Radiation

1. Introduction

Radiation is a mode of heat transfer in which thermal energy is transmitted in the form of electromagnetic waves. Unlike conduction and convection, radiation does not require a material medium and can occur through vacuum.
All bodies at a temperature above absolute zero emit radiant energy. Radiation plays a crucial role in solar energy transfer, furnaces, boilers, space technology, and high-temperature processes.

2. Nature of Thermal Radiation

• Thermal radiation is a part of the electromagnetic spectrum
• It travels at the speed of light
• It does not require a physical medium
• The amount of radiation depends on the temperature and surface characteristics

3. Basic Terms Used in Radiation

3.1 Radiant Energy

Energy emitted by a body in the form of electromagnetic waves due to its temperature.

3.2 Emissive Power (E)

The total radiant energy emitted by a surface per unit area per unit time.

Unit: W/m²

3.3 Absorptivity (α)

The fraction of incident radiation absorbed by a surface.$$\alpha = \frac{\text{Radiation absorbed}}{\text{Radiation incident}}$$

3.4 Reflectivity (ρ)

The fraction of incident radiation reflected by a surface.

3.5 Transmissivity (τ)

The fraction of incident radiation transmitted through a surface.

For any surface:$$\alpha + \rho + \tau = 1$$

For opaque surfaces:$$\alpha + \rho = 1$$

4. Black Body

Definition

A black body is an ideal body that absorbs all incident radiation, regardless of wavelength and direction, and emits the maximum possible radiation at a given temperature.

Characteristics

• Absorptivity (α) = 1
• Emissivity (ε) = 1
• Perfect emitter and absorber

A black body does not exist in practice but is used as a reference standard.

5. Grey Body

A grey body is one whose emissivity is less than unity but constant at all wavelengths.

Most engineering surfaces behave approximately as grey bodies.

6. Emissivity (ε)

Definition

Emissivity is the ratio of radiation emitted by a real surface to that emitted by a black body at the same temperature.$$\varepsilon = \frac{E_{\text{actual}}}{E_{\text{black body}}}$$

$0 < \varepsilon < 1$0<ε<1

Polished metals → low emissivity

Rough, black surfaces → high emissivity

7. Laws of Thermal Radiation

7.1 Planck’s Law

It describes the spectral distribution of radiation emitted by a black body at a given temperature.

(Significant for theoretical understanding)

7.2 Wien’s Displacement Law

States that the wavelength at which maximum radiation occurs is inversely proportional to absolute temperature.$$\lambda_{max} T = \text{constant}$$

7.3 Stefan–Boltzmann Law

States that the total radiant energy emitted by a black body is proportional to the fourth power of absolute temperature.$$E = \sigma T^4$$E=σT4

Where:

• $E$E = emissive power (W/m²)
• $T$T = absolute temperature (K)
• $\sigma$σ = Stefan–Boltzmann constant $$= 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4$$=5.67×10−8W/m2K4

For a real surface:$$E = \varepsilon \sigma T^4$$

7.4 Kirchhoff’s Law

States that:

For a body in thermal equilibrium, emissivity is equal to absorptivity.

$$\varepsilon = \alpha$$

This law helps relate emission and absorption properties.

8. Radiation Heat Exchange Between Surfaces

For two large parallel surfaces:$$Q = \sigma A (T_1^4 – T_2^4)$$

Where:

• $A$A = area
• $T_1, T_2$T1​,T2​ = absolute temperatures

9. View Factor (Shape Factor)

Definition

The view factor is the fraction of radiation leaving one surface that directly reaches another surface.

• Depends on geometry and orientation
• Denoted by $F_{1 \to 2}$F1→2​

10. Comparison of Heat Transfer Modes

Aspect	Conduction	Convection	Radiation
Medium required	Yes	Yes	No
Occurs in vacuum	No	No	Yes
Depends on temperature difference	Yes	Yes	Yes
Depends on surface properties	No	No	Yes

11. Applications of Radiation

• Solar energy systems
• Furnaces and boilers
• Heat treatment processes
• Spacecraft thermal control
• Infrared heaters
• Cooling of high-temperature surfaces

12. Advantages of Radiation Heat Transfer

• Works in vacuum
• Effective at high temperatures
• No contact required

13. Limitations

• Significant mainly at high temperatures
• Calculation is complex
• Strongly dependent on surface condition

---