A fluid containing a solute, \(a\), in dilute solution flows over a flat plate. The solute adsorbs on the plate at a rate characterized by:

\[-r_{a}=\frac{k^{\prime \prime} c_{a}}{1+K c_{a}}\]

Repeat the boundary layer analysis of Section 12.8.2 to calculate:

a. The concentration profile of solute.

b. The mass transfer coefficient, \(k_{c}\).

c. The concentration boundary layer thickness.

Transcribed Image Text:

12.8.2 EFFECT OF CHEMICAL REACTION [20,21] We have seen how high mass transfer rates can affect friction factors as well as mass transfer coef- ficients. Often mass transfer is accompanied by a chemical reaction and that reaction can affect the mass transfer coefficient depending on whether the reaction acts a source of component a or as a sink. In this section we will consider the limiting case of an incompressible fluid flowing over a sparingly soluble substrate with Sc - 1. A first-order or pseudo-first-order chemical reaction occurs in the liquid and the reaction neither liberates nor absorbs heat from the surroundings. We must solve the continuity, momentum, and species continuity equations. The species continu- ity equation now includes a generation term. Continuity of species a = Dab Vx +Vy Cak"Ca (12.266) The boundary conditions for this problem are virtually identical to the conditions we used for the heat transfer situation in Section 12.7. The only difference is at the plate's surface where due to the chemical reaction, aca/y 0. y= 8,8c V = Voo C = 0 = = =0 (12.267) y= 0 vx V = 0 Ca = Cas = 0 (12.268)