Numerical Study of Natural Convection in an Inclined Porous Cavity

Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30∘ is investigated numerically. The vertical walls are differentially heated, and the horizontal walls are adiabatic. The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed. The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm (TDMA). The results are obtained for a porosity equal to 0.45, a Darcy number and a Prandtl respectively equal to 10−3 and 0.71; they are analyzed in terms of streamlines, isotherms, phase portrait, attractors, and spectra amplitude as a function of the Rayleigh number. It is found that, as Rayleigh number increases, the natural convection changes from a steady state to a time-periodic state and finally to a chaotic condition.