Two-Dimensional Periodic Natural Convection in a Rectangular Enclosure of Aspect Ratio One

1985 ◽  
Vol 107 (4) ◽  
pp. 850-854 ◽  
Author(s):  
D. G. Briggs ◽  
D. N. Jones
Keyword(s):  
Natural Convection ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Lower Boundary ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Vertical Walls ◽  
Rayleigh Numbers

A two-dimensional rectangular cavity of aspect ratio one is studied experimentally using a laser-doppler velocimeter. The enclosure is air filled and consists of two vertical walls at unequal isothermal temperatures and two connecting horizontal walls with temperatures varying linearly between the two vertical surfaces. This study clearly defines the existence of periodic laminar flow regimes detectable at Ra numbers above 0.3 × 107. These periodic variations in velocity are induced by the upper and lower boundary conditions. The envelopes of vertical and horizontal velocity fluctuations are reported as a function of position for Rayleigh numbers of 0.25 × 107, 0.50 × 107, and 0.85 × 107. In addition, the effect of Ra number on frequency of flow is reported.

A study of laminar flow in low aspect ratio lid-driven cavities

2002 ◽  
Vol 29 (3) ◽  
pp. 436-447 ◽  
Author(s):  
Y Yang ◽  
A G Straatman ◽  
R J Martinuzzi ◽  
E K Yanful
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Numerical Solutions ◽  
Cavity Flow ◽  
Momentum Equation ◽  
Laser Doppler Velocimeter ◽  
Countercurrent Flow ◽  
Two Dimensional ◽  
Low Aspect Ratio

The evolution to fully developed laminar flow in low aspect ratio, two-dimensional, lid-driven cavities has been studied experimentally and numerically. Velocity measurements were made in water in a moving-lid apparatus using a laser Doppler velocimeter (LDV). Numerical solutions for the cavity flow were obtained by solving the two-dimensional mass-momentum equation set in a finite-volume framework. The measured and predicted results were in excellent agreement. Fully developed cavity flow is said to exist when the main regions of the flow field become independent of the aspect ratio. When fully developed conditions prevail, a region of countercurrent flow (CCF) separates the end structures, which are decoupled. The extent of the end regions is shown to grow linearly with increasing Reynolds number Re, based on the lid speed and the cavity height. Consequently, the critical aspect ratio for the onset of fully developed flow is also linearly dependent on Re. Above a critical Reynolds number, Re [Formula: see text] 300, the flow becomes unsteady, and a lower-wall, tertiary vortex appears, which is thought to be associated with the onset of hydrodynamic instability.Key words: lid-driven cavity, laminar flow, shallow water cover, countercurrent flow.

scholarly journals Natural Convection in Undivided and Partially Divided Rectangular Enclosures

1981 ◽  
Vol 103 (4) ◽  
pp. 623-629 ◽  
Author(s):  
M. W. Nansteel ◽  
R. Greif
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Two Dimensional ◽  
Injection Flow ◽  
Stabilizing Effect ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Rayleigh Numbers

Heat transfer by natural convection in a two-dimensional rectangular enclosure fitted with partial vertical divisions is investigated experimentally. The horizontal walls of the enclosure are adiabatic while the vertical walls are maintained at different temperatures. The experiments are carried out with water, Pr ≃ 3.5, for Rayleigh numbers in the range, 2.3 × 1010 ⩽ RaL ⩽ 1.1 × 1011, and an aspect ratio, A = H/L = 1/2. The effect of the partial vertical divisions on the fluid flow and temperature fields is investigated by dye-injection flow visualization and by thermocouple probes, respectively. The effect of the partitions on the heat transfer across the enclosure is also studied and correlations for the Nusselt number as a function of RaL and partition length are generated for both conducting and non-conducting partition materials. Partial divisions are found to have a significant effect on the heat transfer; especially when the divisions are adiabatic. The results also indicate that the partial divisions may have a stabilizing effect on the laminar-transitional flow on the heated vertical walls of the enclosure.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

scholarly journals Thermally Optimum Spacing between Inner Plates in Natural Convection Flows in Cavities by Numerical Investigation

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 554 ◽  
Author(s):  
Blas Zamora
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Numerical Investigation ◽  
Thermophysical Properties ◽  
Electronic Equipment ◽  
Passive Devices ◽  
Wide Range ◽  
Optimum Spacing ◽  
Rayleigh Numbers ◽  
Wall Spacing

Buoyancy-driven airflow that included two isothermal inner plates established in a vented cavity is investigated numerically. The thermally optimum wall-to-wall spacing of the immersed channel, as well as its dependence with respect to the relevant governing parameters, are determined. Results are presented as a function of the aspect ratio b/H for a wide range of Rayleigh numbers RaH. A logarithmic correlation for the optimum (b/H)opt as a function of RaH is presented. In addition, since the outlined configuration might be subject to intense heating conditions, the influence of considering variable thermophysical properties is also included in the analysis. In fact, an appreciable influence of the variation of properties on (b/H)opt is also detected for a representative value of RaH = 109. Obtained results can be directly applied to the optimization of electronic equipment cooling, or even to thermal passive devices in buildings.

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