An analytical solution for natural convective gas microflow in a tall vertical enclosure

An analytical solution for buoyancy-induced gas microflow in a tall differentially heated enclosure with isothermal vertical walls is presented. The Navier—Stokes system has been solved. The Boussinesq approximation has been employed. Wall—fluid interactions are modelled by first-order velocity slip and temperature jump conditions. The analysis presented covers continuum to slip-flow regime. A functional form for the Nusselt number has been derived analytically. The results indicate that as the Knudsen number increases, the Nusselt number decreases.