This paper focuses on the mesoscopic methodology of density-internal energy lattice Boltzmann computation of two-dimensional natural convection in a square cavity filled with porous medium. It is realized that the impact of permeable media is acquainted by including porosity with the balance molecule thickness conveyance capacity and by adding energy term to the molecule thickness dispersion capacity. In the present paper, density-internal energy distribution function lattice Boltzmann model is utilized to recreate convection in permeable medium at the Representative Elementary Volume (REV) scale. The two-dimensional nine-speed model (D2Q9) with nine discrete speeds is utilized as a part of the work. The impact of Rayleigh number, Darcy number and porosity are mulled over. The boundary conditions used are stable and also correct. It is concluded that the present study on finite porous enclosure produces results that are in excellent conformity with earlier conventional numerical observations.

Research on natural convection heat transfer in finite porous enclosure is motivated by its wide application in engineering such as ground-water hydrology, thermal management of electronic cooling, chemical catalytic reactors, heat transfer improvement in heat exchanger equipment and plenty of others (Scheidegger, 1974). Over the last five decades, fluid flow and convection heat transfer in finite porous enclosure have been studied by several aut hors (Palm et al., 1972; Vafai and Tien, 1981; and Prasad et al., 1985). Nield and Bejjan (1992) have composed a survey paper on the subject. It is realized that the stream in permeable media includes the domain scale, Representative Elementary Volume (REV) scale and the pore scale (Guo and Zhao, 2002).

Mechanical Engineering Journal, Incompressible flow, Lattice Boltzmann method, Natural convection, Porous medium, D2Q9 model.