A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

侧加热腔体内重力波演化过程的数值模拟

利用二维数值模拟的方法研究了侧加热腔体内的自然对流．基于数值模拟结果，描述了水平热入侵流(intrusion)的整个演化过程，并对该过程的物理机制进行了讨论．结果表明：当热入侵流抵达腔体冷壁后，由于冷壁无法卷入所有的热入侵流，热入侵流在冷上角堆积并产生一个反向流动，在冷壁边界层附近形成一个顺时针涡，该涡在浮力效应驱动下可返回热壁，并在腔体的冷热壁之间形成了腔体尺度的流体振荡，即内重力波．

Design of gas filled solar collectors

With a suitable gas filling used between cover glass and absorber in a flat plate solar collector, it is possible achieving better thermal performance at the same time as the distance betweenabsorber and glass can be reduced. Though, even if there is no vacuum inside the box, there will be potential risks for exhaustion due to stresses depending on the gas volume varies as the temperature varies. This study found out that it is possible build such a collector with less material in the absorber and the tubes and still getting better performance, without risks for exhaustion.

Gas-filled, flat plate solar collectors

This work treats the thermal and mechanical performances of gas-filled, flat plate solar collectors in order to achieve a better performance than that of air filled collectors. The gases examined are argon, krypton and xenon which all have lower thermal conductivity than air. The absorber is formed as a tray connected to the glass. The pressure of the gas inside is near to the ambient and since the gas volume will vary as the temperature changes, there are potential risks for fatigue in the material. One heat transfer model and one mechanical model were built. The mechanical model gave stresses and information on the movements. The factors of safety were calculated from the stresses, and the movements were used as input for the heat transfer model where the thermal performance was calculated. It is shown that gas-filled, flat plate solar collectors can be designed to achieve good thermal performance at a competitive cost. The best yield is achieved with a xenon gas filling together with a normal thick absorber, where normal thick means a 0.25 mm copper absorber. However, a great deal of energy is needed to produce the xenon gas, and if this aspect is taken into account, the krypton filling is better. Good thermal performance can also be achieved using less material; a collector with a 0.1 mm thick copper absorber and the third best gas, which is argon, still gives a better operating performance than a common, commercially produced, air filled collector with a 0.25 mm absorber. When manufacturing gas-filled flat plate solar collectors, one way of decreasing the total material costs significantly, is by changing absorber material from copper to aluminium. Best yield per monetary outlay is given by a thin (0.3 mm) alu-minium absorber with an argon filling. A high factor of safety is achieved with thin absorbers, large absorber areas, rectangular constructions with long tubes and short distances between glass and absorber. The latter will also give a thin layer of gas which gives good thermal performance. The only doubtii ful construction is an argon filled collector with a normal thick (> 0.50 mm) aluminium absorber. In general, an assessment of the stresses for the proposed construction together with appropriate tests are recommended before manufacturing, since it is hard to predict the factor of safety; if one part is reinforced, some other parts can experience more stress and the factor of safety actually drops.

Transition to an unsteady flow induced by a fin on the sidewall of a differentially heated air-filled square cavity and heat transfer

The transition from a steady to an unsteady flow induced by an adiabatic fin on the sidewall of a differentially heated air-filled cavity is numerically investigated. Numerical simulations have been performed over the range of Rayleigh numbers from Ra = 105–109. The temporal development and spatial structures of natural convection flows in the cavity with a fin are described. It has been demonstrated that the fin may induce the transition to an unsteady flow and the critical Rayleigh number for the occurrence of the transition is between 3.72 × 106 and 3.73 × 106. Furthermore, the peak frequencies of the oscillations triggered by different mechanisms are obtained through spectral analysis. It has been found that the flow rate through the cavity with a fin is larger than that without a fin under the unsteady flow, indicating that the fin may improve the unsteady flow in the cavity.

Numerical computation of laminar flow in a heated rotating cavity with an axial throughflow of air

A heated rotating cavity with an axial throughflow of cooling air is used as a model for the flow in the cylindrical cavities between adjacent discs of a high-pressure gas-turbine compressor. In an engine the flow is expected to be turbulent, the limitations of this laminar study are fully realised but it is considered an essential step to understand the fundamental nature of the flow. The three-dimensional, time-dependent governing equations are solved using a code based on the finite volume technique and a multigrid algorithm. The computed flow structure shows that flow enters the cavity in one or more radial arms and then forms regions of cyclonic and anticyclonic circulation. This basic flow structure is consistent with existing experimental evidence obtained from flow visualization. The flow structure also undergoes cyclic changes with time. For example, a single radial arm, and pair of recirculation regions can commute to two radial arms and two pairs of recirculation regions and then revert back to one. The flow structure inside the cavity is found to be heavily influenced by the radial distribution of surface temperature imposed on the discs. As the radial location of the maximum disc temperature moves radially outward, this appears to increase the number of radial arms and pairs of recirculation regions (from one to three for the distributions considered here). If the peripheral shroud is also heated there appear to be many radial arms which exchange fluid with a strong cyclonic flow adjacent to the shroud. One surface temperature distribution is studied in detail and profiles of the relative tangential and radial velocities are presented. The disc heat transfer is also found to be influenced by the disc surface temperature distribution. It is also found that the computed Nusselt numbers are in reasonable accord over most of the disc surface with a correlation found from previous experimental measurements. © 1994, MCB UP Limited.

