Multiple solutions for free convection flow in inclined enclosures

Abstract

In this paper, we investigated the free convection flow in inclined rectangular enclosures filled with air. The analysis is carried out by a numerical solution of the full governing equations of the problem employing the finite volumes approach with staggered grid arrangement by the iterative SIMPLE-C algorithm. We propose for three aspect ratio's AR = 3, 4 and 8 a parametric description illustrated the influence of the inclination angles 0° ≤ φ ≤ 90° and Rayleigh number 103 ≤ Ra ≤ 104, on the flow patterns likely to develop in each configuration. The results indicate that the effects of inclination on flow mode transition and multiplicity of solutions for each aspect ratio at various Rayleigh numbers, the existence of such multi-steady solutions strongly depends on the value of the Rayleigh number. For that the Hysteresis phenomenon for Ra ≥ 2000 are demonstrated and also the parameter maps of Ra vs φ are constructed.