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 of the object (one 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 lies in the range 0 < tyle: italic;">ε < 1 depending on the type of material and the temperature of the surface. The emissivity of some common materials

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 

نوشته شده در تاریخ سه شنبه 11 مرداد 1390    | توسط: عباس خداقلیزاده    | طبقه بندی: مفاهیم گرمایش تابشی،     |