A spherical condensed phase with a uniform surface temperature that is placed in a slow uniform flow of its vapor gas is considered. The steady behavior of the gas accompanied by evaporation and condensation on the sphere is investigated mainly numerically on the basis of the Boltzmann equation for hard-sphere molecules. The numerical method is a combination of the hybrid-difference-scheme method, capable of describing the discontinuity of the velocity distribution function in the gas, and the numerical kernel method [Phys. Fluids A 5, 716 (1993)]. The velocity distribution function of the gas molecules, the macroscopic variables such as the density, velocity, and temperature of the gas, and the force (drag) acting on the sphere are obtained precisely for the whole range of the Knudsen number (the mean free path of the uniform flow divided by the radius of the condensed phase). In particular, the behavior of the discontinuity of the velocity distribution function in the gas is described accurately.
An intelligent hybrid measurement method, which is successfully developed for linear elastic deformation fields (Nishioka et al. Exp Mech 40:170-179, 2000), is investigated for steady-state temperature field. First, a variational principle is derived to minimize the errors and noises associated with experimental temperature measurements. This variational principle assures also the satisfaction of the governing steady-state heat conduction equation. On the basis of this variational principle, an intelligent hybrid experimental-numerical method is developed for the measurement of temperature field, and for the subsequent visualization of higher-order quantities such as the heat flux distribution. Furthermore, a concept is presented for selfrestoring heat generation that automatically restores temperature field against experimental errors and noises. The present intelligent hybrid method successfully demonstrates automatic detection and automatic elimination of experimental measurement errors, and smooth visualization of heat flux distribution.
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