Natural Convection in Shallow Enclosures With Differentially Heated Endwalls

Abstract

We consider a low-aspect-ratio two-dimensional rectangular cavity, differentially heated with an arbitrarily large horizontal temperature difference. Steady-state results obtained from numerical solutions of the transient Navier-Stokes equations are given for air using the ideal gas law and Sutherland law transport properties. We clarify the different flow regimes possible by using numerical results for aspect ratios 0.025 < A < 1 and for Rayleigh numbers (based on height) 10 2 < Ra < 10 9 . We present Nusselt numbers, and temperature and velocity distributions, and compare them with existing data. At high Ra in the Boussinesq limit we show the existence of weak secondary and tertiary flows in the core of the cavity. In addition we present novel solutions in the non-Boussinesq regime. We find that the classical parallel flow solution, accurate in the core of the cavity in the Boussinesq limit, does not exist when variable properties are introduced. For higher Rayleigh numbers, we generalize the well-known analytical boundary layer solution of Gill. The non-Boussinesq solutions show greatly reduced static pressure levels and lower critical Rayleigh numbers. Problem DefinitionConsider a two-dimensional rectangular enclosure of width L and height H filled with a gas. The gas is initially quiescent at a uniform temperature T 0 and pressure p 0 . The walls of the vessel are initially at the same temperature T 0 . At times larger

Numerical heat transfer in a cavity with a solar control coating deposited to a vertical semitransparent wall

“…At later times the effect is more pronounced, even for the two cases. This turn over effect has been already reported in natural convection cavities but for greater Grashof numbers [1,3,4] and not in combined natural convection and radiation. Figure 8 shows the vertical components of the velocity for cases A, B, and C for Gr = 10 5 and 10 6 .…”

“…Natural convection in cavities heated differentially with adiabatic top and bottom walls has become the classical research problem that has been studied extensively by experimental, analytical, and numerical methods to get a better understanding of the governing processes [1][2][3][4]. Combined natural convection, conduction, and radiation in a cavity appears in the work of Larson [5].…”

Interaction between natural convection and surface thermal radiation in tilted slender cavities

“…In the literature review the enclosure phenomena can be classified as: (1) vertical and inclined cavities heated from the side and (2) horizontal enclosures heated from below. In cavities heated from the side, the problem of natural convection in square cavities heated differentially with adiabatic top and bottom walls has become the classical research problem extensively studied by experimental, analytical and numerical methods to get a better understanding of the governing processes [1][2][3]. In other geometries and orientations, natural convection in rectangular cavities for various aspect ratios also has been studied extensively; for example, Ozoe et al [4,5] dealt with the problem of natural convection in inclined rectangular channels heated on one side and cooled on the opposing side.…”

Visualization of diffusion and convection heat transport in a square cavity with natural convection

“…Valencia and Frederick [19] studies heat transfer in square cavities with partially active vertical walls. The problem of natural convection in shallow enclosures with differentially heated end walls was studied by Paolucci and Chenoweth [20]. Ho and Chang [21] investigated natural convection heat transfer in a vertical rectangular enclosure with two-dimensional discrete heating.…”