G.H PATEL COLLEGE OF ENGINEERING & TECHNOLOGY HEAT TRANSFER (2151909) TOPIC : RADIATION Made By : 130110119001 Guided By : Prof. Bharat Sunar

Introduction All solids and liquids surface at all temperature emit thermal radiation. It may be defined as “ the transfer of heat across a system boundary by means of electromagnetic waves which is caused by temperature difference.” Characteristics: 1) They travel with a certain speed 2) They are distinguish according to wavelength The significance of the radiation will be the only mechanism for heat transfer whenever a vacuum is present.

Examples Heat leakage from furnaces, combustion chambers Space application Solar energy incident upon earth Heat libration during nuclear explosions Heat dissipation from the bulb filament Heat leakage through the evacuated walls of thermos flask

Electromagnetic spectrum

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Continue… This spectrum contain Gamma rays , X-rays, ultraviolet rays, visible light, infra-red rays, micro waves. Thermal radiation spectrum range: 0.1 to 100μm It includes some UV radiation and all visible (0.4μm-0.7 μm) and infrared radiation.

Facts of Radiation Electromagnetic wave doesn’t require a material medium for propagation. In addition to emitting radiation, the surface of a body has the capacity for absorbing all/part of the radiation emitted by surrounding surfaces and falling on it. Directional nature: A surface emits radiation in all directions encompassed by a hemisphere.

Black Body An ideal body which absorbs all its radiation falling on it regardless of its wavelength and direction. For a given temperature and wavelength, it emits the maximum amount of energy. Real surfaces may approaches black surfaces but not exactly black surfaces. It is perfect emitter. It is non-reflective and opaque body (i.e. ρ=τ=0).

Examples of Black body Text Examples For example, the Sun and piece of charcoal is approximate a black body. So, we call it as a bench mark for us!!! No perfect black surface has been found in nature.

Total emissive power At a given temperature, radiant flux emitted from a surface of a body. The energy emitted by any real surface (E) is less than the energy emitted by a black body (Eb) at the same temperature. E = f ( T , λ , ε ) Hence, the emissive power depends upon the temperature of surface and all its characteristics. where, ε= emissivity λ= wavelength of radiation, μm E= Total emissive power

Total hemispherical emissivity The ratio of the emissive power of real body E to the blackbody emissive power Eb at the same temperature is the hemispherical emissivity of the surface. By definition 0 ≤ ε ≤ 1 because no surface emit more than black surface

Monochromatic emissive power The amount of radiation energy emitted from a given surface at a given temperature varies with radiation in wavelength. At a given temperature, radiant flux emitted per unit wavelength is called monochromatic emissive power. It is denoted by El.

Continue… So mathematically, To get total emissive power, Eλ is the quantity which is integrated overall wavelengths The graphical representation of above equation is given below:

Figure

Monochromatic emissivity It is ration of monochromatic emissive power of real surface to black surface at the same temperature and wavelength.

Intensity of Radiation(Irradiation) It is defined as the total incident radiation on a surface from all the directions per unit area, per unit time, expressed in W/ m2. It is denoted by G.

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Radiosity(J) It is defined as the total radiant energy leaving from the surface from all the directions per unit area, per unit time, expressed in W/m2 . It is denoted by J.

Gray surface To simplify matters it is common to assume the emissivity to be independent on wavelength and direction. Such a surface is called gray surface. Eλ(λ,T)= ελ • Eλ,black (λ,T) ελ= constant=ε (0≤ ε≤ 1) Neglect variation in Eλ and take some constant value.

Laws of Radiation Plank’s Law ( Emissive power of a black body) Wien’s Law ( Maximum radiant intensity) Stefan- Boltzmann Law ( Amount of radiant energy from a black body) Kirchhoff’s Law ( Relates the radiated energy to absorbed energy)

Planck’s Radiation Law Developed by physicist Mr. Max Plank Stefan-Boltzmann law is useful to study overall energy , it doesn't allow us to treat those interactions, which specifically wavelength λ. It is based on quantum theory It gives relationship between for monochromatic emissive power of the black body.

Equation of Plank’s Law

Another Equation Plank’s equation can also be written as, Where, C1 = 0.596⨯10-16 W/m2 C2 = 0.014387 m K λ= wavelength T= absolute temperature in K

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Comments on Graph Monochromatic emissive power of the black body at a given temperature first increases with increase in wavelength, attains a certain maximum value and then decreases. At a particular wavelength, Ebλ increases with temperature. The maximum value of Ebλ occurs at a smaller wavelength as temperature increases. Most of the thermal radiations lie between the range 0.3 to 10 μm.

