G • COOLING BY PROTECTIVE FLUID FILMS 



is inversely proportional to the thickness of the thermal boundary layer 

 adjacent to the wall. Since the thickness of the thermal boundary layer is 

 directly proportional to the Reynolds number of length in the direction 

 of flow, the first phenomenon is clear. As mentioned in the previous article 

 the increase of Prandtl number does not increase appreciably the thick- 

 ness of the thermal boundary layer. On the other hand, the increase in 

 fluid viscosity due to the increases in the Prandtl number may give a 

 sufficiently low Reynolds number of boundary layer thickness to increase 

 the final heat transfer to the wall. 



T w — To 



Fig. G,4b. Temperature ratio vs. mass flow ratio. (From [7,9].) 



The film heat transfer coefficient h-, between the hot gas and the wall 

 can be determined by Eq. 4-8. The ratio of film heat transfer coefficient 

 hi with transpiration cooling to the film heat transfer coefficient h with 

 impermeable plate under the same conditions of flow over the plate as a 

 function of Vy,/U ratio is given in Fig. G,4c. It is interesting to see that 

 for an injected coolant velocity equal to 1 per cent of the hot gas velocity, 

 the heat transfer to the wall can be reduced to about one-fifth of the value 

 without transpiration cooling. 



Compressible boundary layer on a porous flat plate. In order to under- 

 stand the phenomena of heat transfer in transpiration cooling in which 

 large temperature differences occur across the boundary layer [9], the 

 physical properties of the fluid must be taken into consideration. The 



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