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Research Papers: Natural and Mixed Convection

Unsteady Conjugate Natural Convective Heat Transfer and Entropy Generation in a Porous Semicircular Cavity

[+] Author and Article Information
Ali J. Chamkha

Mem. ASME
Mechanical Engineering Department,
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
RAK Research and Innovation Center,
American University of Ras Al Khaimah,
Ras Al Khaimah 10021, United Arab Emirates

Igor V. Miroshnichenko, Mikhail A. Sheremet

Laboratory on Convective Heat and
Mass Transfer,
Tomsk State University,
Tomsk 634050, Russia

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 12, 2016; final manuscript received December 4, 2017; published online March 9, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(6), 062501 (Mar 09, 2018) (19 pages) Paper No: HT-16-1506; doi: 10.1115/1.4038842 History: Received August 12, 2016; Revised December 04, 2017

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall.

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Figures

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Fig. 1

Physical model and coordinate system

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Fig. 2

Flow chart of the used numerical algorithm

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Fig. 3

Comparison of streamlines and isotherms for R = 2.0 and Ra = 200: (a) numerical results of Charrier-Mojtabi [47] and (b) present study

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Fig. 4

Comparison of local entropy generation due to heat transfer Sgen,ht and fluid friction Sgen,ff for Ra = 103: (a) numerical data of Ilis et al. [51], (b) numerical data of Bhardwaj et al. [34], and (c) present results

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Fig. 5

Comparison of local entropy generation due to heat transfer Sgen,ht and fluid friction Sgen,ff for Ra = 105: (a) numerical data of Ilis et al. [51], (b) numerical data of Bhardwaj et al. [34], and (c) present results

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Fig. 6

Comparison of streamlines ψ and isotherms θ at D = 0.5, Λ = 1: (a) numerical results of Saeid [15] and (b) present study

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Fig. 7

Comparison of streamlines ψ and isotherms θ at D = 0.2, Λ = 0.1: (a) numerical results of Saeid [15] and (b) present study

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Fig. 8

Variations of (a) Nuinterface¯, (b) Beavg, and (c) Sgen,avg versus the dimensionless time and mesh parameters for Ra = 105, Pr = 0.7, Da = 10−2, Λ = 1.0

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Fig. 9

Variations of (a) Beavg and (b) Sgen,avg versus the Rayleigh number, Darcy number, and the irreversibility factor for Λ = 5

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Fig. 10

Isolines of ψ and θ for Da = 10−3, Λ = 5, τ = 200: (a) Ra = 104, (b) Ra = 105, and (c) Ra = 106

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Fig. 11

Isolines of Sgen,ht and Sgen,ff for Da = 10−3, Λ = 5, τ = 200: (a) Ra = 104, (b) Ra = 105, and (c) Ra = 106

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Fig. 12

Variations of (a) Nuinterface¯ and (b) |ψ|maxRa⋅Pr versus the dimensionless time and Rayleigh number for Da = 10−3, Λ = 5.0

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Fig. 13

Variations of (a) Beavg and (b) Sgen,avg versus the dimensionless time and Rayleigh number for Da = 10−3, Λ = 5.0

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Fig. 14

Isolines of ψ and θ for Ra = 105, Λ = 5, τ = 200: (a) Da = 10−5, (b) Da = 10−4, (c) Da = 10−3, and (d) Da = 10−2

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Fig. 15

Isolines of Sgen,ht and Sgen,ff for Ra = 105, Λ = 5, τ = 200: (a) Da = 10−5, (b) Da = 10−4, (c) Da = 10−3, and (d) Da = 10−2

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Fig. 16

Variations of (a) Nuinterface¯ and (b) |ψ|maxRa⋅Pr versus the dimensionless time and Darcy number for Ra = 105, Λ = 5.0

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Fig. 17

Variations of (a) Beavg and (b) Sgen,avg versus the dimensionless time and Darcy number for Ra = 105, Λ = 5.0

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Fig. 18

Isolines of ψ and θ for Ra = 105, Da = 10−3, τ = 200: (a) Λ = 1, (b) Λ = 5, (c) Λ = 20, and (d) Λ = ∞

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Fig. 19

Isolines of Sgen,ht and Sgen,ff for Ra = 105, Da = 10−3, τ = 200: (a) Λ = 1, (b) Λ = 5, (c) Λ = 20, and (d) Λ = ∞

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Fig. 20

Variations of (a) Nuinterface¯ and (b) |ψ|maxRa⋅Pr versus the dimensionless time and thermal conductivity ratio for Ra = 105, Da = 10−3

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Fig. 21

Variations of (a) Beavg and (b) Sgen,avg versus the dimensionless time and thermal conductivity ratio for Ra = 105, Da = 10−3

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