Nondimensionalization convective diffusion equation

It may be noted that for dilute solutions, Sc = v/D = 10. Hence, Pe = Rex Sc is generally large. The nondimensional convective diffusion equation is... 

Referring to the nondimensional equation of convective diffusion (3.3), it is of interest to examine the conditions under which the diffusion term, on the one hand, or convection, on the other, is the controlling mode of transport. The Peclet number, dUfD, for flow around a cylinder of diameter r/ is a measure of the relative importance of (he two term.s. For Pe 1, transport by llte flow can be neglected, and the deposition rate can be determined approximately by solving the equation of diffusion in a non flowing fluid with appropriate boundary conditions (Carslaw and Jaeger, 1959 Crank, 1975). 

The region in which convective diffusion plays a dominant role is known as the convective diffusion layer. We describe the relevant governing equations and important nondimensional number in this section. 

These substitutions replace the eight dimensional parameters in the original equations by the four nondimensional parameters above. The parameter Pe is the Peclet number (37) and shows the relative importance of convection compared to diffusion. The advantage of this formulation becomes obvious when typical parameter values are substituted into the equations. 

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