Abstract: The exact expressions of concentration and local or average Sherwood number,Sh or Sh for non-Newtonian fluids which obey the famous power law:τ={K|1/2(1/2)~(1/2)|~(n=1)}in which the flow index n takes any positive rational value,have been obtained by solving the differen-tial equation of diffusion together with the velocity distribution in the falling film flow.The use of Fourth-order Runge-Kutta method and Wegstien’s iteration method by means of thecomputer yields results which are a series of values of dimensionless concentration O,local and averageSherwood number for n equal to 1/4,1/3,1/2,1/1.4,1/1.2,1,1.25,2.5,and ∞.When the flow indexn=1,i.e.for Newtonian fluids,the result agrees well with the data from the literature.