1. Absorption Factor Method of
Radiation
Presented By
Shyamala.C
M.Tech (Storage Engineering)
2015604605
2. Absorption Factor Method of Radiation
The ratio of the total absorbed radiant or luminous flux to the
incident flux is called absorptance (formerly also called
absorption factor).
This method was developed by Gebhart (1957, 1959, and 1961) and
is based on the absorption factor 𝐵𝑖𝑗 that is fraction of emitted energy
from surface 𝑖 that is absorbed by surface j. The governing algebraic
equation for 𝐵𝑖𝑗 and 𝐸𝑖 are:
-----(1)
-----(2)
3. Cont…
• Where 𝑟 varies as 1,2, … . , 𝑛 for a given 𝑗 and then 𝑗 varies as
1,2, … . , 𝑛 giving rise to n2 equations. Since the energy emitted by
each surface is absorbed by the collection of 𝑛 surfaces, which
form the enclosure,
• ---------(3)
• Gebhart (1957, 1959) also proved a reciprocity relationship
between the absorption factors. For diffuse radiation and
reflection, this gives:
---------(4)
4. • The equations for the determination of 𝐵𝑖𝑗 are linear. The
absorption factors B1j, B2j….Bnj for a given surface j may be
determined by the corresponding n equations obtained from Eq.
(1).
• This may be repeated for other surfaces, employing Eqs. (3)
and (4) to simplify the computation. If Fri, þi is denoted by ari
and Bij/੬j A j by Si, Eq. (1) may be put in matrix form as:
• -- ------------(5)
• Where F is the angle factor matrix, I is the unit diagonal matrix,
and A is the matrix for area Ai.
5. Cont…..
Thus,
------(6)
• This equation gives a convenient formulation for numerical
computation. Various available methods or computer programs
for matrix inversion may be used to determine Bij.
• For a small number of equations, the direct methods for linear
equations may be employed, resorting to iterative methods when
a very large number of surfaces is involved.
• It must be noted that the absorption factors depends only on the
geometry, through the view factors and on the properties, ੬ and
þ, of the diffuse and gray surfaces comprising the enclosure.
6. Cont….
• They do not depend on the surface temperatures if the properties are
independent of temperature. The radiosity values, on the other hand,
do depend on the surface temperatures.
• Therefore, once the Bij values are obtained, energy balance equations
can be written for surfaces in thermal equilibrium and for various other
thermal conditions.
• This makes the absorption factor particularly attractive for the
simulation and design of thermal systems where the thermal conditions
are frequently varied over wide range to provide inputs needed to
obtain an acceptable or optimal design.
• The absorption factors need to be determined only once for a given
geometry and the given thermal conditions are considered, using the
calculated Bij values, to obtain the resulting transport rates.
• However, the system of equations to be solved for the absorption
factors is larger than that for the radiosity method, since n2 unknowns
are involved as compared to the n radiosity values. As a result, the
radiosity method is much more widely used to calculate radiative
transport.
