incident (solar or longwave) radiation that is reflected by the surface. Stainless steel For specular surface spectral directional reflectivity is determined For diffuse surfaces: Total or spectral (hemispherical) reflectivity 𝐺 𝐺𝑟𝑒𝑓 𝐺𝜆,𝑟𝑒𝑓 (𝜆) 𝐺𝑟𝑒𝑓 𝜌= 𝜌𝜆 (𝜆) = 𝐺 𝐺𝜆 (𝜆) Black paint Energy conservation law: energy can neither be created nor destroyed - only converted from one form of energy to another. From the radiation balance following relation is obtained for opaque surfaces: 𝛼𝜆 + 𝜌𝜆 = 1 𝛼+𝜌=1 UL, FS, LOTZ © specular surface Radiation characteristics Semitransparent surfaces Surface property termed the emissivity 𝜀 is associated with thermal 𝐸 𝑇 𝑄𝑟𝑒𝑎𝑙 𝑄𝑔𝑟𝑒𝑦 𝜀 𝑇 = = = emission from a real surface. 𝐸𝑏 𝑇 𝑄𝑏𝑙𝑎𝑐𝑘 𝑄𝑏𝑙𝑎𝑐𝑘 To determine the net radiative heat flux, it is necessary to consider properties that determine the absorption and reflection. Transmissivity 𝜏 is a property of a surface and is defined as the fraction of the incident (solar) radiation that is transmitted trough Fused quartz the material. Total or spectral (hemispherical) transmissivity 𝐺 𝐺𝑡𝑟 𝐺𝜆,𝑡𝑟 (𝜆) 𝜏= 𝜏𝜆 (𝜆) = 𝐺 𝐺𝜆 (𝜆) 𝐺𝑡𝑟 Energy conservation law: energy can neither be created nor destroyed - only converted from one form of energy to another. From the radiation balance following relation is obtained for semitransparent surfaces: 𝛼𝜆 + 𝜌𝜆 + 𝜏𝜆 = 1 𝛼+𝜌+𝜏 =1 UL, FS, LOTZ © Radiation characteristics From spectral to total… Spectral radiative properties are known for most materials. They can vary greatly with wavelength. In engineering practice integral values are preferred: For solar radiation 0,3-3 m; For longwave radiation 3-100 m; For light 0,38-0,76 m; For atmospheric window ≈8-13 m Atmospheric window: is a range of wavelengths within which most of the terrestrial radiation passes to the outer edge of the atmosphere; radiation exchange with space UL, FS, LOTZ © Radiation characteristics From spectral to total… Spectral radiative properties are known for most materials. They can vary greatly with wavelength. In engineering practice integral values are preferred: For solar radiation 0,3-3 m; For longwave radiation 3-100 m;… ∞ 𝜆1 𝜆2 ∞ ‫𝜆( 𝑏𝜆𝐸 ∙ )𝜆( 𝜆𝜀 ׬‬, 𝑇) ∙ 𝑑𝜆 ‫𝜆𝑑 ∙ )𝜆( 𝑏𝜆𝐸 ׬‬ ‫𝜆𝑑 ∙ )𝜆( 𝑏𝜆𝐸 ׬‬ ‫𝜆𝑑 ∙ )𝜆( 𝑏𝜆𝐸 ׬‬ 𝜖= 0 𝜖 = 𝜀𝜆1 0 + 𝜀𝜆2 𝜆1 + 𝜀𝜆3 𝜆2 𝐸𝑏 (𝑇) 𝐸𝑏 𝐸𝑏 𝐸𝑏 For surfaces with gray surface behavior (𝛼𝜆 = 𝜖𝜆 ) [directional independent properties=diffuse] blackbody functions 𝐹0−𝜆 (radiative tables) can be used. 𝜖 = 𝜀𝜆1 ∙ 𝐹0−𝜆1 + 𝜀𝜆2 ∙ (𝐹0−𝜆2 −𝐹0−𝜆1 ) + 𝜀𝜆3 ∙ (𝐹0−𝜆3 −𝐹0−𝜆2 ) 𝛼 = 𝛼𝜆1 ∙ 𝐹0−𝜆1 + 𝛼𝜆2 ∙ (𝐹0−𝜆2 −𝐹0−𝜆1 ) + 𝛼𝜆3 ∙ (𝐹0−𝜆3 −𝐹0−𝜆2 ) ·T (m K) F0- (-) ·T (m K) F0- (-) ·T (m K) F0- (-) 200 0,000000 4.200 0,516014 8.500 0,874608 400 Caution! Temperature in ·T is different for 0,000000 4.400 solar and longwave 0,548796 radiation. 