Radiation Process and Properties Thermal radiation is the transmission of thermal energy without any physical contact between the bodies involved. Salient Features and Characteristics of Radiation. i)The electromagnetic waves are emitted as a result of vibrational and rotational movements of the molecular, atomic or sub atomic particles comprising the matter. ii)The distinction between one form of radiation and another lies only in its frequency and wavelength which are related by – c (speed of light) = λ (wavelength) f (frequency). iii) Each photon can be thought of as a particle having mass m, energy e and momentum ( = mass* velocity) e = mc2 =hf. iv)The general phenomenon of radiation covers the propagation of electromagnetic waves of all the wavelengths, from short wavelength gamma rays, X-rays and ultrvoilet radiation to the long wavelength microwaves and radio waves.

v)Thermal radiations exhibit characteristics similar to those of visible light, and follow optical laws. vi)All matter emits radiant energy and bodies at high temperature emit at a greater rate than bodies at low temperature. vii)Heat transfer by conduction and convection depends primarily on the temperature difference gradient and is little affected by temperature level.

Absorptivity, Reflectivity and Transmissivity The total radiant energy (Q0) impinging upon a body would be partially or totally absorbed by it (Qa), reflected from its surface (Qr), or transmitted through (Qt) in accordance with the characteristics of the body.

Dividing throughout by (Q0), we have The factors α,  and  are dimensionless and vary from 0 to 1. Black surfaces are effective absorbers of radiation in the wavelengths that are encountered in heat transfer. Accordingly the name black body is assigned to a perfect absorber of radiation. A body that reflects all the incident thermal radiations is called a specular body or an absolutely white body. A body that allows all the incident radiations to pass through it is called transparent or diathermaneous

Specular and diffused reflections

Large hollow sphere or cylinder provided with only one small opening

Spectral and Spatial Energy Distribution Spectral distribution – The radiation emitted by a surface consists of Electromagnetic waves of various wavelengths, and the term spectral refers to the variation in thermal radiations with wavelength.

Spatial or directional distribution – A surface element emits radiation in all directions the intensity of radiation is however different in different directions.

Radiation of black body as a function of wavelength and temperature

Wavelength Distribution of Black Body Radiation: Plank’s Law The energy emitted by a black surface varies in accordance with wavelength, temperature and surface characteristics of the body. For a prescribed wavelength, the body radiates much more energy at elevated temperatures. The law governing the distribution of radiant energy over wavelength for a black body at a fixed temperature were formulated by Plank. The above equation is written as Where

The quantity denotes the monochromatic emissive power, and is defined as the energy emitted by the black surface at a given wavelength λ per unit wavelength interval around λ. Spectral energy distribution is the variation of distribution of the monochromatic emissive power with wavelength. The important features are The monochromatic emissive power varies across the wavelength spectrum, the distribution is continuous but non-uniform. At any wavelength the magnitude of the emitted radiation increases with increasing temperature. The wavelength at which the monochromatic emissive power is maximum shifts in the direction of shorter wavelengths as the temperature increases. At any temperature, the area under the monochromatic emissive power versus wavelength gives the rate of radiant energy emitted within the wavelength interval dλ.

For Shorter wavelengths, the factor becomes very large in that case For Shorter wavelengths, the factor becomes very large in that case . The Planks law then reduces to This is called Wien’s law. b) For longer wavelengths, the factor is small in that case can be expanded in series to give The Plank’s distribution law then becomes This Identity is known as Rayleigh-Jean’s Law.

Total Emissive Power : Stefan Boltzman Law The total emissive power E of a surface is defined as the total radiant energy emitted by the surface in all directions over the entire wavelength range per unit surface area per unit time. This rate equation can be set-up by the Integration of monochromatic emissive power over entire band width of wavelength for Let New Integration limits are At

The integral is of the form Substituting the value for constants

We get Where is the Radiation coefficient or the Stefan-Boltzman constant. The net radiant heat flux is then given by

Fraction of black body emission occuring in the range 0 to 1T

Expressing it as fraction of the total emissive power, Or The fraction can be expressed

Wien’s Displacement law From the spectral distribution of black body emissive power, it is apparent that the wavelength associated with maximum rate of emission depends upon the absolute temperature of the radiating surface. With respect to λ and setting the derivative equal to zero Since the denominator ,we have

Whose solution by hit and trial method gives Combination of Plank’s law and the Wien’s displacement law yields the correlation for maximum monochromatic emissive power for a black body.

Kirchoff’s Law The emissivity and absorptivity of a real surface are equal for radiation with identical temperature and wavelength

This relationship can be extended by considering different surfaces in turn, or

Gray body and Selective Emitters Gray body :When the emissivity of non-black surface is constant at all temperatures and throughout the entire range of wavelength, the surface is called Gray body. Selective Emitters :For many materials the emissivity is different for the various wavelengths of the emitted energy. The radiating bodies exhibiting this behavior are called selective emitters.

Emission from black, gray and selective emitters

Stefan-Boltzman law when applied to a gray body takes the form The emissivity of the gray surface expressed as Values of emissivities range from 0.0 to 1.0 The emitted radiant energy flux density for non-black body is

Emissivities of real bodies Monochromatic emissivity : Ratio of the monochromatic emissive power of a surface to the monochromatic emissive power of a black surface at the same wavelength and temperature. Total emissivity : Ratio of the total emissive power of a surface to the total emissive power of a black surface at the same temperature. Normal total emissivity : Ratio of the normal component of the total emissive power of a surface to the normal component of the total emissive of a black body at the same temperature. Mean emissivity : Emissivity of most of the engineering materials is influenced by temperature as well as wavelength. For a particular temperature, the average of monochromatic emissivity at various wavelengths is called wavelength-mean emissivity. equilibrium emissivity :The emissivity of a material through varying with temperature and thr nature of its surface is not affected in any way by the nature of surface surrounding it. The total emissivity remains constant whether the material is in equilibrium with the surroundings or not. The total emissivity is called as equilibrium emissivity.

Intensity of Radiation and Lambert's cosine law Subtended plane and solid angles: The plane angle α is defined by a region by the rays of the circle, and is measured as the ratio of the element of arc of length l on the circle to the radius r of the circle: The solid angle is defined by a region by the rays of a sphere, and is measured as:

The relationship between A, and has been shown in fig The relationship between A, and has been shown in fig. Projection of an incident surface normal to the line of propagation

Intensity of radiation: The intensity of radiation I is the energy emitted in a particular direction per unit surface area and through a unit solid angle. The intensity of radiation in a direction from the normal to a black emitter is proportional to cosine of the angle .

Relation between the normal intensity and emissive power: Differential solid angle in terms of zenith and azimuthal angles

Thus for a unit surface, the intensity of normal radiation Area of collector Then the radiations leaving the emitter and striking the collector is Thus, Combining the equations Thus for a unit surface, the intensity of normal radiation is the times the emissive power