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Journal of Heat Transfer | Volume 140 | Issue 8 | research-article
Research Papers: Thermal Systems

Optimization of the Heat Transfer Rate of Energy Systems of Conductive Bodies Confined to the Center of a Cavity

[+] Author and Article Information
Fatma Habbachi, Afif Elcafsi

Faculté des Sciences de Tunis,
Université Tunis El Manar,
LETTM,
Campus Universitaire El-Manar,
El Manar 2092, Tunisia

Fakhreddine S. Oueslati

Ecole Nationale d'Ingénieurs de Carthage,
Université de Carthage,
45 rue des entrepreneurs Charguia 2,
Tunis-Carthage 2035, Tunisia;Tianjin Key Lab of Refrigeration Technology,
Tianjin University of Commerce,
Tianjin 300134, China
e-mail: fakhreddine.oueslati@fst.rnu.tn

Rachid Bennacer

LMT/ENS-Paris-Saclay/CNRS/Université
Paris Saclay,
61 Avenue du Président Wilson,
Cachan 94235, France;Tianjin Key Lab of Refrigeration Technology,
Tianjin University of Commerce,
Tianjin 300134, China
e-mail: rachid.bennacer@ens-cachan.fr

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 8, 2017; final manuscript received November 13, 2017; published online June 29, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(8), 082802 (Jun 29, 2018) (12 pages) Paper No: HT-17-1256; doi: 10.1115/1.4038828 History: Received May 08, 2017; Revised November 13, 2017
Article
References
Figures
Tables

This paper is a numerical study conducted to investigate the conjugate flow and heat transfer occurring in three-dimensional (3D) natural convection. A cubical enclosure partially filled with porous block (central cubic) and considered in local thermal equilibrium with the fluid. The physical case considered concerns the existence of a horizontal temperature difference across the enclosure, between the left and the right wall, with the other external surfaces being adiabatic. Under these conditions, flow inside the enclosure is generated by the density (temperature) difference across the enclosure and the interaction between the solid porous blocks and the fluid. The Nusselt number on the hot and cold walls is presented to illustrate the overall characteristics of heat transfer consequence of the constrained flow inside the enclosure. The study focuses on the fluid flow and heat transfer evolution versus the dimensionless thickness of the inserted porous layer (0% ≤ η ≤ 100%) and the relative thermal conductivity of the solid matrix to that of the fluid (10−3≤λ̃≤103). The obtained complex flow structure and the corresponding heat transfer (velocity, temperature profiles) are discussed in a steady-state situation. The numerical results are illustrated in terms of isotherms, velocity, streamlines fields, and averaged Nusselt number. Thus, the results of this work can help developing new tools and to optimize the overall heat transfer rate, which is important in many electronic energy components and other energy recovering systems.
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References

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Figures

Grahic Jump Location
Fig. 1

Physical domain considered and coordinates system (a), streamtrace and thermal fields (b)

+Physical domain considered and coordinates system (a), streamtrace and thermal fields (b)
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Physical domain considered and coordinates system (a), streamtrace and thermal fields (b)
Grahic Jump Location
Fig. 2

Isotherms, velocity field, and streamlines on vertical (x–z) plane for different y positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1

+Isotherms, velocity field, and streamlines on vertical (x–z) plane for different y positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
View Large  |  Save Figure  |  Download Slide (.ppt)
Isotherms, velocity field, and streamlines on vertical (x–z) plane for different y positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
Grahic Jump Location
Fig. 3

Isotherms, velocity field, and streamlines on horizontal (y–z) plane for different x positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1

+Isotherms, velocity field, and streamlines on horizontal (y–z) plane for different x positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
View Large  |  Save Figure  |  Download Slide (.ppt)
Isotherms, velocity field, and streamlines on horizontal (y–z) plane for different x positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
Grahic Jump Location
Fig. 4

Isotherms, velocity vector field, and streamlines on vertical (x–y) plane for different z positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1

+Isotherms, velocity vector field, and streamlines on vertical (x–y) plane for different z positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
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Isotherms, velocity vector field, and streamlines on vertical (x–y) plane for different z positions, Ra = 105, Da = 10−6, η = 20%, and λ̃=1
Grahic Jump Location
Fig. 5

Isotherms, velocity field, and streamlines on vertical (x–z) midplane for different η, Ra = 105, Da = 10−6, and λ̃=1