Natural convection experiments on a heated horizontal cylinder in a differentially heated square cavity

Natural convection heat transfer from a heat generating horizontal cylinder enclosed in a square cavity, where a temperature difference exists across its vertical walls has been experimentally investigated for the range 2×104

Numerical and experimental analysis of natural convection in a cavity heated from below

In this work, an analysis of the natural convection flow caused by heat sources dissipating energy at a constant rate simulating electronic components mounted at the bottom surface of a cavity symmetrically cooled from the sides and insulated at the top is performed. This problem was studied numerically and experimentally for several aspect ratios (height/width), for different levels of dissipation in the sources, and for different side wall temperatures. Temperature and velocity fields were determined as well as the temperature variation along the surface where the sources are mounted and the average Nusselt number in the source surfaces. Numerical and experimental results were found to agree.

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 105 to 108 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh Number with corrugation amplitude and frequency.

Morphological transitions and buckling characteristics in a nanoparticle-laden sessile droplet resting on a heated hydrophobic substrate

In this work, we have established the evaporation-liquid flow coupling mechanism by which sessile nanofluid droplets on a hydrophobic substrate evaporate and agglomerate to form unique morphological features under controlled external heating. It is well understood that evaporation coupled with internal liquid flow controls particle transport in a spatiotemporal sense. Flow characteristics inside the heated droplet are investigated and found to be driven by the buoyancy effects. Velocity magnitudes are observed to increase by an order at higher temperatures with similar looking flow profiles. The recirculating flow induced particle transport coupled with collision of particles and shear interaction between them leads to the formation of dome shaped viscoelastic shells of different dimensions depending on the surface temperature. These shells undergo sol-gel transition and subsequently undergo buckling instability leading to the formation of daughter cavities. With an increase in the surface temperature, droplets exhibit buckling from multiple sites over a larger sector in the top half of the droplet. Irrespective of the initial nanoparticle concentration and substrate temperature, growth of a daughter cavity (subsequent to buckling) inside the droplet is found to be controlled by the solvent evaporation rate from the droplet periphery and is shown to exhibit a universal trend.

The Hydrothermal Wave Of Large-Prandtl-Number Fluid In A Shallow Cavity

The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite to the surface flow (upstream) in the case of zero gravity when the applied temperature difference grows and over the critical value. The phase relationships of the disturbed velocity, temperature and pressure demonstrate that the traveling wave is driven by the disturbed temperature, which is named hydrothermal wave. The hydrothermal wave is so weak that the oscillatory flow field and temperature distribution can hardly be observed in the liquid layer. The exciting mechanism of hydrothermal wave is analyzed and discussed in the present paper.

Shroud heat transfer measurements from a rotating cavity with an axial throughflow of air

The paper discusses measurements of heat transfer obtained from the inside surface of the peripheral shroud. The experiments were carried out on a rotating cavity, comprising two 0.985-m-dia disks, separated by an axial gap of 0.065 m and bounded at the circumference by a carbon fiber shroud. Tests were conducted with a heated shroud and either unheated or heated disks. When heated, the disks had the same temperature level and surface temperature distribution. Two different temperature distributions were tested; the surface temperature either increased, or decreased with radius. The effects of disk, shroud, and air temperature levels were also studied. Tests were carried out for the range of axial throughflow rates and speeds: 0.0025 ≤ m ≤ 0.2 kg/s and 12.5 ≤ Ω ≤ 125 rad/s, respectively. Measurements were also made of the temperature of the air inside the cavity. The shroud Nusselt numbers are found to depend on a Grashof number, which is defined using the centripetal acceleration. Providing the correct reference temperature is used, the measured Nusselt numbers also show similarity to those predicted by an established correlation for a horizontal plate in air. The heat transfer from the shroud is only weakly affected by the disk surface temperature distribution and temperature level. The heat transfer from the shroud appears to be affected by the Rossby number. A significant enhancement to the rotationally induced free convection occurs in the regions 2 ≤ Ro ≤ 4 and Ro ≥ 20. The first of these corresponds to a region where vortex breakdown has been observed. In the second region, the Rossby number may be sufficiently large for the central throughflow to affect the shroud heat transfer directly. Heating the shroud does not appear to affect the heat transfer from the disks significantly.