For steady flow conditions, the complete set of fluid equations, expressed in the two dimensional coordinate system, (x,y), consists of the continuity, Navier-Stokes and energy equations where Boussinesq approximation is considered for the temperature density dependence.
As it can be seen, the behavior of these simulation results seems to be quite reasonable, thus confirming, qualitatively, the validity of the proposed numerical method, in particular, the concentration of the hot air in the upper part of the nacelle which is due to the decrease in its density, thus confirming the suitability of the adopted Boussinesq approximation.
Temperature is increasing from the cold plate temperature on the bottom of the nacelle to reach a maximal value in the upper part of the nacelle ( 80% of the nacelle height), confirming again the adopted Boussinesq approximation, then it decreases to the cold plate temperature at the top wall of the nacelle.
Making use of the Boussinesq approximation
, the equations that we consider in the present paper are as follows:
According to the Boussinesq approximation
these equations get the following expressions (M.
The Boussinesq approximation for the buoyancy force is adopted in momentum equation.
For problem having small or medium density gradient, the governing equations can be simplified by invoking the Boussinesq approximation (Chen and Jaw, 1998).
In the Eulerian frame, two second-order models have been proposed: an algebraic model, in the spirit of single phase flow, and a Reynolds stress differential model, in which only the equations for the three particle fluctuating velocity correlations [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (i = 1, 2, 3) had to be solved, while the calculation of the shear stresses relied on a Boussinesq approximation
which has been justified theoretically and numerically.
is used in oceanography and then [rho] can be take as a constant.
Keywords and Phrases: Free convective flow, radiation, buoyancy, boussinesq approximation
, corrugated channel, and incompressible viscous fluid.
The buoyancy effect (natural convection) is supported through a source term incorporated in the momentum equations in agreement with the Boussinesq approximation.
For this laminar flow the terms of the buoyancy are modeled by the well-known Boussinesq approximation.