Mass transfer rate of a first-order chemical reaction on a wall at high Schmidt numbers

In this study, we propose a simple formula to calculate the steady-state surface averaged Sherwood number at high Schmidt numbers when a first-order chemical reaction occurs on a wall. The formula uses the surface averaged Sherwood number corresponding to the mass transfer rate with an infinitely fast kinetic and the Damkhöler number. The validity of the prediction is analyzed. It has been found that it predicts the surface averaged Sherwood number of the analytical solution within 5% for wide ranges of Reynolds and Damkhöler numbers. The mathematical form of the prediction is suitable to compute the initial transient of the time evolution of the surface averaged Sherwood number in unsteady state conditions. The validity of this time evolution is determined by comparing it with numerical simulations.