Heat transfer & heat exchangers - Lecture 4: Radiation - Khoa Ta Dang
Concepts
Stefan–Boltzmann’s law 𝑞𝑒𝑚𝑖𝑡,𝑚𝑎𝑥 = 𝜎𝑇4
𝑞𝑚𝑎𝑥: maximum heat flux emitted from a blackbody 𝑊Τ𝑚2
𝜎: Stefan–Boltzmann constant 𝜎 = 5,669 × 10−8 𝑊Τ𝑚2. 𝐾4
For real bodies 𝑞𝑒𝑚𝑖𝑡 = 𝜀𝜎𝑇4
• 𝜀: emissivity of the body 0 ≤ 𝜀 ≤ 1
• For the blackbody, 𝜀 = 1
• Both 𝜀 and 𝛼 of a surface depend on the temperature and the wavelength of the
radiation (to be usually ignored in the most practical applications)
Blackbody is an idealized surface that emits radiation at the maximum
rate given by the Stefan–Boltzmann law (also perfect emitter).
Stefan–Boltzmann’s law 𝑞𝑒𝑚𝑖𝑡,𝑚𝑎𝑥 = 𝜎𝑇4
𝑞𝑚𝑎𝑥: maximum heat flux emitted from a blackbody 𝑊Τ𝑚2
𝜎: Stefan–Boltzmann constant 𝜎 = 5,669 × 10−8 𝑊Τ𝑚2. 𝐾4
For real bodies 𝑞𝑒𝑚𝑖𝑡 = 𝜀𝜎𝑇4
• 𝜀: emissivity of the body 0 ≤ 𝜀 ≤ 1
• For the blackbody, 𝜀 = 1
• Both 𝜀 and 𝛼 of a surface depend on the temperature and the wavelength of the
radiation (to be usually ignored in the most practical applications)
Blackbody is an idealized surface that emits radiation at the maximum
rate given by the Stefan–Boltzmann law (also perfect emitter).
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27/12/2022
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Nội dung text: Heat transfer & heat exchangers - Lecture 4: Radiation - Khoa Ta Dang
- RADIATION
- Concepts • All bodies at a temperature above absolute zero emit thermal radiation. • Blackbody is an idealized surface that emits radiation at the maximum rate given by the Stefan–Boltzmann law.
- Concepts 3,743 × 108휆−5 Planck’s law 푞 휆 = 4 푒1,4387×10 Τ휆 − 1 2 • 푞 휆: monochromatic emissive power of a blackbody 푊Τ • 휆: wavelength 휇 • : temperature 퐾
- Concepts • Blackbody is an idealized surface that emits radiation at the maximum rate given by the Stefan–Boltzmann law (also perfect emitter)
- The effects Body Geometry Interaction properties Emissivity Shape Position 휀 Absorptivity Dimension Distance 훼
- Two bodies 푞푛푒푡 푞 ,1 푒 ,1 푒 ,2 푞 ,2 1 − 휀1 1 1 − 휀2 푅푠 푒 = 휀1 1 1퐹12 휀2 2 푞 − 푞 𝜎 4 − 4 푞 = ,1 ,2 = 1 2 푛푒푡 1 − 휀 1 1 − 휀 1 − 휀 1 1 − 휀 1 + + 2 1 + + 2 휀1 1 1퐹12 휀2 2 휀1 1 1퐹12 휀2 2
- Three bodies • Third surface is insulated (reradiating) 푞 ,1 푒 ,1 푒 ,2 푞 ,2 1 1 − 휀1 1 − 휀2 퐹 휀1 1 1 12 휀2 2 1 1 1 1 − 퐹12 2 1 − 퐹21 푞 ,3 = 푒 ,3
- Infinite concentric cylinders 𝜎 4 − 4 푞 = 1 1 2 1 1 + 1 − 1 휀1 2 휀2
- Convex object in large enclosure 4 4 푞 = 1휀1𝜎 1 − 2
- Absorbing & transmitting medium 푞 ,1 푒 ,1 푒 ,2 푞 ,2 1 1 − 휀1 1 − 휀2 1퐹12 1 − 휀 휀1 1 휀2 2 1 1 1퐹1 휀 2퐹2 휀 푞 ,
- Absorbing & transmitting medium Absorptivities of surface to solar Surface 휶 흀~ , 흁 Aluminum, highly polished 0,15 Copper, highly polished 0,18 Copper, tarnished 0,65 Cast iron 0,94 Stainless steel (301), polished 0,37 White marble 0,46 Asphalt 0,90 Brick, red 0,75 Gravel 0,29 Flat black lacquer 0,96 White paints, various types of pigments 0,12 – 0,16
