Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation

It is shown analytically and numerically on the basis of the kinetic theory that the heat-conduction equation is not suitable for describing the temperature field of a gas in the continuum limit around bodies at rest in a closed domain or in an infinite domain without flow at infinity, where the flow vanishes in this limit. The behavior of the temperature field is first discussed by asymptotic analysis of the time-independent boundary-value problem of the Boltzmann equation for small Knudsen numbers. Then, simple examples are studied numerically: as the Knudsen number of the system approaches zero, the temperature field obtained by the kinetic equation approaches that obtained by the asymptotic theory and not that of the heat-conduction equation, although the velocity of the gas vanishes.