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Technical Note (National Research Council of Canada. Division of Building Research), 1962-05-01
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Mean Configuration Factor: Infinite Strips McGuire, J. H.
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DIVISION OF BUILDING RESEARCH
NATIONAL RESEARCH COUNCIL OF CANADA
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NOT FOR PUBLICATION
PREPARED BY J. H. McGuire
PREPARED FOR Record Purposes
CHECKED BY GWS
FOR INTERNAL USE
APPROyED By NBH
Rlll.. May 1962
SUBJECT MEAN CONFIGURATION FACTOR: INFINITE STRIPS
An important factor in the transfer of heat by radiation from one surface to another is the geometrical ｲ･ｬ｡ｴｩｯｮｳｨｾｰ of the radiating and receiving surfaces. Its effect is discussed in tenns of the "configuration factortt which may be defined as the ratio of the radiant intensity, at a small receiving element, to the radiant intensity near the radiator. The range of values which a configuration factor can assume is thus zero to unity.
When a receiver, with finite dimensions, is being considered, the configuration factor may vary over the surface and a value of the mean configuration factor over the surface may be required. In this note, the mean configuration factor over an infinite strip receiver is evaluated,' the radiator being a second infinite strip and the axes of the two strips being parallel.
In Fig. 1, where AB and OC represent strips which are infinite in the dimension perpendicular to the plane of the drawing, the configuration factor of AB at a point D
is (1):
l(J . == ｾＨ｣ｯｳｯＨ + cos;/3)
(X2 - x) (x - Xl)
= + •
2
-The mean configuration factor ｾ over OC will be given by X 3 X3 - 1
f
1I
(X2 - x)dx 'P =X3
'Pdx = 2X 3j
(X _ x) 2 .. Y1 ..
o 0 2 " 2Changing the variables to a
=
(X2 - x) and b=
(x - Xl)(X2 - X 3) (X3 -Xl) \p - -1
f
a. da 1r
b. db-
ｾ
ja
2
+ Y 2 + 2X3J j
ｾ｢Ｒ
+ Y 2 X2 2 -Xl 1 = 2i 3[j
x/ ..
Y2 2 ..j
(X 3 - Xl) 2 .. YI 2 -Jx/
.. y
l 2-JX2-
X 3)2 .. Y2 2 ] 1 = 20C (OB + AC - OA - BC) •This last expression has been referred to as the "crossed string rule." It is a very convenient geometric
method of evaluating the mean configuration factor (Fig. 2) in this particular case. It is not likely that any such simple construction will" apply for other geometrical relationships of a radiator and a receiver for which the expression for the mean configuration factor is often quite complex. Reference
1. McGuire, J. H. Heat transfer by radiation. Fire Research Special Report No.2, HMSO 1953.
./ , IY I I I I I I I -- I 0' I I I FIGURE
