What is emissivity, and why is it important?

In heat treatment, we are often concerned with calculating how fast a part will heat (Eq. 1)[1] or how rapidly it will cool. Furnace size/length is influenced by both emissivity and the practical problem of having enough length or surface area for installing the required number of radiant tubes or electric elements to provide adequate radiation angles.
  • t is heating time, in hours
  • W is (gross) weight, in pounds
  • ε is emissivity
  • Ar is the effective radiation area, in square feet
  • φ(t) is a functional value obtain by knowing the metal temperature and chamber temperature

Formally, emissivity is defined as the relative power of a surface to emit heat by radiation and is ratio of the radiation emitted by a surface to the radiation emitted by a blackbody at the same temperature. Planck’s law (Eq. 2)[1] allows us to predict how much energy exits a black body. From a practical perspective, we are interested in having a value comparable to “black-body” radiation, having an assumed value of ε = 1 (c.f. Table 1).

  • I is the energy radiated per unit time per unit surface area per unit solid angle per unit frequency or wavelength
  • v is the frequency, in hertz
  • λ is the wavelength, in meters
  • T is the temperature (of the black body), in Kelvin
  • h is Planck’s constant, in joule-second
  • c is the speed of light, in meters per second
  • ε is the natural logarithm (2.718281)
  • k is Boltzmann’s constant, in joules per Kelvin

As we heat (or cool) a metal, its surface absorbs or emits radiant energy. And depending on the condition of the surface (oxidized, polished, etc.), the amount of energy varies. For example, a highly polished (mirror-like) surface will reflect about 98% of the energy it sees, meaning that only 2% of the available energy is absorbed. In other words, it takes a longer period of time to heat an object with a highly reflective surface than a dull one. By contrast, a dark (black-body-like) surface will absorb about 98% of the available energy.

When doing calculations involving emissivity, be aware that values are affected by a number of factors including geometry (shape), uniformity of temperature, surface condition (e.g., rough/smooth, scaly/clean) and exposure (viewing area).