Dimensional scaling factors boundary conditions

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

One final remark should be made about the nondimensionalization that led to (7-2) and (7 3), and thence for Re creeping-flow equations, (7-6). This concerns the scale factor chosen to nondimensionalize the pressure. Assuming for simplicity that the geometry and boundary conditions lead to a single characteristic length, velocity, and time scale, the nondimensionalization of u, t, and V in (7-1) is unambiguous. However, even for this simplest case there is a second possible choice for nondimensionalization of p, namely, pU2, which is another combination of dimensional parameters with dimensions of... 

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