Radiation Heat Transfer Study Notes for Mechanical Engineering

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.

MONOCHROMATIC (OR) SPECTRAL EMISSIVE POWER (E_λ):

E_λ at a particular wavelength λ is defined as a quantity which when multiplied by dλ shall give the radiation energy emitted from the surface of a body per unit time per unit area in the wavelength region λ to λ + dλ.

 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 = 0.5 = 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

LAWS OF THERMAL RADIATION:

KIRCHOFF’S LAW OF RADIATION:

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

 PLANCK’S LAW OF THERMAL RADIATION:

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 E_bλ will be maximum at a specified temperature can be found out by differentiating E_bλ  w.r.t  λ and then putting equal to zero.

We get,  λ_mT = 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= I_n cos θ, I_n = normal intensity of radiation

RADIATION INTENSITY:

The ideal intensity I_b 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.

For the detailed schedule of the GATE 2022  Mechanical Engineering(ME) Champion Study Plan, click here

If you are preparing for ESE/ GATE or other PSU Exams (Mechanical Engineering), then avail Online Classroom Program for ESE and GATE ME: 

Comprehensive Preparation for GATE & ESE ME Exams(500+ Hours of Live Classes, 300+ Quizzes for Practice and 60+ Mock Tests)

You can avail Test Series specially designed for all Mechanical Engineering Exams:

Get Unlimited Access to all 161+ Mock Tests

All the Best!

#DreamStriveSucceed.

Update BYJU’S Exam Prep, Best GATE exam app for Preparation