**Lattice Boltzmann Method investigations of natural
convection heat transfer instabilities in a rectangular cavity heated
from below**

Mustapha Faraji^{1, ⋆}, El
Mehdi Berra^{1}

^{⋆} : farajimustapha@yahoo.fr

^{1} Hassan II
university

**Mots clés :** LBM; Natural convection; aspect ratio;
oscillation; Square cavity.

**Résumé :**

In this paper a numerical study with Lattice Boltzmann Method (LBM) of the natural convection flows into a square cavity filled by air and cooled by the top wall with a heat source attached to the bottom wall of the cavity presented as an electronic component. In order to observe the change of the heat transfer into the cavity with time, in a first step a series of numerical simulations are done by varying the aspect ratio of the cavity while A=1, 1.6, 1.7 and 2. Results show that the cavity’s aspect ratio has an impact on the heat transfer behavior and for the aspects ratio A=1 and A=1.6 the numerical results show a stable steady state on the temperature distribution into the cavity and for A=1.7 and A=2 a stable oscillatory state is found. In a second step a numerical simulation is done to study the oscillation of heat transfer into the cavity for the aspect ratio A=2. The choice of Lattice Boltzmann Method (LBM) as a simulation method which experienced great progress and has become an alternative method for solving fluid dynamics problems and has challenged traditional methods in many sectors by its simplicity of implementation.

In the present work, the Lattice Boltzmann Method is used to do a numerical study of natural convection flows in a square cavity cooled by the upper wall and heated from below by a heat source considered as an electronic component. In the first step we study the effect of the aspect ratio on heat transfer with time, four different aspect ratio values are considered A=1, A=1.6, A=1.7 and A=2. In a second step we choose the configuration A=2 that we get a stable oscillatory state with time and we try to study the oscillation by choosing four points on the oscillation curve. Therefore, it should be noted that the objective of this present work resident in the observation of the change of natural convection heat transfer into the cavity with time by changing the aspect ratio. The numerical simulations are done with a computational FORTRAN code that it’s validated with a result from a published paper.

Work In Progress