Stresses produced in gasses by temperature and concentration inhomogeneities. New types of free convection

The main results of theoretical investigation of slow $(\mathbf{Re}\sim1)$ non-isothermal (temperature drop in the gas $\theta=\Delta T/T\sim1$) are reported. These flows are described by equations that differ from the classical Navier–Stokes equations for a compressible liquid in that the momentum equation contains besides the viscous-stress tensor, also a temperature-stress tensor of the same order of magnitude. The question of the influence of temperature stresses on the motion of the gas are analyzed, as are the forces acting on bodies placed in the gas. This question was first raised long ago by J. Maxwell, who used implicitly linearization in $\theta$ and reached the conclusion that the temperature stresses cause neither motion of the gas nor forces. However, when $\theta$ is not small, a new type of convection of the gas appears in the absence of external forces (e.g., of gravitation), namely, the temperature stresses cause the gas to move near uniformly heated (cooled) bodies; some examples of this convection are presented. In addition, for the case of small $\theta$, an electrostatic analogy is established, describing the force interaction between these bodies as a result of the temperature stresses. The problem of the flow around a uniformly heated sphere at $\mathbf{Re}_\infty\ll1$ (the Stokes problem) is solved: the temperature stresses exert an ever increasing influence on the resistance of the sphere with increasing sphere temperature. Analogous phenomena, produced in gas mixtures by concentration (diffusion) stresses, are indicated.