F,3 • FLAT PLATE SOLUTION 



CHAPTER 1. SURVEY OF THEORETICAL RESULTS 



APPLICABLE TO AERODYNAMIC HEAT TRANSFER. 



STATUS OF EXPERIMENTAL KNOWLEDGE 



LAMINAR FLOW 



F,3. Flat Plate Solution. The investigation of the thin laminar 

 boundary layer (cf. IV,B) in steady state on a smooth flat plate is of 

 fundamental importance in aerodynamic-heating problems, because of its 

 practical possibilities and relative simplicity of solution. Typical velocity 

 and temperature curves across a thin compressible laminar boundary 

 layer with heat transfer are shown in Fig. F,2. The heat transfer to or 

 from such a layer in the steady state is obtained upon solution of the 

 continuity, momentum, and energy equations, viz. 



p«I? + P"I^ = ^(m|^)-$ (3-2a) 



dx dy dy\ dyj dx 



dp 

 dy 



^ = (3-2b) 



dh . dh /duV . a A dT\ . dp .„ „. 



'-e-x^''dy = '[-3y) ^ey['^)'-^rx ^'''^ 



respectively. 



In these equations, u and v are the x and y components of the velocity 

 at any point, the x axis being taken along the plate in the direction of 

 the free stream and the y axis perpendicular to the plate. The symbols 

 p, n, k, Cp, T, h, and p represent the density, absolute viscosity, thermal 

 conductivity, specific heat at constant pressure, absolute temperature, 

 enthalpy per unit mass, and pressure, respectively. Since Cp = dh/dT, 

 Eq. 3-3 can be written in terms of the Prandtl number Pr = CpiJi/k as 

 follows : 



dh , dh fduV , d f fi dh\ , dp .^ .. 



in which the Prandtl number is variable and a function of temperature. 

 The equations include the variation of free stream velocity and surface 

 temperature in the direction of flow. 



While the above equations have been studied by many investigators 

 after Prandtl first announced the concept of the boundary layer in 1904, 

 a complete solution of the equations is not readily available. However, 

 under certain restricted conditions, such as constant free stream velocity 



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