B,7 • INTRODUCTION 



energy diffusion dE^/dXj or dE/dXj if we introduce xo according to Eq. 

 5-3c and x according to Eq. 5-3d. In this way, Eq. 6-3a and 6-4a become 

 respectively 



o (-S.) + y,.^ (^) + B (^^^,y,) _ g ^ „^.^ 



- 4 ("'"'■' 



fc 5^0 



= ~ TT ( p''i^j-E'*' + UipUiUj + CppT'uj — 





^^p^-O^u 



+ X0 (6-3b) 



5 / 



= --^. [pujE' + p'wy^ + p'ujE' + C7,p'^' - ^ ^ , 



^P OJij/ 



dXj 



1 1^1 



i'a^^^^ + ^^^^ 



+ X (6-4b) 



where Pr = nCp/k is the Prandtl number. The specific heat Cp is taken as 

 constant. Eq. 6-3b and 6-4b become much simpler if Pr = 1, and if xo 

 and X are negligible. 



Since in the incompressible case ju = const, Pr = 1 and xo = x = Oj 

 we can reduce Eq. 6-3b and 6-4b respectively to 





Dt 



dXi 



Dt ^'^^ = " a^ 



^o\ 



(6-3c) 



("^'-^S) («-^«) 



Eq, 6-4c is the well-known equation of turbulent heat transfer in an 

 incompressible flow. Here pUjE' is the flux of energy transported by tur- 

 bulent diffusion. 



CHAPTER 3. TURBULENT BOUNDARY LATER 

 OF A COMPRESSIBLE FLUID 



B,7. Introduction. When a fluid flows past the solid boundary of a 

 body, a shear flow results. The condition of no-slip requires that the fluid 

 immediately in contact with the wall be brought to rest. Next to it the 

 fluid is retarded by the internal shear stresses. The retardation decreases 

 with increasing distance from the wall and becomes vanishingly small in 



(87) 



