Monotonicity principle in the rayleigh problem for an isothermally incompressible fluid.

Tyaglov, M. Yu.

The convection of an isothermally incompressible fluid in a horizontal layer with free undeformable boundaries kept at a constant temperature is considered. Under the fairly common assumptions of the temperature dependence of the specific volume, it is shown that the monotonicity principle holds and that the spectrum of critical Rayleigh numbers is countable and prime. Models with linear and quadratic temperature dependences of the specific volume are given as examples. The results on the spectrum of the critical Rayleigh numbers are also valid for some other boundary conditions.

RAYLEIGH number; HEAT transfer; VISCOUS flow; FLUID dynamics; VISCOSITY; HYDRODYNAMICS

Journal of Applied Mechanics & Technical Physics, 2007, Vol 48, Issue 5, p649

0021-8944

Academic Journal

10.1007/s10808-007-0083-y