1,5 • ENCLOSURE OF GRAY SOURCE-SINK SURFACES 



{S\ -\- Sr). If Eq. 4-20 is used as an approximation for a system which 

 does not have a speckled enclosure, however, use of the true value of Fri 

 is preferable. 



Eq. 4-18 and 4-20 are well-known solutions, available and in use for 

 many years [5, Chap. 3; 37] before the determinant method of derivation 

 was available; and their derivation from first principles was perhaps as 

 simple as the one here presented, but only because of restriction to a 

 two-zone system. With the new method available, summarized in Eq. 4-3, 

 the decision as to the number of zones of heat-sink or refractory area into 

 which the enclosure should be divided can be made to depend, as it should, 

 on the importance of the particular problem and the time available for 

 handling it, rather than on whether the engineer can see his way through 

 a multizone solution. 



Allowance for space variation in gas temperature. Many problems of 

 heat exchange between combustion gases and their enclosing walls may 

 be satisfactorily approximated by using mean values of gas temperature 

 and composition. Where an accurate solution to the problem is of suf- 

 ficient importance, however, allowance can be made for gradients in tem- 

 perature and gas composition provided that knowledge is available of the 

 flow pattern and progress of combustion; but the method is time-con- 

 suming [38]. For orientation as to the need for allowing for radiation due 

 to gas temperature gradients, a simple solution is available [39,40,4^,4^) 

 43] for the following special case: When a unidirectional temperature 

 gradient exists in the interior of a strongly absorbing gas far from its 

 bounding walls, the radiant flux density q/S is given by 



g _ 4 M^ cZr^ ^ _ 16 m! ^j.3 ^ (4.21) 



a 



S 3 k dx 3 k dx 



where k is the absorption coefficient of the gas (see Art. 5), and m is the 

 refractive index of the medium (1 for gases). To minimize the effect of a 

 wall at distance L from the plane of flux, the value of kL must be greater 

 than about 3; and to satisfy the condition of strong absorption 



dlnr 



kdx 



«1 



Radiation exchange between a plane wall and an overlying gas, the 

 isothermal surfaces in which are parallel to the wall, has also been treated 

 [5, Chap. 4]. 



1,5. Enclosure of Gray Source-Sink Surfaces Containing a Real 

 (Nongray) Gas. In the derivation of interchange factors for gray gas 

 systems the single value of transmittance ri2 appUed to all radiation 

 leaving »Si for S2, whether originally emitted by Si or reflected from it 

 after any number of passages through the gas. Only for gray gas is this 



( 531 ) 



