A SERIES SOLUTION FOR MASS-TRANSFER IN LAMINAR-FLOW WITH SURFACE-REACTION

We present an explicit analytical solution for the Leveque's problem with the boundary condition of the third kind. This solution is applicable to problems of mass (heat) transfer with surface reaction (surface resistance) in the entry region of fully developed flow fields of power law fluids, and to the developing boundary layer flows that admit Falkner-Skan solutions, provided that the Schmidt (Prandtl) number is large. The series form of the solution developed by inversion of the Laplace transform has excellent convergence properties within the concentration (temperature) boundary layer in contrast to the integral forms that are usually reported for problems of this type. An efficient computational algorithm for evaluation of the surface concentration is presented, as well as accurate approximate formulas in the form of simple algebraic expressions for the local and average mass (heat) transfer coefficients and the surface concentration (temperature).