The paper studies boundary‐value
problems for dynamic-diffusion boundary
layers occurring near a vertical wall at
high Schmidt numbers and for dynamic
boundary layers whose inner edge is
adjacent to the dynamic-diffusion
layers. Exact solutions for boundary
layers at small and large times are
derived. The well-posedness of the
boundary-value problem for a steady
dynamic-diffusion layer is studied.
V. K. Andreev and V. B. Bekezhanova
Institute of Computational Modeling, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036
Pages: 208-216
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.
