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.

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.

A 2D-PIV Study on Natural Convective Heat Transfer in a Square Enclosure With Partially Active Side Walls

2009 ◽  
Author(s):  
Massimo Paroncini ◽  
Francesco Corvaro ◽  
Alessia Montucchiari
Keyword(s):  
Holographic Interferometry ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Number Range ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Side Walls ◽  
Dynamic Structures ◽  
Rayleigh Numbers

The present study is an experimental and numerical analysis on the natural convection of air in square enclosures with partially active side walls. The experimental equipment is based on two different systems: an holographic interferometer and a 2D-PIV. The test cell is a square enclosure filled of air with vertical partially active side walls at different temperatures. The hot and cold regions on these sides are located in the middle of the cavity. The remaining vertical walls are made up of glass to allow an optical access to the cavity. The top and bottom surfaces of the enclosure are made up of plexiglas to reduce heat leakages. The experimental study is carried out both through the holographic interferometry, in order to obtain the average Nusselt numbers at different Rayleigh numbers, and through the 2D-PIV, in order to analyse the dynamic behaviour of the phenomenon at the same Rayleigh numbers. The average Nusselt numbers are obtained measuring the temperature distribution in the air layer trough the real-time and double-exposure holographic interferometry; the dynamic structures are the velocity vector distribution, the streamlines and the velocity maps. Finally these experimental data are compared to the results obtained through a numerical study carried out using the finite volume code, Fluent 6.2.3. The aim of this comparison is the validation of the numerical procedure. In this way it is possible to use the numerical code to enlarge the Rayleigh number range.

NUMERICAL STUDY OF LAMINAR CONVECTION AND THERMOSOLUTAL CONVECTION IN A TWO-DIMENSIONAL TRAPEZOIDAL CAVITY

1994 ◽  
Vol 18 (3) ◽  
pp. 207-224 ◽  
Author(s):  
M. Lacroix
Keyword(s):  
Schmidt Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Thermosolutal Convection ◽  
Governing Equations ◽  
Concentration Gradients ◽  
Height Ratio ◽  
Vertical Walls ◽  
Laminar Convection ◽  
Rayleigh Numbers

Heat transfer driven by temperature gradients and simultaneous temperature and concentration gradients has been studied numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top and insulated vertical walls. Results are presented for a cavity with width-to-mean height ratio of 4, thermal and concentration Rayleigh numbers up to 106 and 5.105 respectively, and top surface inclinations from 0 to 15 deg to the horizontal. The Prandtl and the Schmidt number used are 0.71 and 0.6 respectively. The governing equations are expressed in terms of stream function and vorticity and body-fitted coordinates are used for mapping the sloping top wall. As the inclination of the top surface is increased, the Nusselt and Sherwood numbers decrease. The effect of opposing thermal and concentration gradients on the Nusselt and Sherwood numbers is however more important than the effect of the inclination of the top surface. Theoretical Nusselt and Sherwood numbers are compared with available experimental data.

Numerical Study of the Onset of Double-Diffusive Cellular Convection Due to a Uniform Lateral Heat Flux

1982 ◽  
Vol 104 (4) ◽  
pp. 649-655 ◽  
Author(s):  
S. Takao ◽  
M. Tsuchiya ◽  
U. Narusawa
Keyword(s):  
Heat Flux ◽  
Numerical Study ◽  
Vertical Wall ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Physical Experiments ◽  
Diffusive Convection ◽  
The Stability ◽  
Double Diffusive ◽  
Lateral Heat

When a fluid with a vertical solute gradient of (−dS/dy)0 is heated laterally, roll cells start to form at the boundary, developing into a series of convective layers. Numerical experiments were performed to investigate the onset of the abovementioned double-diffusive convection under the application of a uniform lateral heat flux. The paper reports the results and discussion of the following aspects of the stability of double-diffusive convection; (i) the relationship between the critical value, (Ra/Rs)c, above which convection cells form along the vertical wall and the nondimensional slot width, (d/L), (ii) the effect of the Lewis number on (Ra/Rs)c. It was also confirmed that values of (Ra/Rs)c as well as H/L (the nondimensional vertical size of incipient cells) obtained in this numerical experiment for wide slot widths (d/L>∼30), agreed well with those obtained previously by physical experiments.

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.

Free Convective Flow in a Two Enclosure Arrangement With a High Aspect Ratio Side Enclosure Joined to a Large Square Enclosure

2000 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Vertical Wall ◽  
Heated Wall ◽  
Free Convective Flow ◽  
Square Enclosure

Abstract A numerical study of free convective flow in a vertical joined two-enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is separated from a larger square enclosure by a vertical dividing wall which is impermeable but offers no resistance to heat transfer. The vertical wall of the main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. All remaining walls in both enclosures are adiabatic. The situation considered is an approximate model of a window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number and the dimensionless width of the side enclosure on the Nusselt number have been investigated. The results show that there is a minimum in the Nusselt number variation with side enclosure width for a fixed Rayleigh number. The effect of Rayleigh number on the conditions under which this minimum occurs and on the value of the minimum Nusselt number has been investigated.

Influence of Non Uniform Boundary Conditions on Laminar Free Convection in Wavy Square Cavity With Partial Partitions

Volume 1 ◽  
2004 ◽  
Author(s):  
A. Sabeur-Bendehina ◽  
M. Aounallah ◽  
L. Adjlout ◽  
O. Imine ◽  
B. Imine
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Numerical Study ◽  
Laminar Regime ◽  
Uniform Temperature ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Rayleigh Numbers ◽  
Partial Partitions

In the present work, a numerical study of the effect of non uniform boundary conditions on the heat transfer by natural convection in cavities with partial partitions is investigated for the laminar regime. This problem is solved by using the partial differential equations which are the equation of mass, momentum and energy. The tests were performed for different boundary conditions and different Rayleigh numbers while the Prandtl number was kept constant. Four geometrical configurations were considered namely three and five undulations with increasing and decreasing partition length. The results obtained show that the non uniform temperature in the vertical walls affects the flow and the heat transfer. The mean Nusselt number decreases comparing with the heat transfer in the undulated square cavity without partitions for all non uniform boundary conditions tested.

Natural Convection From a Porous Cavity With Sublayers of Nonuniform Thickness: A Lumped System Analysis

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
R. L. Marvel ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
System Analysis ◽  
Numerical Study ◽  
Temperature Fields ◽  
Porous Cavity ◽  
Nonuniform Thickness ◽  
Sublayer Thickness ◽  
Vertical Walls ◽  
Quick Estimate ◽  
Rayleigh Numbers

A numerical study has been performed to further investigate the flow and temperature fields in layered porous cavity. The geometry considered is a two-dimensional square cavity comprising of three or four vertical sublayers with nonuniform thickness and distinct permeability. The cavity is subjected to differential heating from the vertical walls. The results obtained are used to further evaluate the capacity of the lumped-system analysis in the prediction of heat transfer results of layered porous cavities. It has been found that predictions by the lumped-system model are reasonably good for the range of Rayleigh numbers encountered in engineering applications. In addition, the predictions improve when the number of sublayers increases as well as the sublayer thickness becomes more uniform. Thus, it proves that the lumped-system analysis can offer a quick estimate of heat transfer result from a layered porous cavity with reasonable accuracy.

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.

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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