Radiation Exchange Between
Surfaces
EGR 4345
Heat Transfer
View Factor Fij
(Configuration or Shape Factor)
View Factor Fij

Defined as the fraction of the radiation leaving
surface i that is intercepted by surface j
Energyi  j
Fij 
Total Energy Leaving i
Total Rate Equation qij

Rate at which radiation leaves dAi and is
intercepted by dAj
Assumes surface i emits and reflects diffusely
Assumes radiosity Ji is uniform over surface Ai
View Factor Fij

Defined as the fraction of the radiation leaving
surface i that is intercepted by surface j
Assumes surfaces emit and reflect diffusely
Assumes uniform radiosity
Use View Factor to Calculate Net
Radiative Exchange, qij
 qij
–
–
=
4
Ai Fij (Ti
–
4
Tj )
Net rate at which radiation leaves surface i as a
result of interaction with j
Equal to the net rate at which j gains radiation due
to its interaction with i
View Factor Relations 1

Tables and Figures
–
–
–
–
–
Table 13.1 – Two-Dimensional Geometries
Table 13.2 – Three-Dimensional Geometries
Figure 13.4 – Aligned Parallel Rectangles
Figure 13.5 – Coaxial Parallel Plates
Figure 13.6 – Perpendicular Rectangles with a
Common Edge
View Factor Relations 2
 Reciprocity
AiFij = AjFji
Determine one view factor from
knowledge of the other
View Factor Relations 3

Summation rule for enclosures
N
 Fij  1
j 1
–
–
Fii – fraction of radiation that leaves surface i and is directly
intercepted by i
For a plane or convex surface, Fii = 0
View Factor Relations 4

By inspection
View Factor Relations 5

Symmetry - Isosceles Triangle
1
3
2
F12 = F13
View Factor Relations 6

Multiple component surfaces
reciprocity