Transport to a Chemically Active Thin Liquid Film Over a Spinning Disk

Abstract

An analytical solution for the process of mass transfer from a spinning disk to a chemically active thin liquid film flowing over the disk is presented. By analogy, the results are also applicable to heat transfer to the film with temperature-dependent heat generation. The process is modeled by establishing equations for the conservation of mass, momentum, and species concentration, and solving them analytically. The partial differential equation for species concentration is solved using the separation of variables technique along with the application of the Duhamel’s theorem. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and chemical reaction rate as parameters. It was found that Sherwood number increases with Reynolds number (flow rate) as well as inverse of Ekman number (rate of rotation). These fundamental results will be useful to design advanced energy transport processes for a low-gravity space environment.