The term microconvection was originally introduced to characterize non- solenoidal flows driven by density (depending on temperature only) changes. These phenomena were analyzed for thermal buoyancy-driven convection (Pukhnachov, 1991) and for diffusive-induced flows (Perera and Sekerka, 1997). The effect on non-solenoidality is equally important for the description of non- stationary convection in microgravity conditions and in microscales. Recently this approach was extended up to convective motions of a weakly compressible liquid (Pukhnachov, 2002). On the basis of the microconvection model, there are studied a number of problems describing the convection in a vertical layer with the thermal fluxes oscillating in a phase and in an anti-phase, flows in a circular ring and in a prolate rectangular, mixed thermocapillary/gravitational convection in a semicircle with a free flat boundary.