On the /non linear/ foundations of Boussinesq approximation applicable to a thin layer of fluid
Abstract
A twoparameter perturbation scheme for the thermohydrodynamic description of a horizontal layer of a single component arbitrary fluid heated from below (RayleighBenard problem) is presented. The first approximation leads to the BoussinesqOberbeck equations. This agrees with previous results obtained by Mihaljan (1962). Contrary to Mihaljan's theory however, the series expansion given here is free from inherent difficulties in obtaining higher order approximations viz. nonBoussinesq effects. This is done by choosing a suitable adiabatic hydrostatic reference field and two parameters of the same order of magnitude. In a well defined limit the theory presented here recovers earlier results obtained by Malkus (as yet unpublished) for dilute ideal gas layers.
 Publication:

Journal de Physique
 Pub Date:
 August 1975
 Bibcode:
 1975JPhys..36..591P
 Keywords:

 Boussinesq Approximation;
 Fluid Films;
 Heating;
 Perturbation Theory;
 Thermodynamic Properties;
 Adiabatic Conditions;
 Benard Cells;
 Convective Heat Transfer;
 Flow Stability;
 Hydrodynamic Equations;
 Hydrostatics;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer