I • ENGINEERING CALCULATIONS OF RADIANT HEAT EXCHANGE 



at the same temperature), that 



^11 + Fll + ^13 + 



= 1 



(2-3) 



and that, of course, Fn = when S\ can "see" no part of itself. 



Values of F have been calculated for various surface arrangements 

 on the assumption that emissivity ee is constant and independent of d 

 (exact for black surfaces, quite good for most nonmetallic, tarnished, or 

 rough metal surfaces) . These values of F for a surface element dS and a 

 rectangle in a parallel plane appear in Fig. I,2a; for opposed parallel rec- 

 tangles and disks of equal size as lines 1 to 4 of Fig. 1, 2b; for adjacent 

 rectangles in perpendicular planes in Fig. 1, 2c; and for concentric cylin- 

 ders in Fig. 1, 2d [8]. An important class of surfaces exists for which the 



L), L2 = sides of rectangle 



K = distance from dS to rectangle 

 F = fraction of direct radiation from dS intercepted 

 I by rectangle 1 



2.0 3.0 4.0 



Dimension ratio K/Li 



6.0 



Fig. 



1, 2a. View factor F for direct radiation between an element dS 

 and a parallel rectangle with corner opposite dS. 



view factor F is capable of easy evaluation without a multiple integration 

 of Eq. 2-1. These are surfaces, infinite in extent in one direction, which 

 are generated by a straight line moving always parallel to itself. The 

 surface is then represented by a curve on a plane normal to the gener- 

 ating line. If a surface S\ is represented by the heavy-line curve AB (Fig. 

 I,2e) and a surface S2 by the heavy-line curve CD, it may readily be 

 shown {5, Chap. 4] that, per unit dimension normal to the drawing, 

 SiFi2{=S2F2i) is equal to the sum of the lengths of dotted lines in the 

 figure representing crossed strings stretched from the ends of Si to the 

 ends of *S2, less the sum of the lengths of uncrossed strings stretched be- 

 tween the ends of Si and the ends of *S2, all divided by 2; or, in terms of 

 the sketch, by (AD -f- BEFGHC - AJGHC - BEKLD)/2. Values of F 

 for other arrangements are treated in the literature [9,10,11,12,13,14]- 

 The rate of radiation from a black surface *Si to a black surface S-2 



{ 508 ) 



