Unsteady Natural Convection in an Initially Stratified Air-Filled Trapezoidal Enclosure Heated from Below

Abstract

Natural convection is intensively explored, especially in a valley-shaped trapezoidal enclosure, because of its broad presence in both technical settings and nature. This study deals with a trapezoidal cavity, which is initially filled with linearly stratified air. Although the sidewalls remain adiabatic, the bottom wall is heated, and the top wall is cooled. For the stratified fluid (air), the temperature of the fluid adjacent to the top and the bottom walls is the same as that of the walls. Natural convection in the trapezoidal cavity is simulated in two dimensions using numerical simulations, by varying Rayleigh numbers (Ra) from 100 to 108 with constant Prandtl number, Pr = 0.71, and aspect ratio, A = 0.5. The numerical results demonstrate that the development of natural convection from the beginning is dependent on the Rayleigh numbers. According to numerical results, the development of transient flow within the enclosure owing to the predefined conditions for the boundary may be categorized into three distinct stages: early, transitional, and steady or unsteady. The flow characteristics at each of the three phases and the impact of the Rayleigh number on the flow’s growth are quantified. Unsteady natural convection flows in the enclosure are described and validated by numerical results. In addition, heat transfer through the bottom and the top surfaces is described in this study.