Wien’s Displacement Law It gives the relationship between the maximum wavelength λmax at which the maximum monochromatic emissive power is obtained and the absolute temperature, T of a black body. According to this law,

Wien’s Law for three different stars

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Stefan-Boltzmann Law It states that total emissive power of a black body is directly proportional to fourth power of its absolute temperature. Integrating monochromatic emissive power to overall wavelengths gives Eb.

Continue… where, T=absolute temperature in K σ=Stefan Boltzman constant= 5.67⨯10-8 W/m2K4 Eb = Total emissive power of black body

Equation The total energy emitted by a surface other than black surface is given by, E= εAσT4 where, ε=emissivity of body A=surface area T= absolute temperature in K σ=5.67⨯10-8 W/m2K4

Example

Kirchhoff’s Law Proposed by Gustav Kirchhoff in 1859 It states that “ At thermal equilibrium, the emissivity of a body equal to its absorptivity at a given temperature and wavelength. So, Emissivity of body ελ = Absorptivity αλ Important: It applies wavelength dependent A good absorber is a good emitter A good reflector is a poor emitter and vice versa i.e thermal blanket

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Comments on Kirchhoff’s Law If this law is not obeyed, an object can never reach thermal equilibrium. It would either be heating up or cooling down. Since absorptivity ranges between 0 to 1 , it implies that emissivity also ranges between 0 to 1. Though we have proved the results in case the body in thermal equilibrium with its surroundings, however this results have also been verified experimentally. Water is good absorber and emitter so ε is close to 1 Metal is good reflector and poor emitter so ε is close to 0.

Radiative Properties When radiation strikes a surface, a portion of it is reflected, and the rest enters the surface. Of the portion that enters the surface, some are absorbed by the material, and the remaining radiation is transmitted through.

Continue…. Consider a semi-transparent sheet that receives incident radiant energy flux, also known as irradiation, G . Let dG represent the irradiation in the waveband l to l + dl. Part of it may be absorbed, part of it reflected at the surface, and the rest transmitted through the sheet. We define monochromatic properties by as follows

Reflectivity It is defined as the fraction of total incident radiations that are reflected by body or surface. Reflectivity (ρ)= Energy reflected Gρ / Total energy incident on it G Monochromatic reflectivity: Total reflectivity:

Absorptivity It is defined as the fraction of total incident radiations that are absorbed by the surface. Absorptivity (α)= Energy absorbed Gα/ Total incident radiation G Monochromatic Absorptivity: Total Absorptivity:

Transmissivity It is defined as the fraction of the total incident radiations that are transmitted through the surface. Transmissivity (τ)= Energy transmitted Gτ/ Total incident radiation G Monochromatic transmissivity: Total transmissivity:

Absorptivity and Reflectivity of Different Material

Conservation of Irradiation The total Irradiation , (from Conservation of energy) G = Gα + Gρ + Gτ By dividing G, we get, α + ρ + τ = 1 Monochromatic properties of a body are independent on the temperatures of the source radiation and the nature and preparation of the surface. In case of solids and liquids, the transmissivity is negligible , hence α+ρ =1, in case of gases the reflectivity is very small , hence α+τ=1.

Types of Surfaces/ Bodies Black body 2)White body 3)Grey body 4)Opaque body 5)Transparent body

Black Body An ideal body which absorbs all its radiation falling on it regardless of its wavelength and direction. For a given temperature and wavelength, it emits the maximum amount of energy. Real surfaces may approaches black surfaces but not exactly black surfaces. It is perfect emitter. It is non-reflective and opaque body (i.e. ρ=τ=0). No body in nature has been found completely black.

White Body The surfaces which reflect the total radiant energy are called white body. For such bodies, α=τ=0 and ρ=1

Grey Body The body which has its absorptivity equal to its emissivity is called a grey body provided the temperature of the surface of incident radiation and the body are the same. The body having the same value of emissivity at all wave lengths, which is equal to emissivity is called Grey body. i.e. all metals

Opaque Body The bodies which have negligible transmissivity are called opaque bodies. So, α+ρ=1, τ=0. i.e. solid and liquid surfaces.

Transparent Body The surface which transmits the entire radiations are called transparent body. For this surface α=ρ=0, τ=1. i.e. dry air

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