Stability of the equilibrium of a flat layer in a microconvection model

The stability of the equilibrium state of a flat layer bounded by rigid walls is studied using a microconvection model. The behavior of the complex decrement for long-wave perturbations has an asymptotic character. Calculations of the full spectral problem were performed for melted silicon. Unlike in the classical Oberbeck–Boussinesq model, the perturbations in the microconvection model are not monotonic. It is shown that for small Boussinesq parameters, the spectrum of this problem approximates the spectra of the corresponding problems for a heat-conducting viscous fluid or thermal gravitational convection when the Rayleigh number is finite.