| Abstract: |
| When a sphere is moving slowly in a gas, it experiences a resistive force (drag). Considering the case where the moving sphere is uniformly heated (or cooled), we investigate the effect of the temperature difference on the drag on the basis of the Boltzmann equation, which provides a mesoscopic description of the motion of the surrounding medium. More precisely, we consider the time-independent behavior of a slow flow of a rarefied gas past a heated (or cooled) sphere in the following situations: (i) the normalized temperature difference is of the same order as the (small) Mach number, (ii) the Knudsen number (the mean free path) is finite, and (iii) gas molecules are diffusely reflected on the sphere. A matched asymptotic analysis for small Mach numbers is employed to derive a formula for the drag up to the second order of the Mach number, whose second-order term expresses the coupling effect of the linearized uniform flow and heat transfer problems. As the result, we show that the drag is increased by the heating of the sphere. The effect is attributed to the ballistic motion of molecules, which enhances the effect of temperature dependency of the viscosity and the pressure effect. |
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