Multiple solutions for flow mode−transition in an inclined cavity generated by natural convection

Abstract

An investigation of natural convection in a rectangular cavity (AR = 4) filled with air (Pr =
0.71) heated from the side with adiabatic horizontal walls is carried out numerically. To describe
the flow regime, we propose a description of the influence of the angle of inclination and Rayleigh
number on the flow patterns likely to develop in this configuration. The numerical analysis of the
governing equations of the problem is based on finite volume method with non‐staggered grids
arrangement and is solved through the iterative SIMPLEC algorithm. Results indicate that the angle
of inclination has a significant effect on flow mode transition. The existence of multi‐steady
solutions closely depends on the value of the Rayleigh number. For that the Hysteresis
phenomenon (multi−steady solutions) for Ra ≥ 2000 are demonstrated and parameter maps of Ra
vs. φ are proposed.