III. On stresses in rarefied gases arising from inequalities of temperature

Abstract

1. In this paper I have followed the method given in my paper “On the Dynamical Theory of Gases” (Phil. Trans., 1867, p. 49). I have shown that when inequalities of temperature exist in a gas, the pressure it a given point is not the same in all directions, and that the difference between the maximum and the minimum pressure at a point may be of considerable magnitude when the density of the gas is small enough, and when the inequalities of temperature are produced by small; solid bodies at a higher or lower temperature than the vessel containing the gas. 2. The nature of this stress may be thus defined: let the distance from the given point, measured in a given direction, be denoted by h , and the absolute temperature by θ ; then the space-variation of the temperature for a point moving along this line will be denoted by dθ / dh , and the space-variation of this quantity along the same line by d 2 θ / dh 2 . There is in general a particular direction of the line h , for which d 2 θ / dh 2 is a maximum, another for which it is a minimum, and a third for which it is a maximum-minimum. These three directions are at right angles to each other, and are the axes of principal stress at the given point; and the part of the stress arising from inequalities of temperature is in each of these principal axes a pressure equal to— 3 μ 2 / ρθ d 2 θ / dh 2 , where μ is the coefficient of viscosity, ρ the density, and θ the absolute temperature.