Page 144 - Industrial Ventilation Design Guidebook

I 06 CHAPTER 4 PHYSICAL FUNDAMENTALS
4.3.1.3 Radiation
Heat radiation is electromagnetic radiation that all bodies emit due to
their temperature. The wavelength of electromagnetic radiation is be-
tween 0.3 and 50 jjim. This mode of heat transfer does not depend on an
intermediate agent. When radiation falls on a body, part of the energy is
absorbed, part is reflected, and the remainder is transmitted through the
body. These components of the incoming radiation are the absorption ra-
tio a, reflectance ratio p and transmission ratio r. When a body is in a
state of equilibrium, the incoming and outgoing radiation are equal.
Hence, a + p + r — 1.
A body having good electrical conductivity will absorb the incoming ra-
diation on a distance of one wavelength. Now r = 0 and a + p = 1.
A planar polished surface reflects heat radiation in a similar manner with
which it reflects light. Rough surfaces reflect energy in a diffuse manner; hence
radiation is reflected in all directions. A blackbody absorbs all incoming radi-
ation and therefore has no reflection. A perfect blackbody does not exist; a
near perfect blackbody surface such as soot reflects 5% of the radiation, mak-
ing it the standard for an ideal radiator.
The radiant emittance of a blackbody is

2
4
where cr is the Stefan-Boltzmann constant, 11.865 W m~ (MJ/kmol)" .
The radiation emitted by a body due to its temperature is defined by the
factor e, the emissivity,

for a given temperature, angle, and frequency. For approximate calculations
the emissivity can be assumed constant over the whole frequency spectrum. In
this case the body is classified as a gray body.
The net heat transfer between two surfaces according to Eq. (4.159)
is proportional to the first or second power of the temperature differ-
ence; hence the radiation heat transfer dominates at a high temperature
or for large temperature differences. When the temperature difference is
small, a heat transfer factor is used similar to that used for convective
heat transfer:

4.3.2 Analogy with the Theory of Electricity
Equation (4.154) gives conduction for the one-dimensional case with constant
thermal conductivity: