Microconvection in vertical channel at given heat flux

Abstract

A problem on stability of the viscous heat-conducting liquid flow in the vertical channel at given heat flux on the permeable solid walls is studied. The two-dimensional flow is described by an exact invariant solution of the microconvection equations. The investigation of the exact solution allows one to find out the extent of influence of the thermal load, gravity and the system geometry on the flow structure. Stability of the solution is investigated in the framework of the linear theory. The spectrum of the spatial characteristic perturbations is analyzed in the space of problem parameters. Typical forms of the hydrodynamic and thermal disturbances are presented and dependence of characteristics of the arising structures on the thermal load and gravity is established. Convective cells, hydrothermal rolls and polygonal structures can appear in the channel. By weak gravity the hydrothermal rolls are not formed. Changing heat flux and disturbance wave length lead to deformation of the cells and complication of the spatial form of the structures.