NATURAL CONVECTION SIMULATIONS OF BINGHAM FLUID WITHIN A SQUARE CAVITY WITH DIFFERENTIALLY HEATED VERTICAL WALLS

2017 ◽  
Vol 20 (1) ◽  
pp. 93-106
Author(s):  
Oussama Seghier ◽  
Lakhdar Rahmani ◽  
Belkacem Draoui ◽  
Marc Médale ◽  
Chérifa Abid
Keyword(s):  
Natural Convection ◽  
Bingham Fluid ◽  
Square Cavity ◽  
Vertical Walls

Numerical Investigation of the Onset of Steady Natural Convection in a Square Cavity Partially Filled With a Single Porous Block

2014 ◽  
Author(s):  
Vinicius Daroz ◽  
Silvio L. M. Junqueira ◽  
Admilson T. Franco ◽  
José L. Lage
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Contour Plot ◽  
Viscous Effects ◽  
Square Cavity ◽  
Heterogeneous Model ◽  
Porous Block ◽  
Vertical Walls ◽  
Volume Method

The critical Rayleigh number at the onset of natural convection within a square cavity filled with a centralized porous block was investigated. The porous medium is modeled by using the heterogeneous model and the governing equations are solved for each phase separately. The thermal gradient is applied from the bottom to the top horizontal walls while the vertical walls are kept adiabatic. The amount of solid within the cavity was kept constant by fixing both external and internal porosity in 36% and 40%, respectively. The equations are solved using the Finite Volume Method and the interpolation scheme for the convective terms is the Hybrid Scheme. For the pressure-velocity coupling, the SIMPLEC method is used. The effects on the conductive-convective regime transition, reads critical Rayleigh Number, characterized by the average Nusselt number and the heatlines contour plot, was investigated by varying the Rayleigh number and the porous block permeability. The results show that the so called critical Rayleigh number is affected by the block permeability. As the permeability decreases, the flow tends to recirculate around the block being squeezed against the cavity walls and therefore, more susceptible to viscous effects. A correlation to the critical Rayleigh number is presented as a function of the agglomerate permeability showing that the higher the permeability the lower the amount of energy required to trigger the convection.

Scaling of the Turbulent Natural Convection Flow in a Heated Square Cavity

1994 ◽  
Vol 116 (2) ◽  
pp. 400-408 ◽  
Author(s):  
R. A. W. M. Henkes ◽  
C. J. Hoogendoorn
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection ◽  
Convection Boundary ◽  
Vertical Walls ◽  
Rayleigh Numbers

By numerically solving the Reynolds equations for air and water in a square cavity, with differentially heated vertical walls, at Rayleigh numbers up to 1020 the scalings of the turbulent natural convection flow are derived. Turbulence is modeled by the standard k–ε model and by the low-Reynolds-number k–ε models of Chien and of Jones and Launder. Both the scalings with respect to the Rayleigh number (based on the cavity size H) and with respect to the local height (y/H) are considered. The scalings are derived for the inner layer, outer layer, and core region. The Rayleigh number scalings are almost the same as the scalings for the natural convection boundary layer along a hot vertical plate. The scalings found are almost independent of the k–ε model used.

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.

Study of Adiabatic Obstacles on Natural Convection in a Square Cavity Using Lattice Boltzmann Method

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Pawan Karki ◽  
Ajay Kumar Yadav ◽  
D. Arumuga Perumal
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Transfer Rate ◽  
Square Cavity ◽  
Square Enclosure ◽  
The Core ◽  
Vertical Walls ◽  
Boltzmann Method

This study involves the effect of adiabatic obstacles on two-dimensional natural convection in a square enclosure using lattice Boltzmann method (LBM). The enclosure embodies square-shaped adiabatic obstacles with one, two, and four in number. The single obstacle in cavity is centrally placed, whereas for other two configurations, a different arrangement has been made such that the core fluid zone is not hampered. The four boundaries of the cavity considered here consist of two adiabatic horizontal walls and two differentially heated vertical walls. The current study covers the range of Rayleigh number (103 ≤ Ra ≤ 106) and a fixed Prandtl number of 0.71 for all cases. The effect of size of obstacle is studied in detail for single obstacle. It is found that the average heat transfer along the hot wall increases with the increase in size of obstacle until it reaches an optimum value and then with further increase in size, the heat transfer rate deteriorates. Study is carried out to delineate the comparison between the presences of obstacle in and out of the conduction dominant zone in the cavity. The number of obstacles (two and four) outside of this core zone shows that heat transfer decreases despite the obstacle being adiabatic in nature.

