Numerical investigation of the heat and mass transfer analogy in rarefied gas flows

Transport of heat and mass to surfaces in fluid flows lies at the heart of a vast array of engineering problems. The Colburn analogy that relates the transport of heat and mass to the surface is often applied to approximate mass transport using correlations developed for heat transport. Here we use a numerical method that solves the Shakhov model Boltzmann equation of fluid mechanics coupled to a simple monolayer adsorption model to show that this analogy does not apply for selected rarefied flows. We consider steady flow of gas through a micro-channel and the flow in a lid-driven cavity. We define a breakdown parameter indicating the departure of the relative rates of heat and mass transport from that predicted using the analogy, and give simple analytic expressions for this parameter in the free-molecular and continuum limits. Results show that the analogy breaks down even for Knudsen numbers corresponding to slip and transition region flows, and that the magnitude of this departure is such that mass transfer is many times slower than predicted using the analogy. These results have important application to the design of micro-scale devices involving mass transport to surfaces.