G,4 • TRANSPIRATION-COOLED BOUNDARY LAYER 



wall and property changes in the fluid due to large temperature differ- 

 ences between the wall and the free stream [18] will be treated in the 

 present article. In order to simplify the analysis, the following assump- 

 tions are made: (1) The Mach number M is small, (2) the Euler num- 

 ber m is constant, (3) the wall temperature T^ is constant, and (4) the 

 fluid property variation is expressible as some power of the absolute 

 temperature. 



M ~ T", k'^ T% Cp ^T-, p ~ T-i (4-22) 



On the basis of assumption 1, the last two terms in Eq. 4-16 can be neg- 

 lected and the quantities pw and T^ can be treated as constants. 



It was mentioned in the previous article that, for a wedge-type flow, 

 the transformation methods of Pohlhausen [19] and of Falkner and Skan 

 [20] can be applied. With the following changes in variables: 



/ = 



V/iwPwWea; 



(4-23) 



the momentum equation (Eq. 4-14) and the energy equation (Eq. 4-16) 

 can be transformed into two ordinary differential equations with / and 6 

 as functions of rj only. With the boundary conditions given in Eq. 4-17 

 the above two equations can be solved numerically for any prescribed 

 Euler number m, Prandtl number Pr, temperature ratio (stream temper- 

 ature divided by wall temperature), and coolant flow parameter /w. From 

 the boundary condition at the wall, the following expression gives for a 

 dimensionless measure of the coolant flow in terms of the coolant velocity : 



where /w is considered to be a constant which yields a constant wall tem- 

 perature if the conduction along the wall and the radiation are neglected. 

 The expressions for the local skin friction coefficient at the wall and the 

 local heat transfer coefficient (Nusselt number) to the wall are obtained, 

 respectively, as follows : 



c, VR^. = 2 (0)_ (4-25) 



and 



^^ -^dd\ (4.26) 



■y/Rex \d7] 

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