Effects of the Dimension of a Localized Heat Source on the Natural Convection in Square Enclosures: Comparison Between Numerical and Experimental Investigation

2003 ◽  
Author(s):  
Massimo Paroncini ◽  
Barbara Calcagni ◽  
Federico Marsili
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Lower Surface ◽  
Source Surface ◽  
Electronic Components ◽  
Square Cavity ◽  
Symmetrical Form ◽  
Partial Heating ◽  
Vertical Walls ◽  
Double Exposure Holographic Interferometry

The present study investigates experimentally and numerically the natural convection of air in square enclosures with a localized heat source from below and symmetrical cooling from the sides. The heat source was centered on the bottom wall and the study analysed the effect of the variation in the heat source length on the natural convection inside the square cavity; the length of the heat source investigated are 1/5 and 2/5 of the wall The cooling was achieved by the two vertical walls and all the other zones were adiabatic; the symmetrical cooling from the sides is expected to be an efficient cooling option while the partial heating at the lower surface simulates the electronic components such as a chip. The experimental data are obtained by measuring the temperature distribution in the air layer by the real-time and double-exposure holographic interferometry and the numerical investigation was conducted using the commercial finite volumes code Fluent 6.0. Convection was studied for Rayleigh number from 103 to 106. Different convection forms were obtained depending on Ra and on the heat source length. The Nusselt number was evaluated on the heat source surface and it showed a symmetrical form raising near the heat source borders. Graphs with relations between average Nu, Ra and the heat source length are finally presented.

Natural Convection in a Square Cavity With Thin Porous Layers on Its Vertical Walls

1991 ◽  
Vol 113 (4) ◽  
pp. 892-898 ◽  
Author(s):  
P. Le Breton ◽  
J. P. Caltagirone ◽  
E. Arquis
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Layer Thickness ◽  
Stokes Equations ◽  
Square Cavity ◽  
Porous Layers ◽  
Simpler Algorithm ◽  
Main Effect ◽  
Vertical Walls ◽  
Benchmark Solutions

Natural convection in a square cavity in which differentially heated vertical walls are covered with thin porous layers is studied by using a control volume formulation and a SIMPLER algorithm for pressure-velocity coupling. Comparisons with benchmark solutions for natural convection in fluid-filled cavities are first presented for Rayleigh numbers up to 108. The problem of the square cavity with thin porous layers on its vertical walls is then studied by using a modified form of the Navier-Stokes equations by addition of a Darcy term. It is shown that the main effect of the introduction of porous layers is to produce a large decrease of the overall Nusselt number when the permeability is reduced. The higher the Rayleigh number is, the stronger is the decrease, and obviously the decrease also increases with the layer thickness. Moreover, porous layers having a thickness of the order of the boundary layer thickness are sufficient, and taking thicker ones only induces a small decrease of the heat transfer. The main effect of porous layers is to reduce the upwind flow and then to decrease the convective heat transfer.

scholarly journals Natural convection in a square cavity with partially active vertical walls: Time-periodic boundary condition

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
N. Nithyadevi ◽  
P. Kandaswamy ◽  
S. Sivasankaran
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Active Regions ◽  
Governing Equations ◽  
Square Cavity ◽  
Side Walls ◽  
Vertical Walls ◽  
Volume Method ◽  
Time Periodic

A numerical study of transient natural convection in a square cavity with partly thermally active side walls is introduced. The thermally active regions of the side walls are periodic in time. Top and bottom of the cavity are adiabatic. Nine different positions of the thermally active zones are considered. The governing equations are solved using control volume method with power-law scheme. The results are obtained for various values of amplitude, period, and Grashof numbers ranging from104–106and different thermally active situations. It is found that the average heat transfer increases by increasing amplitude forP=1,5, and decreasing forP=3. The average Nusselt number behaves nonlinearly as a function of period.

Laminar Natural Convection in an Air-Filled Square Cavity With Partitions on the Top Wall

2009 ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Thermal Effect ◽  
Rear Surface ◽  
Vertical Wall ◽  
Square Cavity ◽  
Recirculating Flow ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Temperature And Flow Fields

The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number GrH of approximately 1.3 × 108) and non-dimensional top wall temperatures θT of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height HP/H of 0.0625 and 0.125 attached to the top wall at x/H = 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and θT. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and Nu near the corner region were affected by the partition height due to the changes in the recirculating flow and due to the thermal effect on the rear surface of the partition.

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