A Numerical Study of Three-Dimensional Roll Cells within Rigid Boundaries

1979 ◽  
Vol 101 (2) ◽  
pp. 233-237 ◽  
Author(s):  
A. M. C. Chan ◽  
S. Banerjee
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Numerical Study ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Convection Roll ◽  
Marker And Cell Method

Three-dimensional natural convection, roll cells within rigid enclosures have been studied with a previously developed numerical technique based on the marker and cell method. Given identical initial conditions, the velocity and temperatures fields are found to be sensitive to the thermal boundary conditions on the side walls and the aspect ratio of the enclosure. Two-dimensional results are also obtained and compared with the corresponding three-dimensional results. The two-dimensional calculations do not agree well with the three dimensional ones, especially for enclosures having aspect ratios less than unity. This indicates that care must be taken in analyzing natural convection problems of this type with two-dimensional methods.

Three-Dimensional Steady and Oscillatory Natural Convection in a Rectangular Enclosure With Heat Sources

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Amin Bouraoui ◽  
Rachid Bessaïh
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Three Dimensional ◽  
Air Cooling ◽  
Heat Sources ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Simpler Algorithm ◽  
Strong Relation

In this paper, a numerical study of three-dimensional (3D) natural convection air-cooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region.

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.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

Three-dimensional natural convection in a box: a numerical study

1977 ◽  
Vol 83 (1) ◽  
pp. 1-31 ◽  
Author(s):  
G. D. Mallinson ◽  
G. De Vahl Davis
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Inertial Interaction ◽  
Longitudinal Temperature

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

EXPERIMENTAL AND NUMERICAL STUDY OF THREE-DIMENSIONAL NATURAL CONVECTION AND FREEZING IN WATER

1994 ◽  
Author(s):  
C. Abegg ◽  
Graham de Vahl Davis ◽  
W.J. Hiller ◽  
St. Koch ◽  
Tomasz A. Kowalewski ◽  
...  
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Three Dimensional

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

2016 ◽  
Vol 831 ◽  
pp. 83-91
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Maximum Temperature ◽  
Cubical Enclosure ◽  
Simplec Algorithm ◽  
Volume Method

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

Three-Dimensional Natural Convection From Vertical Heated Plates With Adjoining Cool Surfaces

1992 ◽  
Vol 114 (1) ◽  
pp. 115-120 ◽  
Author(s):  
B. W. Webb ◽  
T. L. Bergman
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Control Volume ◽  
Three Dimensional ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Uniform Heat Flux ◽  
Infrared Thermal Imaging ◽  
Transfer Rates ◽  
Thermal Boundary Conditions

Natural convection in an enclosure with a uniform heat flux on two vertical surfaces and constant temperature at the adjoining walls has been investigated both experimentally and theoretically. The thermal boundary conditions and enclosure geometry render the buoyancy-induced flow and heat transfer inherently three dimensional. The experimental measurements include temperature distributions of the isoflux walls obtained using an infrared thermal imaging technique, while the three-dimensional equations governing conservation of mass, momentum, and energy were solved using a control volume-based finite difference scheme. Measurements and predictions are in good agreement and the model predictions reveal strongly three-dimensional flow in the enclosure, as well as high local heat transfer rates at the edges of the isoflux wall. Predicted average heat transfer rates were correlated over a range of the relevant dimensionless parameters.

scholarly journals Numerical study of the turbulent natural convection of nanofluids in a partially heated cubic cavity

2021 ◽  
pp. 57-57
Author(s):  
Zakaria Lafdaili ◽  
Sakina El-Hamdani ◽  
Abdelaziz Bendou ◽  
Karim Limam ◽  
Bara El-Hafad
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Heat Exchange ◽  
Metallic Nanoparticles ◽  
Volume Fraction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Stability Characteristic ◽  
Horizontal Strip ◽  
Turbulent Natural Convection

In this work we study numerically the three-dimensional turbulent natural convection in a partially heated cubic cavity filled with water containing metallic nanoparticles, metallic oxides and others based on carbon.The objective is to study and compare the effect of the addition of nanoparticles studied in water and also the effect of the position of the heated partition on the heat exchange by turbulent natural convection in this type of geometry, which can significantly improve the design of heat exchange systems for better space optimization. For this we have treated numerically for different volume fractions the turbulent natural convection in the two cases where the cavity is heated respectively by a vertical and horizontal strip in the middle of one of the vertical walls. To take into account the effects of turbulence, we used the standard turbulence model ? - ?. The governing equations are discretized by the finite volume method using the power law scheme which offers a good stability characteristic in this type of flow. The results are presented in the form of isothermal lines and current lines. The variation of the mean Nusselt number is calculated for the two positions of the heated partition as a function of the volume fraction of the nanoparticles studied in water for different Rayleigh numbers.The results show that carbon-based nanoparticles intensify heat exchange by convection better and that the position of the heated partition significantly influences heat exchange by natural convection. In fact, an improvement in the average Nusselt number of more than 20% is observed for the case where the heated partition is horizontal.

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