A Numerical Study of Natural Convection in Partially Open Enclosures With a Conducting Side-Wall

2004 ◽  
Vol 126 (1) ◽  
pp. 76-83 ◽  
Author(s):  
G. Desrayaud ◽  
G. Lauriat
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Side Wall ◽  
Practical Applications ◽  
Hot Air ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Rayleigh Numbers

A numerical study of natural convection generated by a cold vertical wall of an enclosure with two openings on the opposite wall of finite thickness is presented. The enclosure is connected to an infinite reservoir filled with hot air. A two-dimensional laminar flow is assumed both within the enclosure and along the side of the bounding wall immersed into the reservoir. The effects of the size of the openings, spacing between the vertical walls and thermal resistance of the bounding wall are investigated. Numerical results are discussed for aspect ratios of the enclosure and Rayleigh numbers relevant to practical applications.

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.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

scholarly journals Simulation of Natural Convection Heat Transfer in a 2-D Trapezoidal Enclosure

2019 ◽  
Vol 16 (4) ◽  
pp. 7375-7390 ◽  
Author(s):  
K. Venkatadri ◽  
S. Abdul Gaffar ◽  
Ramachandra Prasad V. ◽  
B. Md. Hidayathulla Khan ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Practical Applications ◽  
Wide Range ◽  
Trapezoidal Enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energyrelated applications, in case of proper design of enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 103 ≤ Ra ≤ 105 and Prandtl number (Pr = 0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra = 104 ). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported. 

Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall(s)

2007 ◽  
Author(s):  
E. Natarajan ◽  
Tanmay Basak ◽  
S. Roy
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Vertical Wall ◽  
Side Wall ◽  
Convection Flow ◽  
Left Wall ◽  
Wide Range ◽  
Stream Functions ◽  
Side Walls

The present numerical study deals with natural convection flow in a trapezoidal cavity when the bottom wall is uniformly heated and the vertical wall(s) are linearly heated and cooled whereas the top wall is well insulated. Nonlinear coupled partial differential equations governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Parametric study for the wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 105 and Prandtl number (Pr), 0.07 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For linearly heated side walls symmetry is observed while representing the flow patterns in terms of stream functions whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. Local Nusselt number becomes negative at the side wall for linearly heated side walls and at the left wall for linearly heated left wall and cooled right wall indicating the reversal of heat flow. The effect of Prandtl number in the variation of average Nusselt numbers is more significant for Prandtl numbers in the range 0.07 to 0.7 than 10 to 100.

Numerical Study of Natural Convection in a Partially Open Environment With a Heat Generating Source

2006 ◽  
Author(s):  
Viviana Cocco Mariani ◽  
Adriano da Silva
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Vertical Wall ◽  
Internal Heat ◽  
Internal Heating ◽  
Heating Source ◽  
Vertical Walls ◽  
The Difference

A numerical study of the thermal and fluid dynamic behavior of air in a partially open two-dimensional enclosure is presented The enclosure has an opening on the right-hand vertical wall, which is kept at a low given temperature, while the opposite wall has a high given temperature. The natural convection in the enclosure is influenced simultaneously by the difference in temperature between the vertical walls, represented by the Rayleigh number (Rae) and by the internal heating source in the enclosure, represented by the Rayleigh number (Rai). The internal heat source is located on the lower horizontal wall, occupying three different positions. The numerical simulations were executed for 103 ≤ Rae ≤ 106 while the intensity of the two effects - the difference in temperature of the vertical walls and the internal heating source - was evaluated based on the relation R = Rai/Rae, which assumed the values of 400, 1000 and 2500. The results obtained in this study are compared with the results reported in the literature, showing a good congruence.

