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 Effect of Fin Number and Position on Non-linear Characteristics of Natural Convection Heat Transfer in Internally Finned Horizontal Annulus

2021 ◽  
Vol 9 ◽  
Author(s):  
Kun Zhang ◽  
Yu Zhang ◽  
Xiaoyu Wang ◽  
Liangbi Wang
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Convection Heat Transfer ◽  
The Self ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Simpler Algorithm

Detailed numerical calculations are performed for investigating the effect of fin number and position on unsteady natural convection heat transfer in internally finned horizontal annulus. The SIMPLER algorithm with Quick scheme is applied for solving the Navier Stokes equations of flow and heat transfer. The results show that the heat transfer rate in annulus with fins increases with the increasing numbers of fin and Rayleigh numbers. For Ra = 2 × 105, the effect of numbers of fins and fins position at the bottom part on the unsteady solutions can be neglected, because the self-oscillation phenomenon is mainly affected by natural convection at the upper part of annulus. Although the fin positions cannot increase heat transfer rate significantly in the case of four fins, the self-oscillated solutions can be suppressed by altering fins position.

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.

scholarly journals Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall

2014 ◽  
Vol 18 (4) ◽  
pp. 1119-1132 ◽  
Author(s):  
Saeid Jani ◽  
Mostafa Mahmoodi ◽  
Meysam Amini ◽  
Jafar Jam
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Constant Temperature ◽  
Convection Heat Transfer ◽  
Bottom Wall ◽  
Square Cavity ◽  
Remarkable Effect ◽  
Simpler Algorithm ◽  
The Right ◽  
Volume Method

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature Tc, while the bottom wall is kept at a constant temperature Th ,with Th > Tc. The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

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.

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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