F,4 • HEAT TRANSFER 



Defining 



and 



St = 



1 gJO) 

 S{l)2VRe 



h, = K + 2R{1) 



(4-5) 



(4-6) 

 (4-7) 



Eq. 4-4 becomes 



5w = —StpeUeiK — /iw) 



The symbol Re is the Reynolds number. 



The dimensionless heat transfer coefficient St is called the Stanton 

 number. Since heat transfer is proportional to skin friction by Eq. 4-2, 

 it is sometimes desirable to write the heat transfer coefficient St in terms 

 of the local skin friction coefficient defined by c/ = 2Tw/peW^, thus 



St = 



'S(l)2 



(4-8) 



The factor S{1) is called the Reynolds analogy factor and is denoted by 

 the symbol s. Hence [3] 



s = Sil) = Prexp - / 

 Jo L Jg 



(1 - Pr) ^ 



'ff*(o) g* J 



du^ 



(4-9) 



Now the quantity [K + 2R(l)ul/2] in Eq. 4-4 is equal to the total 

 enthalpy of the free stream, except for the factor 2/2(1). Furthermore, 

 when the plate is insulated, i.e. when q^ = 0, it follows from Eq. 4-7 that 

 h„ = he + 2R{l)ul/2. For these reasons, the quantity [K + 2R(l)ul/2] 

 will be called the boundary layer enthalpy (or simply) recovery enthalpy, 

 hj, and the factor 2/2(1) the enthalpy recovery factor r. Therefore [3] 



fi r /-ff* 



r = 2/2(1) =2 Prexp - (1 - Pr) 



Jo L Jg*(0) 



dg 



exp 



r* (1 - Pr) ^^* 



Jg 



'g*(0) 



g* J 



Eq. 4-9 and 4-10 reduce to Crocco's results, viz. 



s = Pr 



L£7*(0). 



and 



r = 2Pr 



/ -^^ / 



;o LS'*(0)J Jo 



du. 



g* 

 lg*iO) 



du^ \ du^ (4-10) 



(4-11) 



duji, du^ 



(4-12) 



when Pr is constant. 



It will be found that in general both s and r are functions of speed and 

 heat transfer. However, for moderate speeds and heat transfer rates, 



(349 ) 



