Radiation Heat Transfer

Overview

Radiation heat transfer occurs via electromagnetic waves and does not require a medium. It depends on the fourth power of absolute temperature (Stefan-Boltzmann law).

Formula

$Q = \varepsilon \sigma A T^4$

Calculator

Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Emissivity Coefficients

Gray Body Radiation

For real-world objects ("gray bodies"), the radiation heat transfer rate is modified by the emissivity (ε) of the surface.

$q = \varepsilon \sigma T^4 A$

Where:

• ε is the emissivity coefficient (0 < ε < 1).

The net radiation heat transfer rate from a hot object to its cooler surroundings is given by:

$q = \varepsilon \sigma \left( T_h^4 - T_c^4 \right) A_h$

Where:

• $T_h$ = absolute temperature of the hot body (K)
• $T_c$ = absolute temperature of the cool surroundings (K)
• $A_h$ = surface area of the hot object (m²)

Lambert's Cosine Law

The heat emission from a surface is not uniform in all directions. According to Lambert's cosine law, the intensity of radiation emitted at an angle β to the normal of the surface is:

$q_\beta = q \cdot \cos(\beta)$

Where:

• $q_\beta$ = heat emission in direction at angle β from the normal
• $q$ = heat emission from the surface perpendicular to it (β = 0)

Interactive Charts

References

• Original Source