Radiation Heat Transfer

1. Radiation Heat Transfer The Nature and Characteristics of Thermal Radiation

2. The Sun • Formed 49 x 109 years ago when a hydrogen molecular cloud collapsed rapidly • Surface composition • 92.0% H2 • 7.0% He • 1.0% Fe, Ni, O2. Si, S, Mg, C, Ne, Ca & Cr Rotates as a gaseous body at 27 days at the equator and 30 days at the poles Suns energy results from continuous fusion reactions, for eg. H2 + H2 He + 25 MeV

3. Structure of the Sun Core T=1.5x107K Ρ=1.6x105km/m3 0.5 Mm Photosphere T=6000K 2.5Mm Radiative zone T=8.4x106K Ρ=70 km/m3 500Mm Chromosphere T=20000K R=700Mm Corona T=106K Convective zone T=2x105K Ρ=70 km/m3

4. Radiation Basics No medium needed Rate of energy transfer at speed of light Propagation is by Electromagnetic Radiation c = f*λ (c=2.9979 x 108 ms-1) Discrete energy packets propagation (quanta) • NRG is inversely proportional to λ so gamma & X-rays (short wavelengths) are very destructuve

5. Electromagnetic wave spectrum Ultraviolet Visible ɤ-Rays Electrical power waves Infrared X-Rays Radio & TV waves Thermal radiation Cosmic Rays Microwaves Λ,μm 102 107 103 1010 109 108 105 10 1 10-2 10=6 10-7 10-8 10-1 10-9

6. Blackbody radiation Emitted radiation depend on the material and surface Different bodies emit different amount of radiation Blackbody absorbs all the radiation incident upon it For a given temperature and wavelength no surface can emit more energy than a blackbody Total emissive power = the rate at which radiation energy is emitted per unit time per unit area of surface over all wavelengths in all directions

7. Stefan-Boltzman law Example Electrically heated carbide elements, 10.0 mm in diameter and 0.5 m long, radiating essentially as black bodies are to be used in the construction of a heater in which thermal radiation from the surroundings is negligible. If the surface temperature of the carbide is limited to 1750 K, how many elements are required to provide a radiated thermal output of 500.0 kW?

8. Black surface • Total absorption of light ( visible radiation) • Total reflection of light : white appearance • Snow & white paint reflect light but are black bodies to infrared radiation due to strong absorption of long wavelength radiation • Surfaces coated with lampblack paint approach the idealized blackbody behaviour.

9. Spectral (monochromatic) emissive power Blackbody radiation about a specific wavelength Light bulb radiation in the visible wavelength spectrum more important than total amount emitted Plank’s Law (from quantum theory) Valid for a blackbody surface in a gas or vacuum at temperature, T

10. Other medium • Replace C1 with C1/n2, where n is the index of refraction. • A plot of Eλ vs. λat various temperatures yield the following: • Emitted radiation is a continuous function of wavelength through a maximum. • At any wavelength the emitted radiation increases with increasing temperature • Curves shift towards shorter wavelengths with increasing temperature

11. Maximum wavelemgth • Wein’s Displacement Law • The wavelength at maximum emission:

12. Radiation from real surfaces • Emissivity, ε • Radiation per unit area emitted from a real or grey surface (emissivity is independent of wavelength) to that emitted by a blackbody at the same temperature. • A measure of how closely a surface approximates a blackbody where ε=1 • 0<ε< 1 and depend on type, condition and roughness of the material.

13. Emissivity, ε • Total hemispherical emissivity is the radiation energy emitted over all wavelengths in all directions as: • ε (T)=E(T)/Eb(T) Surface is diffuse when its properties are independent of direction and greyif its properties are independent of wavelength. Emissivity of a grey, diffuse surface is the total hemispherical emissivity of that surface

14. Incident radiation • Surfaces receive radiation emitted or reflected from other surfaces • Intensity of incident radiation, I (W m-2): • The rate at which radiation energy, dG is incident from a particular direction per unit area of the receiving surface normal to this direction • Irradiation, G (W m-2): • The radiation flux incident on a surface from all directions.

15. Radiosity, J (W m-2) • The rate at which radiation energy leaves a unit area of a surface in all directions. Reflected ρG Incident Radiation G, Wm-2 Absorbed αG Semitransparent material Transmitted τG

16. Irradiation • Gabs+Gref+Gtr=G • α+ρ+τ=1 • since for opaque surfaces τ=0 α+ρ=1 • Average absorptivity, reflectivity & transmissivity of a surface is:

17. Kirchoff’s Law • For any opaque surface the absorptivity (fraction of incident radiation absorbed) = emissivity • ε (T) = α (T) • The total emissivity of a surface at temperature T is equal to its total hemispherical absorptivity for radiation coming from a blackbody at the same temperature • Similarly the spectral form of the law( for specified wavelength): • ελ (T) = αλ (T) valid when the irradiation is independent of direction

18. The Greenhouse Effect • A car left in the sun acts as a heat trap due to the spectral transmissivity curve of the glass. • Windscreen is transparent in the 0.3μm <λ< 3.0 μm range • At that thickness glass transmits 90.0% of radiation in the visible range • At that thickness glass is opaque to radiation in the infrared region λ >3.0μm • Surfaces at room temperature emit radiation in the infrared region • Solar radiation enters but infrared radiation from the interior surfaces are trapped • The interior temperature of the car rises due to the nongray characteristic of the car’s windscreen

19. Atmospheric solar radiation • Radiation energy emitted or reflected by the constituents of the atmosphere • Diameter of the sun ~ 1.39 x 109 m • Mass of the sun ~2.0 x 1030 kg • Distance from earth of the sun ~ 1.5 x 1011 m • Sun’s radiation emission ~3.8 x 1026 W • Temperature at the sun’s core ~ 4.0 x 107 K • Total solar irradiance (solar constant) Gs = 1373 W m-2 • The rate at which solar energy is incident on a surface normal to the sun’s rays at the outer edge of the atmosphere when the earth is at its mean distance from the sun

20. Effective temperature of the sun • Total solar irradiance: • (4πL2)Gs = (4πr2)σT4 • R – sun’s radius, L - mean distance bet sun & earth • LHS = total solar energy passing through a spherical surface with radius equivalent to the mean sun-earth distance • RHS = total energy leaving the sun’s surface • T = 5780 K • So the sun’s a blackbody at temperature of 5780 K • Direct, GD and diffused, Gd solar radiation

21. Solar radiation Diffused solar radiation Direct solar radiation • Gsolar = GDcosϴ + Gd • Diffused radiation ca. 10.0 % of total on clear day • Treat atmosphere as a blackbody at a lower temp., Tsky Gd ϴ GD

22. Example • Consider a surface exposed to solar radiation. At a given time, the direct and diffused components of solar radiation are GD=400 and Gd=300 W m-2, and the radiation makes a 20.0 o angle with the normal to the surface. The surface temperature is observed to be 320.0 K at that time. Assuming an effective sky temperature of 260.0 K, determine the net rate of radiation heat transfer for: • (a) αs=0.9 & εs=0.9 (b)αs=0.1 & εs=0.1 • (c)αs=0.9 & εs=0.1 (d)αs=0.1 & εs=0.9

23. END • That’s all folks!!