Radiation — Basic Definition (Mechanical GATE)

Introduction

Thermal radiation is the transfer of energy by electromagnetic waves emitted due to the temperature of a body. Unlike conduction and convection, radiation does not require a medium and can occur in a vacuum.

Key Characteristics

• Radiation travels at the speed of light.
• It is emitted by all bodies above absolute zero.
• It depends on surface properties and temperature.
• It is governed by electromagnetic wave theory and quantum mechanics.

Stefan–Boltzmann Law

The total emissive power of a black body is given by: \[ E_b = \\sigma T^4 \] where:

• \( \\sigma = 5.67 \\times 10^{-8} \, \\mathrm{W/m^2K^4} \): Stefan–Boltzmann constant
• \( T \): absolute temperature in Kelvin

Real Surface Emission

For a real surface: \[ E = \\varepsilon \\sigma T^4 \] where:

• \( \\varepsilon \): emissivity of the surface \((0 \le \\varepsilon \le 1)\)

Radiative Heat Exchange Between Two Surfaces

Net heat exchange between two diffuse, gray surfaces: \[ \\dot{q}_{12} = \\sigma A_1 \\left( T_1^4 - T_2^4 \\right) \\cdot \\frac{1}{\\left( \\frac{1}{\\varepsilon_1} + \\frac{1}{\\varepsilon_2} - 1 \\right)} \] For black bodies: \[ \\dot{q}_{12} = \\sigma A_1 F_{12} \\left( T_1^4 - T_2^4 \\right) \] where \( F_{12} \) is the view factor from surface 1 to 2.

Surface Properties

• Absorptivity: \( \\alpha \)
• Reflectivity: \( \\rho \)
• Transmissivity: \( \\tau \)
• For opaque surfaces: \( \\tau = 0 \), so \( \\alpha + \\rho = 1 \)

Black, Gray, and White Bodies

• Black body: \( \\varepsilon = 1 \), absorbs all incident radiation.
• Gray body: \( \\varepsilon \) is constant and less than 1.
• White body: \( \\rho = 1 \), reflects all incident radiation.

GATE Tips

• Memorize Stefan–Boltzmann law and emissive power formulas.
• Understand the difference between black, gray, and real surfaces.
• Know surface property relationships: \( \\alpha + \\rho + \\tau = 1 \).
• Be familiar with view factor concepts and their role in net exchange.