Natural convection of a dusty gas

Abstract

The natural convection of a gas-particle suspension inside a two-dimensional square region is investigated within the framework of a two-velocity two-temperature model of the medium with allowance for phase relaxation and particle deposition .The natural convection of clean gases in closed spaces has been studied fairly thoroughly (see, for example, [1][2][3]) . However, in many actual situations the gas contains foreign particles, which gives grounds for investigating dusty gas convection . If the particles are so small that their temperature and velocity relaxation proceed much more rapidly than the process develops, then the system can be described by a one-velocity one-temperature model (homogeneous gas-particle suspension) . The convection behavior of such a medium was investigated in [4] . In this model limitations are imposed on the dimensions of the particles . Thus, for dust suspended in air under ordinary conditions within a square cell having a side length L= 10 -2 m the condition d< 10 -4 m (d is the particle diameter) must be satisfied [4], which corresponds to particles not more than a few microns in diameter .1 . We will consider a two-phase medium consisting of a viscous heat-conducting compressible gas (phase 1) and monodisperse spherical particles (phase 2), within a two-dimensional square domain . The volume fraction of the suspension is small, which means that particle collisions can be neglected. The temperatures on the lateral boundaries of the domain are kept constant but different . Under the influence of the force of gravity the system is set in motion : natural convection of the gas develops, entraining the particles, and at the same time particle sedimentation takes place, affecting the dynamics of the carrier phase .Within the framework of the basic assumptions of the mechanics of heterogeneous media [5] the gas-particle suspension can be treated as two interacting and interpenetrating continua . In dimensionless variables its motion is described by the equations