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.

Free Convection in an Inclined Square Cavity With Partial Partitions on a Wavy Hot Wall

Volume 1 ◽  
2004 ◽  
Author(s):  
M. Belkadi ◽  
A. Azzi ◽  
O. Imine ◽  
L. Adjlout ◽  
M. Aounallah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Numerical Study ◽  
Wavy Wall ◽  
Square Cavity ◽  
Inclination Angles ◽  
The Mean ◽  
Rayleigh Numbers ◽  
Partial Partitions ◽  
Wall Geometry

In the present investigation, a numerical study of the effect of the hot wavy wall with partial partitions on free convection in an inclined square cavity, differentially heated, was undertaken. 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 inclination angles, partition lenghts and Rayleigh numbers while the Prandtl number was kept constant. A configuration with three undulations and three partitions has been tested. The results obtained show that the hot wall geometry with partions affects the heat transfer rate in the cavity. The mean Nusselt number decreases notably compared with the heat transfer in the square undulated cavity without partitions.

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.

Natural Convection Inside a Square Cavity Heated From Below and Symmetrically Cooled at Both Sides: Effects of Various Dirichlet Boundary Conditions at the Bottom Wall

2005 ◽  
Author(s):  
Satyajit Roy ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Transfer Rate ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Bottom Wall ◽  
Uniform Heating ◽  
Square Cavity ◽  
Rayleigh Numbers

A numerical study is performed to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over the range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained.

Study of mixed convection in closed enclosure with a ceiling fan

2019 ◽  
Vol 86 (2) ◽  
pp. 20902 ◽  
Author(s):  
Lyes Nasseri ◽  
Omar Rahli ◽  
Djamel Eddine Ameziani ◽  
Rachid Bennacer
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rayleigh Number ◽  
Lattice Boltzmann ◽  
Transfer Rate ◽  
Numerical Study ◽  
Square Cavity ◽  
Flow Intensity ◽  
Vertical Walls ◽  
Boltzmann Method

This paper presents a numerical study of heat transfer by convection in a square cavity. The vertical walls of the cavity are differentially heated and the horizontal ones are considered adiabatic. A fan is placed in the middle of the cavity and releases a jet down. Numerical simulation was performed using the lattice Boltzmann method to show the flow patterns and the heat flux depending on the Rayleigh number (thermal convection intensity) and the Reynolds number (fan-driven flow intensity). A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re ≤ 500), Rayleigh number (10 ≤ Ra ≤ 106) and the fan position (0.2 ≤ HF ≤ 0.8). In forced convection mode, the flow structure has been mapped according to the position and the power of the fan. Three structures have emerged: two symmetrical cells, four symmetrical cells and asymmetrical structure. It has been observed that the heat transfer rate increases with the rise of Reynolds number and the reduction of the distance of the fan position from the ceiling. For the latter one, an unfavorable evolution of Nusselt number is observed for Ra > 104.

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.

An Experimental and Numerical Analysis of Natural Convective Heat Transfer in a Square Cavity With Five Discrete Heat Sources

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Giorgia Nardini ◽  
Massimo Paroncini ◽  
Raffaella Vitali
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Cavity Wall ◽  
Heat Sources ◽  
Square Cavity ◽  
Bottom Cavity ◽  
Vertical Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This paper provides an experimental and numerical investigation of natural convection in a square cavity. The square cavity is full of air (Pr = 0.71) and contains four heat sources of height hW, positioned symmetrically on the vertical walls of the cavity with a fifth heat source of height hB, located in the center of the bottom cavity wall. Two configurations are analyzed for Rayleigh numbers ranging from 1.00 × 104 to 1.00 × 105: configuration 1 has four cold sources located on the vertical cavity wall and configuration 2 has two hot and two cold sources located on the vertical cavity walls. An analysis of the holographic interferograms, numerical isotherms, streamlines, and velocity maps obtained demonstrates an increased development of natural convective heat transfer in configuration 1.

Numerical Study of Natural Convection in a Differentially-Heated Rectangular Cavity Filled with TiO2-Water Nanofluid

2011 ◽  
Vol 13 ◽  
pp. 75-80 ◽  
Author(s):  
Ghanbar Ali Sheikhzadeh ◽  
A. Arefmanesh ◽  
Mostafa Mahmoodi
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Volume Fraction ◽  
Numerical Study ◽  
Rectangular Cavity ◽  
Flow And Heat Transfer ◽  
Shallow Cavities ◽  
The Mean ◽  
Volume Method ◽  
Rayleigh Numbers

In this study, the buoyancy-driven fluid flow and heat transfer in a differentially-heated rectangular cavity filled with the TiO2-water nanofluid is investigated numerically. The left and the top walls of the cavity are maintained at constant temperatures Thand Tc, respectively, with Th> Tc.The enclosure’s right and bottom walls are kept insulated. The governing equations are discretized using the finite volume method. A proper upwinding scheme is employed to obtain stabilized solutions for high Rayleigh numbers. Using the developed code, a parametric study is undertaken, and the effects of pertinent parameters, such as, the Rayleigh number, the aspect ratio of the cavity and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the cavity are investigated. It is observed from the results that by increasing the volume fraction of the nanoparticles, the mean Nusselt number of the hot wall increases for the shallow cavities; while, the reverse trend occurs for the tall cavities. Moreover, the heat transfer enhancement utilizing nanofluid is more effective at Ra = 103.

Natural Convection From a Layered Porous Cavity With Non-Uniform Sublayers

2007 ◽  
Author(s):  
R. L. Marvel ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
System Analysis ◽  
Numerical Study ◽  
Temperature Fields ◽  
Square Cavity ◽  
Porous Cavity ◽  
Differential Heating ◽  
Vertical Walls

A numerical study has been performed to further investigate the flow and temperature fields in layered porous cavity. The geometry considered is a square cavity with 3 or 4 non-uniform sublayers and is subjected to differential heating from the vertical walls. The results obtained are used to further evaluate the feasibility of using the lumped-system analysis for heat transfer in layered porous cavities as proposed in the previous study. To this end, the effective permeabilities based on the arithmetic and harmonic averaging schemes are examined for their use in the conjunction with the lumped-system analysis.

Numerical Study of Natural Convection in a Partitioned Cavity

2008 ◽  
Author(s):  
M. Pirmohammadi ◽  
M. Ghassemi ◽  
G. A. Sheikhzadeh
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Cold Wall ◽  
Governing Equations ◽  
Square Cavity ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Energy Equations

The purpose of this study is to investigate the effect of insulated horizontal baffle placed at the hot wall of a differentially heated square cavity. The vertical walls are at different temperatures while the horizontal walls are adiabatic. In our formulation of governing equations, mass, momentum and the energy equations are applied to the cavity and the baffles. To solve the governing differential equations a finite volume code based on Patankar’s SIMPLER method is utilized [1]. The Results are presented for Rayleigh number from 104 up to 106 and are in form of streamlines, isotherms and Nusselt number. The baffle causes that at low Rayleigh number the horizontal isotherms are replaced by nearly vertical ones, specially around the baffle. Also it is found that thermal boundary layers are thickened, and the temperature gradients at the cold wall are reduced from their values for the case without baffle and this implies that a reduction in the heat transfer through the cavity occurs.

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

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