9.000 0,890029 600 0,000000 4.600 0,579280 9.500 0,903085 UL, FS, LOTZ © 800 0,000016 4.800 0,607559 10.000 0,914199  Radiation characteristics From spectral to total… Example: Determine solar energy transmissivity 𝜏𝑠 of low Fe oxide glass (0,02%) with thickness of 6 mm. 𝜆1 = 0,3 𝜇𝑚 𝜆1 ∙ 𝑇 = 0,3 ∙ = 𝜇𝑚 𝐾 𝐹0−𝜆1 = 𝜆2 = 2,0 𝜇𝑚 𝜆2 ∙ 𝑇 = 2,0 ∙ = 𝜇𝑚 𝐾 𝐹0−𝜆2 = 𝜆3 = 2,9 𝜇𝑚 𝜆3 ∙ 𝑇 = 2,9 ∙ = 𝜇𝑚 𝐾 𝐹0−𝜆3 = ·T (m K) F0- (-) ·T (m K) F0- (-) ·T (m K) F0- (-) 200 0,000000 4.200 0,516014 8.500 0,874608 400 0,000000 4.400 0,548796 9.000 0,890029 600 0,000000 4.600 0,579280 9.500 0,903085 800 0,000016 4.800 0,607559 10.000 0,914199 1.000 0,000321 5.000 0,633747 10.500 0,923710 1.200 0,002134 5.200 0,658970 11.000 0,931890 0 0,9 0,77 1.400 0,007790 5.400 0,680360 11.500 0,939959 𝜏𝑠 = 𝜏𝜆1 ∙ 𝐹0−𝜆1 + 𝜏𝜆2 ∙ (𝐹0−𝜆2 −𝐹0−𝜆1 ) + 𝜏𝜆3 ∙ (𝐹0−𝜆3 −𝐹0−𝜆2 ) 1.600 1.800 0,019718 0,039341 5.600 5.800 0,701046 0,720158 12.000 13.000 0,945098 0,955139 2.000 0,066728 6.000 0,737818 14.000 0,962898 2.200 0,100888 6.200 0,754140 15.000 0,968933 2.400 0,140256 6.400 0,769234 16.000 0,973814 2.600 0,183120 6.600 0,783199 18.000 0,980860 2.800 0,227897 6.800 0,796129 20.000 0,985602 3.000 0,273232 7.000 0,808109 25.000 0,992215 3.200 0,318102 7.200 0,819217 30.000 0,995340 3.400 0,361735 7.400 0,829527 40.000 0,997967 3.600 0,403607 7.600 0,839102 50.000 0,998953 3.800 0,443382 7.800 0,848005 75.000 0,999713 UL, FS, LOTZ © 4.000 0,480877 8.000 0,856288 100.000 0,999905 Radiation characteristics 𝐺𝑔𝑙𝑜𝑏 Selective properties of materials 𝜃𝑠𝑘𝑦 Energy balance of surface exposed to solar radiation: 𝜃𝑎 Conduction, convection, radiation 𝜆 𝜃𝑠𝑒 𝑞ሶ 𝑐𝑜𝑛𝑑 = ∙ 𝜃𝑠𝑒 − 𝜃𝑠𝑖 𝑑 𝑞ሶ 𝑐𝑜𝑛𝑣 = ℎ𝑐𝑜𝑛𝑣 ∙ 𝜃𝑠𝑒 − 𝜃𝑎 𝜃𝑠𝑖 𝑞ሶ 𝑠 = 𝛼𝑠 ∙ 𝐺𝑔𝑙𝑜𝑏,𝛽 𝑛 4 4 𝑞ሶ 𝐼𝑅,𝑠𝑘𝑦 = 𝜀𝐼𝑅,𝑠𝑘𝑦 ∙ 𝜎 ∙ 𝑇𝑠𝑘𝑦 𝑞ሶ 𝐼𝑅,𝑠𝑒 = 𝜀𝐼𝑅,𝑠𝑒 ∙ 𝜎 ∙ 𝑇𝑠𝑒 𝑞ሶ 𝐼𝑅,𝑖𝑛𝑐 = 𝜎 ∙ ෍ 𝜖𝐼𝑅,𝑖 ∙ 𝐹𝐼𝑅,𝑖 ∙ 𝑇𝑖4 𝑖=1 How radiative properties affect surface temperature 𝜃𝑠𝑒 ? 𝜖1 Radiative heat transfer between two parallel plates with narrow gap: 𝜃 𝑠,1 1 𝑞ሶ 𝐼𝑅 = ∙ 𝜎 ∙ (𝑇14 −𝑇24 ) 1 1 + −1 𝜀1 𝜖2 𝜖2 𝜃 𝑠,2 UL, FS, LOTZ © Radiation characteristics 𝐺𝑔𝑙𝑜𝑏 Selective properties of materials 𝜃𝑠𝑘𝑦 Absorber of solar collector: 𝜃𝑎 Must have high absorptivity for shortwave (solar) radiation 𝜃𝑠𝑒 𝑞ሶ 𝑠 = 𝛼𝑠 ∙ 𝐺𝑔𝑙𝑜𝑏,𝛽 𝜃𝑠𝑖 Should have low as possible thermal radiation heat losses 4 𝑞ሶ 𝐼𝑅,𝑠𝑒 = 𝜀𝐼𝑅,𝑠𝑒 ∙ 𝜎 ∙ 𝑇𝑠𝑒 1 𝑞ሶ 𝐼𝑅 = ∙ 𝜎 ∙ (𝑇14 −𝑇24 ) 1 1 + −1 𝜀1 𝜖2 Hypothetical ideal SC selective surface: UL, FS, LOTZ © Radiation characteristics Selective properties of materials Absorber of solar collector: Must have high