+Isotherms, velocity field, and streamlines on vertical (x–z) midplane for different η, Ra = 105, Da = 10−6, and λ̃=1
View Large  |  Save Figure  |  Download Slide (.ppt)
Isotherms, velocity field, and streamlines on vertical (x–z) midplane for different η, Ra = 105, Da = 10−6, and λ̃=1
Grahic Jump Location
Fig. 6

Temperature profiles in the vertical (x–z) (y = 0.5) midplane for different thicknesses of the porous media block (η), Ra = 105, Da = 10−6, and λ̃=1

+Temperature profiles in the vertical (x–z) (y = 0.5) midplane for different thicknesses of the porous media block (η), Ra = 105, Da = 10−6, and λ̃=1
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature profiles in the vertical (x–z) (y = 0.5) midplane for different thicknesses of the porous media block (η), Ra = 105, Da = 10−6, and λ̃=1
Grahic Jump Location
Fig. 7

Velocity component profiles, vertical (a) and horizontal (b) on the vertical midplane, (y = 0.5) for different (η), Ra = 105, Da = 10−6, and λ̃=1

+Velocity component profiles, vertical (a) and horizontal (b) on the vertical midplane, (y = 0.5) for different (η), Ra = 105, Da = 10−6, and λ̃=1
View Large  |  Save Figure  |  Download Slide (.ppt)
Velocity component profiles, vertical (a) and horizontal (b) on the vertical midplane, (y = 0.5) for different (η), Ra = 105, Da = 10−6, and λ̃=1
Grahic Jump Location
Fig. 8

Evolution of the Nusselt number versus the thickness of the porous block (η), for Ra = 105, Da = 10−6, and λ̃=1

+Evolution of the Nusselt number versus the thickness of the porous block (η), for Ra = 105, Da = 10−6, and λ̃=1
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Evolution of the Nusselt number versus the thickness of the porous block (η), for Ra = 105, Da = 10−6, and λ̃=1
Grahic Jump Location
Fig. 9

Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different thermal (λ̃), Ra = 105, Da = 10−6, and η = 80%

+Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different thermal (λ̃), Ra = 105, Da = 10−6, and η = 80%
View Large  |  Save Figure  |  Download Slide (.ppt)
Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different thermal (λ̃), Ra = 105, Da = 10−6, and η = 80%
Grahic Jump Location
Fig. 10

Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different y positions for Ra = 105, Da = 10−6, η = 80%, and λ̃=10

+Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different y positions for Ra = 105, Da = 10−6, η = 80%, and λ̃=10
View Large  |  Save Figure  |  Download Slide (.ppt)
Isotherms, velocity field, and streamlines in the vertical (x–z) midplane for different y positions for Ra = 105, Da = 10−6, η = 80%, and λ̃=10
Grahic Jump Location
Fig. 11

Temperature profiles on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, η = 80% and different thermal conductivity ratios (λ̃)

+Temperature profiles on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, η = 80% and different thermal conductivity ratios (λ̃)
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature profiles on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, η = 80% and different thermal conductivity ratios (λ̃)
Grahic Jump Location
Fig. 12

Velocity component profiles, vertical (a) and horizontal (b) on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, and η = 80%

+Velocity component profiles, vertical (a) and horizontal (b) on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, and η = 80%
View Large  |  Save Figure  |  Download Slide (.ppt)
Velocity component profiles, vertical (a) and horizontal (b) on the vertical (x–z) midplane (y = 0.5) for Ra = 105, Da = 10−6, and η = 80%
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Fig. 13

Evolution of the Nusselt number (Nu) versus thermal conductivity ratio (λ̃) for different thicknesses of the porous block (η), Ra = 105 and Da = 10−6

+Evolution of the Nusselt number (Nu) versus thermal conductivity ratio (λ̃) for different thicknesses of the porous block (η), Ra = 105 and Da = 10−6
View Large  |  Save Figure  |  Download Slide (.ppt)
Evolution of the Nusselt number (Nu) versus thermal conductivity ratio (λ̃) for different thicknesses of the porous block (η), Ra = 105 and Da = 10−6
Grahic Jump Location
Fig. 14

Evolution of the Nusselt (Nu) number versus the porous block thickness (η), for and different Darcy numbers (Da), (λ̃=0.1 and 10), and Ra = 106

+Evolution of the Nusselt (Nu) number versus the porous block thickness (η), for and different Darcy numbers (Da), (λ̃=0.1 and 10), and Ra = 106
View Large  |  Save Figure  |  Download Slide (.ppt)
Evolution of the Nusselt (Nu) number versus the porous block thickness (η), for and different Darcy numbers (Da), (λ̃=0.1 and 10), and Ra = 106

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