Radiation Heat Transfer

Heat transfer due to emission of electromagnetic waves is known as thermal radiation

Heat transfer through radiation takes place in form of electromagnetic waves mainly in the infrared region. Radiation emitted by a body is a consequence of thermal agitation of its composing molecules. Radiation heat transfer can be described by reference to the 'black body'.

The Black Body

black body

The black body is defined as a body that absorbs all radiation that falls on its surface. Actual black bodies don't exist in nature - though its characteristics are approximated by a hole in a box filled with highly absorptive material. The emission spectrum of such a black body was first fully described by Max Planck.

A black body is a hypothetical body that completely absorbs all wavelengths of thermal radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation.

The radiation energy per unit time from a blackbody is proportional to the fourth power of the absolute temperature and can be expressed with Stefan-Boltzmann Law as

q = σ T4 A         (1)


q = heat transfer per unit time (W)

σ = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

T = absolute temperature in Kelvin (K)

A = area of the emitting body (m2)

The Stefan-Boltzmann Constant in Imperial Units

σ = 5.6703 10-8 (W/m2K4)

    = 0.1714 10-8 ( Btu/(h ft2 oR4) )

    =  0.119 10-10 ( Btu/(h in2 oR4) )

heat radiation from a black body - surroundings absolute zero

Example - Heat Radiation from the surface of the Sun

If the surface temperature of the sun is 5800 K and if we assume that the sun can be regarded as a black body the radiation energy per unit time can be expressed by modifying (1) like

 q / A = σ T4

    = (5.6703 10-8 W/m2K4) (5800 K)4

    = 6.42 107 (W/m2

    Gray Bodies and Emissivity Coefficients

    gray body

    For objects other than ideal blackbodies ('gray bodies') the Stefan-Boltzmann Law can be expressed as

    q = ε σ T4 A         (2)


    ε = emissivity coefficient of the object (one - 1 - for a black body)

    For the gray body the incident radiation (also called irradiation) is partly reflected, absorbed or transmitted.

    incident reflected transmitted absorbed radiation irradiation

    The emissivity coefficient is in the range 0 < ε < 1, depending on the type of material and the temperature of the surface.

    Net Radiation Loss Rate

    If an hot object is radiating energy to its cooler surroundings the net radiation heat loss rate can be expressed as

    q = ε σ (Th4 - Tc4) Ac         (3)


    Th = hot body absolute temperature (K)

    Tc = cold surroundings absolute temperature (K)

    Ac = area of the object  (m2)

    Heat loss from a heated surface to unheated surroundings with mean radiant temperatures are indicated in the chart below. 

    heat radiaton from heated surface to unheated surroundings

    Lambert's cosine law

    Heat emission from a surface in an angle β can be expressed with Lambert's cosine law as

    qβ = q cos β   (4)


    qβ = heat emission in angle β 

    q = heat emission from the surface

    β = angle 

      Related Topics

      • Heat Loss and Insulation - Heat loss from pipes, tubes and tanks - with and without insulation - foam, fiberglass, rockwool and more
      • Insulation - Heat transfer and heat loss from buildings and technical applications - insulation methods and coefficients to reduce energy consumption
      • Heat Loss and Insulation - Steam and condensate pipes - heat loss uninsulated and insulated pipes, insulation thickness and more
      • Thermodynamics - The effects of work, heat and energy on a system

      Related Documents

      Tag Search

      • en: radiation heat transfer coefficient
      • es: radiación coeficiente de transmisión térmica
      • de: Strahlungswärmeübergangskoeffizient

      Search the Engineering ToolBox

      - "Search is the most efficient way to navigate the Engineering ToolBox!"

      Engineering ToolBox - SketchUp Extension - Online 3D modeling!

      3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

      Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

      Translate the Engineering ToolBox!
      About the Engineering ToolBox!

      Support the ToolBox

      If you find the Engineering ToolBox useful and want this website to be available tomorrow - and the days after tomorrow - enable ads or make a contribution!

      Contribute to the Engineering ToolBox