3. Reconsider the problem of irreversible chemical reaction in a thin liquid film/catalyst pellet. In the class, we assumed that the mass transfer coefficient k such that the concentrations of species A and B at the top boundary (z=L) are equal to their bulk values C0 and 0 , respectively. With this assumption we evaluated an expression for the concentration of species A,CA, within the domain (z=0 to L). CA=C0,CB=0(BulkConcn.) (a) Rederive the expression for CA using convective boundary condition at the top boundary ( z=L ) for a finite mass transfer coefficient k. (b) Introduce the Damkhler number Da=kvL2/DA=(L/)2 and Biot number for mass transfer, Bim=kL/DA in the derived expression, where DA is the mass diffusivity of species A. (c) Derive the expression for the overall reaction rate per unit area. (d) Show that in the limit k, the expression for CA will approach the expression derived in the class. (e) Explain the impact of Da and Bim on the profile of CA and the overall reaction rate per unit area