Simulation of the transient heat transfer between two coaxial cylinders

Abstract

The transient heat flux between two coaxial cylinders is studied on the basis of the numerical solution of the nonlinear unsteady S-model kinetic equation. A large range of the gas rarefaction and two temperature ratios between the cylinders' walls are considered. The time evolutions of the averaged over the distance between the cylinders heat flux, pressure, and bulk velocity are analyzed. The steady state time, as a time of steady state flow establishment, is introduced. This time depends on the characteristic time of the system and on the gas rarefaction. It is found that this steady state time for the averaged heat flux varies approximately 18 times from the near free molecular to the hydrodynamic flow regime. In the slip flow regime, the analytical expression for the steady state temperature distribution between two cylinders is obtained. It is found that the transient heat flux evolution derived from the energy balance allows to estimate the time of steady state flow establishment in the slip flow regime.