RADIATION HEAT TRANSFER The Nature and Characteristics of Thermal Radiation

The Sun Formed 49 x 10 9 years ago when a hydrogen molecular cloud collapsed rapidly Surface composition 92.0% H 2 7.0% He 1.0% Fe, Ni, O 2. 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. H 2 + H 2 He + 25 MeV

Structure of the Sun 0.5 Mm Photosphere T=6000K Chromosphere T=20000K Corona T=106K Convective zone T=2x10 5 K Ρ =70 km/m 3 Radiative zone T=8.4x10 6 K Ρ =70 km/m 3 Core T=1.5x10 7 K Ρ =1.6x10 5 km/m 3 500Mm R=700Mm 2.5Mm

Radiation Basics No medium needed Rate of energy transfer at speed of light Propagation is by Electromagnetic Radiation c = f*λ (c= x 10 8 ms -1 ) Discrete energy packets propagation (quanta) NRG is inversely proportional to λ so gamma & X- rays (short wavelengths) are very destructuve

Electromagnetic wave spectrum Λ,μmΛ,μm = Electrical power waves Radio & TV waves MicrowavesThermal radiation InfraredX-Rays Visible Ultraviolet ɤ -Rays Cosmic Rays

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

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 kW?

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.

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

Other medium Replace C 1 with C 1 /n 2, where n is the index of refraction. A plot of E λ vs. λ at 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

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

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.

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

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.

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

Irradiation G abs +G ref +G tr =G α+ρ+τ=1 since for opaque surfaces τ=0 α+ρ=1 Average absorptivity, reflectivity & transmissivity of a surface is:

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):  ε λ (T) = α λ (T)valid when the irradiation is independent of direction

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

Atmospheric solar radiation Radiation energy emitted or reflected by the constituents of the atmosphere Diameter of the sun ~ 1.39 x 10 9 m Mass of the sun ~ 2.0 x kg Distance from earth of the sun ~ 1.5 x m Sun’s radiation emission ~ 3.8 x W Temperature at the sun’s core ~ 4.0 x 10 7 K Total solar irradiance (solar constant) G s = 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

Effective temperature of the sun Total solar irradiance: (4πL 2 )G s = (4πr 2 )σT 4 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, G D and diffused, G d solar radiation

Solar radiation G solar = G D cos + G d Diffused radiation ca % of total on clear day Treat atmosphere as a blackbody at a lower temp., T sky Diffused solar radiation Direct solar radiation GDGD GdGd

Example Consider a surface exposed to solar radiation. At a given time, the direct and diffused components of solar radiation are G D =400 and G d =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 K at that time. Assuming an effective sky temperature of K, determine the net rate of radiation heat transfer for: (a) α s =0.9 & ε s =0.9 (b)α s =0.1 & ε s =0.1 (c)α s =0.9 & ε s =0.1(d)α s =0.1 & ε s =0.9

END That’s all folks!!