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12
View Factor
12.1 View Factor
In addition to surface radiation properties such as emissivity, reflectivity, and
absorptivity, view factor is another important parameter for determining radiation heat transfer between two surfaces. View factor is defined as the fraction
of radiation energy (the so-called radiosity including emission and reflection)
from a given surface that can be seen (viewed) by the other surface. It is purely
a geometric parameter, depending on the relative geometric configuration
between two surfaces (depending on how the surfaces can see each other). A
view factor is also called an angle factor or shape factor. The following shows
how to define the view factor between two surfaces [1–4]. Figure 12.1 shows
radiation exchange between the two diffuse isothermal surfaces (i.e., each
surface has uniform emission and reflection from the surface). The differential radiation rate (including emission and reflection) from unit surfaces i to j
is proportional to its intensity and the unit solid angle as discussed before.
cos θ j
dq i−j = I i dA i cos θ i dw j−i = I i cos θ i
dA j dA i
(12.1)
R 2
cos θ i cos θ j
= πI i
dA i dA j
πR 2
Performing integration over surface area i and surface area j, one obtains
radiation rate from surface i to surface j as
q i−j = J i
cos θ i cos θ j dA j dA i
(12.2)
πR 2
A i A j
where πI i ≡ J i = radiosity (emission plus reflection).
If the radiosity J i is uniform, that is, diffuse reflection and isothermal
emission, then
Engery intercepted by A j
q ij
1
cos θ i cos θ j
πR 2
dA j dA i (12.3)
F ij =
=
=
Radiosity leaving A i
A i J i
A i
A i A j
239
� �
12
View Factor
12.1 View Factor
In addition to surface radiation properties such as emissivity, reflectivity, and
absorptivity, view factor is another important parameter for determining radiation heat transfer between two surfaces. View factor is defined as the fraction
of radiation energy (the so-called radiosity including emission and reflection)
from a given surface that can be seen (viewed) by the other surface. It is purely
a geometric parameter, depending on the relative geometric configuration
between two surfaces (depending on how the surfaces can see each other). A
view factor is also called an angle factor or shape factor. The following shows
how to define the view factor between two surfaces [1–4]. Figure 12.1 shows
radiation exchange between the two diffuse isothermal surfaces (i.e., each
surface has uniform emission and reflection from the surface). The differential radiation rate (including emission and reflection) from unit surfaces i to j
is proportional to its intensity and the unit solid angle as discussed before.
cos θ j
dq i−j = I i dA i cos θ i dw j−i = I i cos θ i
dA j dA i
(12.1)
R 2
cos θ i cos θ j
= πI i
dA i dA j
πR 2
Performing integration over surface area i and surface area j, one obtains
radiation rate from surface i to surface j as
q i−j = J i
cos θ i cos θ j dA j dA i
(12.2)
πR 2
A i A j
where πI i ≡ J i = radiosity (emission plus reflection).
If the radiosity J i is uniform, that is, diffuse reflection and isothermal
emission, then
Engery intercepted by A j
q ij
1
cos θ i cos θ j
πR 2
dA j dA i (12.3)
F ij =
=
=
Radiosity leaving A i
A i J i
A i
A i A j
239