Search

The phenomenon of natural convection is the subject of significant research interest due to its widespread occurrence in both natural and industrial contexts. This study focuses on investigating natural convection phenomena within triangular enclosures, specifically emphasizing a valley-shaped configuration. Our research comprehensively analyses unsteady, non-dimensional time-varying convection resulting from natural fluid flow within a valley-shaped cavity, where the inclined walls serve as hot surfaces and the top wall functions as a cold surface. We explore unsteady natural convection flows in this cavity, utilizing air as the operating fluid, considering a range of Rayleigh numbers from Ra = 100 to 108. Additionally, various non-dimensional times τ, spanning from 0 to 5000, are examined, with a fixed Prandtl number (Pr = 0.71) and aspect ratio (A = 0.5). Employing a two-dimensional framework for numerical analysis, our study focuses on identifying unstable flow mechanisms characterized by different non-dimensional times, including symmetric, asymmetric, and unsteady flow patterns. The numerical results reveal that natural convection flows remain steady in the symmetric state for Rayleigh values ranging from 100 to 7 × 103. Asymmetric flow occurs when the Ra surpasses 7 × 103. Under the asymmetric condition, flow arrives in an unsteady stage before stabilizing at the fully formed stage for 7 × 103 < Ra < 107. This study demonstrates that periodic unsteady flows shift into chaotic situations during the transitional stage before transferring to periodic behavior in the developed stage, but the chaotic flow remains predominant in the unsteady regime with larger Rayleigh numbers. Furthermore, we present an analysis of heat transfer within the cavity, discussing and quantifying its dependence on the Rayleigh number. [ABSTRACT FROM AUTHOR]

Numerical findings of natural convection flows in a trapezoidal cavity are reported in this study. This study focuses on the shift from symmetric steady to chaotic flow within the cavity. This cavity has a heated bottom wall, a cooled top wall, and adiabatic inclined sidewalls. The unsteady natural convection flows occurring within the cavity are numerically simulated using the finite volume (FV) method. The fluid used in the study is air, and the calculations are performed for different dimensionless parameters, including the Prandtl number (Pr), which is kept constant at 0.71, while varying the Rayleigh numbers (Ra) from 100 to 108 and using a fixed aspect ratio (AR) of 0.5. This study focuses on the effect of the Rayleigh numbers on the transition to chaos. In the transition to chaos, a number of bifurcations occur. The first primary transition is found from the steady symmetric to the steady asymmetric stage, known as a pitchfork bifurcation. The second leading transition is found from a steady asymmetric to an unsteady periodic stage, known as Hopf bifurcation. Another prominent bifurcation happens on the changeover of the unsteady flow from the periodic to the chaotic stage. The attractor bifurcates from a stable fixed point to a limit cycle for the Rayleigh numbers between 4 × 106 and 5 × 106. A spectral analysis and the largest Lyapunov exponents are analyzed to investigate the natural convection flows during the shift from periodic to chaos. Moreover, the cavity's heat transfers are computed for various regimes. The cavity's flow phenomena are measured and verified. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Natural convection in a V-shaped section cavity heated from below and cooled from above is investigated experimentally for the first time in the literature. Temperature measurements using fast-response thermistors and flow visualization using the shadowgraph technology have been performed. The natural convection development in the cavity including the conductional, the transitional, and the fully developed stages is described. It is experimentally proven that the scaling law of the thermal boundary layer thickness is δT ∼ (κt)1/2 and the scaling law of the plume velocity is vp ∼ κRa7/15/l. Furthermore, the occurrence of Hopf bifurcation in the transition to chaos and the flow structure are also identified experimentally. The power spectral density of the temperature time series reveals that the dominant frequency of the oscillations of the unsteady flow depends on the Rayleigh number, which is quantified. [ABSTRACT FROM AUTHOR]

The mixed convective laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is studied along an isothermal horizontal circular cylinder using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively. Here, it is found that heating the cylinder delays separation and if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a very cold cylinder there will not be boundary-layer on the cylinder. [ABSTRACT FROM AUTHOR]