By Vijay Pratap Singh|Updated : December 26th, 2021

(i) Thermal energy emitted by matter as a result of vibrational and rotational movements of molecules, atoms and electrons.

(ii) The energy is transported by electromagnetic waves (or photons).

(iii) Radiation requires no medium for its propagation, therefore, can take place also in vacuum.

BASIC DEFINITIONS:

TOTAL HEMISPHERICAL EMISSIVE POWER (E):

(i) It is defined as the radiation energy emitted from the surface of a body per unit time & per unit area in all possible hemispherical directions integrated over all the wavelengths (in J/s m2 or W/m2).

BLACK BODY:

(i) Different bodies emits different amount of radiation even if they are at same temperature.

(ii) A body which emits maximum amount of radiation at a given temperature is known as BLACK BODY.

(iii) A black body is defined as perfect emitter and absorber of radiation.

TOTAL EMISSIVITY (Є):

Total emissivity of a body is defined as the ratio between total hemispherical emissive power of a non-black body & total hemispherical emissive power of a black body both being at the same temperature.

ABSORPTIVITY (α), REFLECTIVITY (ρ) & TRANSMISSIVITY (τ)

• Absorptivity(α) is the fraction of incident radiation absorbed.
• Reflectivity(ρ) is the fraction of incident radiation reflected.
• Transmissivity (τ) is the fraction of incident radiation transmitted.

ABSORPTIVITY (α) = 50/100 = 0.50 = Fraction of radiation energy incident upon a surface which is absorbed by it.

REFLECTIVITY (ρ) = 25/100 = 0.25 = Fraction of radiation energy incident upon a surface which is reflected by it.

TRNASMISSIVITY (τ) = 25/100 = 0.25 = Fraction of radiation energy incident upon a surface which is transmitted by it.

• For any Body:

α + ρ + τ = 1

• For opaque body, which do not transmit any energy,

τ = 0,  α + ρ = 1

• For black body, α = 1 [as it absorbs all energy incident]
• For white body, which reflects all energy incident, τ  = 1

The law states that whenever a body is in thermal equilibrium with its surrounding’s its emissivity is equal to its absorptivity.

α = ϵ

STEFAN BOLTZMANN’S Law:

The law states that the total hemispherical emissive power of a black body is directly proportional to fourth power of the absolute temperature of black body.

Stefan BoltzmannConstant= 5.67 × 10-8 W/m2 k4

The planck law describes the theoretical spectral distribution for the emissive power of a black body which is the amount of radiation energy emitted by a blackbody at a thermodynamic temperature T per unit time per unit surface area and per unit wavelength.

WEIN’S DISPLACEMENT LAW:

The wavelength at which Ewill be maximum at a specified temperature can be found out by differentiating E w.r.t  λ and then putting equal to zero.

We get,  λmT = 2897.8  μmK

LAMBERT’S COSINE LAW:

The intensity of radiation in a direction θ from the normal to a diffuse emitter is proportional to cosine of the angle θ.

I= In cos θ, I= normal intensity of radiation

The ideal intensity Ib is defined as the energy emitted from an ideal body(black body which is diffuse emitter) ,per unit projected area, per unit time ,per unit solid angle.

SHAPE FACTOR OR VIEW FACTOR OR CONFIGURATION FACTOR:

Radiation heat transfer between surfaces depends upon the orientation of the surfaces relative to each other as well as their radiation properties and temperatures.

To account for the effects of orientation on radiation heat transfer between the surfaces,a new parameter VIEW FACTOR is defined which is purely geometric quantity and is independent of radiation properties and temperatures.

Assumptions:

• The surfaces are diffuse emitter.
• The radiation that strikes a surface need not to be absorbed by that surface.
• Radiation that strikes a surface after being reflected by other is not considered in the evaluation of view factor.

The radiation shape factor is represented by the symbol Fij ,

which means the shape factor form a surface, Ai to another surface Aj.

Thus the radiation shape factor F12 of surface A1 to surface A2 is

SHAPE FACTOR RELATIONS:

(i) RECIPROCITY RELATION:

A1F12 = AF21

Reciprocity Relation is valid between any two surfaces even when there are more than two number of surfaces involved in Radiation Heat Exchange.

(ii) SUMMATION RULE:

If there are n number of surfaces involved in any radiation heat exchange then.

F11 + F12 + F13 + …………….F1n = 1

F21 + F22 + F23 + ……………. F2n = 1

.

Fn1 + Fn2 + Fn3 + ………..Fnn + 1

SUPERPOSITION RULE:

F1-(2,3) = F1-2 + F1-3

SYMMETRY RULE:

Two or more surfaces that possess symmetry about a third surface will have identical view factors from that surface.

If the surface 2 and 3 are symmetric about surface 1 then F1-2=F1-3

GENERAL CASES:

CROSS STRING METHOD:

The each length is assumed to be a strings connected between two points.

Cross Strings → The strings which crosses each other.

Uncrossed strings → The strings which do not cross each other.

Li = length of string on surface i.

AB → 1 surface

CD → 2 surface

Special Case:

(Length)1 = (Length)2 Both surfaces are infinite in plane perpendicular to plane of paper.

Irradiation (G) is defined as the total thermal radiation incident upon a surface per unit time per unit area (in W/m2)

The total thermal radiation leaving a surface per unit time & per unit area is called radiosity of the surface.

J = Emitted Energy + Reflected Part of Incident energy,

The net radiation heat exchange between the surface & all of its surroundings is given by,

Radiation heat exchange between two finite surfaces:

This space resistance shall exist in the space between two surfaces exchanging heat by radiation.

Radiation Exchange Between two Infinitely Large Plane Surfaces:

F12 = 1, F21 = 1

Since surfaces are very large

A1 = A2 = A3 = 1 and F13 = 1, F32 = 1

Therefore,

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