absorptivity for shortwave (solar) radiation 𝑞ሶ 𝑠 = 𝛼𝑠 ∙ 𝐺𝑔𝑙𝑜𝑏,𝛽 Should have low as possible thermal radiation heat losses 4 𝑞ሶ 𝐼𝑅,𝑠𝑒 = 𝜀𝐼𝑅,𝑠𝑒 ∙ 𝜎 ∙ 𝑇𝑠𝑒 1 𝑞ሶ 𝐼𝑅 = ∙ 𝜎 ∙ (𝑇14 −𝑇24 ) 1 1 + −1 𝜀1 𝜖2 SC absorber selectivity: 𝛼𝑠 𝑆= 𝜖𝐼𝑅 UL, FS, LOTZ © Radiation characteristics Selective properties of materials Semi-selective absorbers: Should have high absorptivity for shortwave (solar) radiation s = 0,626 0,835 0,876 IR = 0,325 0,368 0,400 S 2 Should have low as possible thermal radiation heat losses SC absorber selectivity: 𝛼𝑠 𝑆= 𝜖𝐼𝑅 UL, FS, LOTZ © Radiation characteristics Selective properties of materials Cool coatings: to reduce heat gains (overheating) and mechanical loads due to material expansion Why not using reflective paints ?? UL, FS, LOTZ © Radiation characteristics Selective properties of materials The most ˝cool˝ color: Is green ☺ 13 K UL, FS, LOTZ ©  Radiation characteristics Selective properties of materials Selective properties of glass: Most commonly used transparent material in building and solar technology applications It is not transparent for longwave radiation Greenhous effect, for greenhouses Polyethylene foil IR image Glass Transmissivity should be as high as possible Solar glass Window glass ˝White glass˝ (low Fe oxides) in solar applications Solar protective glazing in glazed facades Glass has high absorptivity for longwave radiation Low-e coating for lower U-value of window glassing UL, FS, LOTZ © Radiation characteristics Selective properties of materials Solar and light transmittance of glazing: Solar transmittance 𝜏𝑠 is ratio between transmitted solar radiation 𝐺𝑖 and incident solar radiation 𝐺 Light transmittance 𝜏𝑣𝑖𝑠 is ratio between transmitted luminous flux 𝜙𝑖 and incident luminous flux on the glazing 𝜙𝑒 𝐺 𝜙𝑒 reflected 𝐺𝑖 reflected 𝜙𝑖 absorbed absorbed 𝐺𝑖 𝜙𝑖 𝜏𝑠𝑜𝑙 = 𝜏𝑠 = 𝜏𝑣𝑖𝑠 = 𝐺 𝜙𝑒 UL, FS, LOTZ © Radiation characteristics Selective properties of materials Solar energy transmittance of glazing: Solar energy transmittance 𝑔 is ratio between transmitted solar heat gains and incident solar radiation 𝐺 Solar heat gains includes transmitted solar radiation and heat flux from inner glass to indoor environment with convection and radiation 𝐺 reflected 𝐺𝑖 absorbed 𝑞ሶ 𝑖 = 𝑞ሶ 𝑖,𝑐+𝑟 𝐺𝑖 + 𝑞ሶ 𝑖 𝑔= ∙ 100 (%) 𝐺 UL, FS, LOTZ © Literature J. A. Duffie et all: Solar Engineering of Thermal Processes, Photovoltaics and Wind, Wiley, 2020 T.L. Bergman, A.S. Lavine: Fundamentals of Heat and Mass Transfer, Wiley, 2017 D. Gerring: Renewable Energy Systems for Building Designers, Fundamentals of Net Zero and High Performance Design, Taylor&Francis, 2023 UL, FS, LOTZ ©