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Review Article

Second Law Analysis Through a Porous Poiseuille–Benard Channel Flow

[+] Author and Article Information
Amel Tayari

Chemical and Process Engineering Department,
National School of Engineers,
Gabès University,
Omar Ibn El Khattab Street,
Gabès 6029, Tunisia
e-mail: tayariamel@yahoo.fr

Nejib Hidouri

Chemical and Process Engineering Department,
National School of Engineers,
Gabès University,
Omar Ibn El Khattab Street,
Gabès 6029, Tunisia
e-mail: n_hidouri@yahoo.com

Mourad Magherbi

Civil Engineering Department,
Higher Institute of Applied
Sciences and Technology,
Gabès University,
Omar Ibn El Khattab Street,
Gabès 6029, Tunisia
e-mail: magherbim@yahoo.fr

Ammar Ben Brahim

Chemical and Process Engineering Department,
National School of Engineers,
Gabès University,
Omar Ibn El Khattab Street,
Gabès 6029, Tunisia
e-mail: ammar.benbrahim@enig.rnu.tn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 2, 2015; final manuscript received September 19, 2015; published online October 27, 2015. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 138(2), 020801 (Oct 27, 2015) (10 pages) Paper No: HT-15-1005; doi: 10.1115/1.4031731 History: Received January 02, 2015; Revised September 19, 2015

This paper proposes a numerical analysis of entropy generation during mixed convection inside a porous Poiseuille–Benard channel flow, where the Darcy–Brinkman model is used. Irreversibilities due to heat transfer and viscous dissipation have been derived, and then calculated by numerically solving mass, momentum, and energy conservation equations, by using a control volume finite element method (CVFEM). For a fixed value of the thermal Rayleigh (Ra = 104) and the modified Brinkman (Br* = 10−3) numbers, transient entropy generation exhibits a periodic behavior for the medium porosity ε ≥ 0.2, which is described by the onset of thermoconvective cells inside the porous channel. Highest irreversibility is obtained at ε = 0.5. More details about the effects of the Darcy, the Rayleigh, and the modified Brinkman numbers on entropy generation and heat transfer are discussed and graphically presented.

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References

Figures

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Fig. 1

Porous Poiseuille–Benard channel and coordinates system

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Fig. 2

Total entropy generation versus dimensionless time for ε = 0.95: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 3

Stream lines for ε = 0.95: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 4

Total entropy generation versus dimensionless time for different values of ε: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 5

Total entropy generation versus dimensionless time for ε = 0.1: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 6

Stream lines versus dimensionless time for ε = 0.1: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 7

Entropy generation maps for different values of the medium porosity: Re = 10, Da = 1, Pr = 0.7, Ra = 104, and Br* = 10−3

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Fig. 8

Time-averaged entropy generation versus Darcy number for different values of the Rayleigh number

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Fig. 9

Space-averaged Nusselt number versus Darcy number for different values of the Rayleigh number

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Fig. 10

Bejan number versus Darcy number for different values of the Rayleigh number

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Fig. 11

Time-averaged entropy generation versus Darcy number for different values of the modified Brinkman number

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Fig. 12

Time-averaged entropy generation versus modified Brinkman number for different values of the Rayleigh number

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