G,3 • TRANSPIRATION-COOLING PROCESS 



wall and through the boundary layers. A cold medium flowing along the 

 bottom surface of the porous wall is pressed through the pores in the wall 

 represented by cylindrical channels in Fig. G,3 and leaves the wall on 

 the upper side. Hot gas with a free stream temperature T^ flows along 

 the upper surface of the porous wall and builds up a boundary layer which 

 is usually turbulent. Within this turbulent boundary layer, a laminar 

 sublayer forms in the immediate vicinity of the surface where the tem- 

 perature drops rapidly to the value T^ (temperature of the upper wall 

 surface). The amount of heat flow q per unit of time and surface area 

 entering the wall through the upper surface is determined by the tem- 

 perature gradient on the wall. Since the layers adjacent to the wall are 



Fig. G,3. Temperature variation between coolant and hot fluid. 



at rest, heat is transferred to the surface of the wall, essentially by con- 

 duction. The heat transfer in the boundary layers is discussed in detail 

 later. 



The investigation of heat transfer inside the transpiration-cooled po- 

 rous wall was made by Weinbaum and Wheeler [6]. In this study it is 

 taken that no change of state of cooling fluid occurs and that its direction 

 of flow is opposite to that of the heat flow through the cylindrical bars of 

 porous metal. It is further assumed that a steady state of heat flow is 

 attained. The time rate of heat flow is, in the case of solid metal, given 

 by the familiar Fourier equation 



q = -kA^ (3-1) 



dz 



where A is the cross-sectional area of the porous wall, fc is the thermal 

 conductivity of the metal, and t is the temperature of the metal at any 



( 435 ) 