On the Natural Convection in a Cavity With a Cooled Top Wall and Multiple Protruding Heaters

1995 ◽  
Vol 117 (1) ◽  
pp. 34-45 ◽  
Author(s):  
C. P. Desai ◽  
K. Vafai ◽  
M. Keyhani
Keyword(s):  
Natural Convection ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Side Wall ◽  
Temperature Fields ◽  
Length Ratio ◽  
Numerical Work ◽  
Steady Solutions ◽  
Heater Length ◽  
Rayleigh Numbers

Natural convection in rectangular enclosures with multiple protruding heaters mounted on one side wall is of relevance to the cooling of electronic equipment. In some configurations, the top wall behaves as the heat sink while the opposing vertical wall and the bottom wall are insulated. The present work examines the peculiarities introduced in the natural convection process for such configurations. The enclosure considered had five protrusions, cavity width to heater length ratio of 1.2 and cavity height to heater length ratio of 11. It is shown that for such configurations, a stable flow exists only at lower Rayleigh numbers and that above a certain critical Rayleigh number, only quasi-steady solutions exist. At low Rayleigh numbers(Ra* ≤ 1.5 × 107), the flow is stable and characterized by the presence of a primary flow cell and a counter-rotating secondary cell at the top of the enclosure. At higher Rayleigh numbers (Ra* ≥ 3 × 108), however, the isothermal top wall causes a periodic flow pattern to develop within the enclosure. Several interesting characteristics of the flow and temperature fields are presented. Results compared with previous experimental and numerical work are found to be in good agreement.

Effect of Imposed Wall Temperature Oscillations on the Stability of Natural Convection in a Square Enclosure

1995 ◽  
Vol 117 (1) ◽  
pp. 113-120 ◽  
Author(s):  
Q. Xia ◽  
K. T. Yang ◽  
D. Mukutmoni
Keyword(s):  
Numerical Study ◽  
Vertical Wall ◽  
Laminar Flows ◽  
Time Dependent ◽  
Square Enclosure ◽  
Temperature Oscillations ◽  
Vertical Walls ◽  
Flow Transitions ◽  
The Stability ◽  
Rayleigh Numbers

The present numerical study is directed toward buoyancy-driven laminar flows in a two-dimensional square enclosure with differential heating at the vertical walls. The top and bottom walls are insulated. A time-dependent temperature varying sinusoidal perturbation is imposed on the hot vertical wall. The cold vertical wall is maintained at a constant temperature. The fluid is air with a Prandtl number of 0.72. Computations were carried out at one imposed frequency, which is of the same order as the first natural frequency of the system. It was found that the perturbations destabilized the flow in that higher amplitudes lead to lower critical Rayleigh numbers for the flow transitions. Computations spanned four regimes: periodic, quasi-periodic with two frequencies, quasi-periodic with three-frequencies, and chaotic.

scholarly journals Numerical study of natural convection in an enclosure with discrete heat sources on one of its vertical walls

2019 ◽  
pp. 448-448
Author(s):  
Mehmet Pamuk
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Heat Sources ◽  
Confined Spaces ◽  
Nusselt Numbers ◽  
Discrete Heat Sources ◽  
Computer Chips ◽  
Vertical Walls ◽  
Comparison Of The Results ◽  
Rayleigh Numbers

In this study, natural convection in a fluid-filled rectangular enclosure is analyzed using Comsol? commercial software. The fluid in which natural convection takes place is a dielectric liquid called FC-75. Attached to one of the vertical walls of the enclosure is an array of rectangular protrusions, each representing computer chips mounted on a PCB. The nominal power consumed by each chip is assumed to be 0.35W, 1.07W, 1.65W and 2.35W. This corresponds exactly to the values used in the experiments, which were performed once by the author of this study. The results of the experiment and the numerical study are shown as Nusselt numbers vs. Rayleigh numbers, both being the most important dimensionless parameters of natural convection. A comparison of the results has shown that Comsol? can achieve reliable results in similar problems, eliminating the need to build expensive experimental setups and spending time conducting experiments. The simulation results are aimed to be used in similar designs of electronic circuits in confined spaces.

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