Theory of Turbulent Flow Between Parallel Plates 



Symbols (some with dimensions, some dimensionless) — in order of first use 



, ::. p ■=■ density ' ' ' - v > 



p = pressure 



/Li,\ = shear viscosity, dilatational viscosity 



T = temperature 



- s = entropy - 



:'::■'- : k = thermal conductivity 



7 = ratio of specific heats (dimensionless) 



C = Laplacian velocity of sound 



a = thermal coefficient of volume expansion 



C = specific heat at constant pressure 



h = half separation of the parallel- plate channel 



V - kinematic viscosity 



n = any harmonic frequency in the field (e.g., rad/sec) 



f = frequency (Hz) > ' 



p, = spatial continuum parameter — ratio of mean free path 

 to dimensions (= v/ch —dimensionless) 



oj = dimensionless frequency (= h^n/v) 



r = temporal continuum parameter — ratio of molecular re- 

 laxation time to the period of a fluctuation (= vQ/c^ = 

 /i'^co — dimensionless) 



R. = dimensionless velocity components (= hVj /v^^) 



T = dimensionless time (= v^^t/h^) 



P = dimensionless pressure (= h^p/^^^v^^) 



E = dimensionless thermal parameter (= a cVCp) 



J = dimensionless temperature (= eooh^Cpo^T/i^^^ ) 



a = Prandtl number (= i^Cp/k) 



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