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ARTICLE

Numerical Study of Natural Convection in an Inclined Triangular Cavity for Different Thermal Boundary Conditions: Application of the Lattice Boltzmann Method

Ahmed Mahmoudi^1,2, Imen Mejri¹, Mohamed Ammar Abbassi¹, Ahmed Omri¹

1 UR:Unité de Recherche Matériaux, Energie et Energies Renouvelables (MEER), Faculté des Sciences de Gafsa, B.P.19, Zarroug, Gafsa, 2112, Tunisie.
2 Corresponding Author. Email: ahmed.mahmoudi@yahoo.fr; Phone: 00216 97953081

Fluid Dynamics & Materials Processing 2013, 9(4), 353-388. https://doi.org/10.3970/fdmp.2013.009.353

Abstract

A double-population Lattice Boltzmann Method (LBM) is applied to solve the steady-state laminar natural convective heat-transfer problem in a triangular cavity filled with air (Pr = 0.71). Two different boundary conditions are implemented for the vertical and inclined boundaries: Case I) adiabatic vertical wall and inclined isothermal wall, Case II) isothermal vertical wall and adiabatic inclined wall. The bottom wall is assumed to be at a constant temperature (isothermal) for both cases. The buoyancy effect is modeled in the framework of the well-known Boussinesq approximation. The velocity and temperature fields are determined by a D2Q9 LBM and a D2Q4 LBM, respectively. Comparison with previously published work shows excellent agreement. Numerical results are obtained for a wide range of parameters: the Rayleigh number spanning the range(10³-10⁶) and the inclination angle varying in the intervals (0° to 120°) and (0° to 360°) for cases I and II, respectively. Flow and thermal fields are given in terms of streamlines and isotherms distributions. It is observed that inclination angle can be used as a relevant parameter to control heat transfer in right-angled triangular enclosures.

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