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Research Papers: Porous Media

Unstable Forced Convection in a Plane Porous Channel With Variable-Viscosity Dissipation

[+] Author and Article Information
A. Barletta, M. Celli

Department of Industrial Engineering,
Alma Mater Studiorum Università di Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy

A. V. Kuznetsov

Department of Mechanical
and Aerospace Engineering,
North Carolina State University,
Campus Box 7910,
Raleigh, NC 27695-7910
e-mail: avkuznet@ncsu.edu

D. A. Nield

Department of Engineering Science,
University of Auckland,
Private Bag 92019,
Auckland 1142, New Zealand

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 20, 2015; final manuscript received September 30, 2015; published online November 17, 2015. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 138(3), 032601 (Nov 17, 2015) (10 pages) Paper No: HT-15-1053; doi: 10.1115/1.4031868 History: Received January 20, 2015; Revised September 30, 2015

Fully developed and stationary forced convection in a plane-parallel porous channel is analyzed. The boundary walls are modeled as impermeable and subject to external heat transfer. Different Biot numbers are defined at the two boundary planes. It is shown that the combined effects of temperature-dependent viscosity and viscous heating may induce flow instability. The instability takes place at the lowest parametric singularity of the basic flow solution. The linear stability analysis is carried out analytically for the longitudinal modes and numerically for general oblique modes. It is shown that longitudinal modes with vanishingly small wave number are selected at the onset of instability.

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Figures

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Fig. 1

Two-dimensional sketch of the porous channel

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Fig. 2

Λ0 as a function of (B1, B2)

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Fig. 3

Basic flow. Plots of ηb(y) for different Λ. Each frame corresponds to a given pair of Biot numbers, (B1, B2), and Λ increases from bottom to top. The parameter Λ ranges from Λ0/20 to 19Λ0/20 in increments of Λ0/20.

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Fig. 4

Oblique modes growth rates: plots of sr versus k with B1 → ∞, B2 → ∞, and different values of Λ and P. Each frame displays three curves characterized by σ = 0,1/2,1.

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Fig. 5

Oblique modes growth rates: plots of sr versus k with B1 → ∞, B2 → 0, and different values of Λ and P. Each frame displays three curves characterized by σ = 0,1/2,1.

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Fig. 6

Oblique modes growth rates: plots of sr versus k with B1=1, B2=1, and different values of Λ and P. Each frame displays three curves characterized by σ = 0,1/2,1.

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Fig. 7

Oblique modes growth rates: plots of sr versus Λ with B1 → ∞, B2 → ∞, and different values of σ and P = 1. Each frame displays six curves characterized by different values of k: from the top k = 0,1,2,3,4,5.

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Fig. 8

Oblique modes growth rates: plots of sr versus Λ with B1 → ∞, B2 → 0, and different values of σ and P = 1. Each frame displays six curves characterized by different values of k: from the top k = 0,1,2,3,4,5.

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Fig. 9

Oblique modes growth rates: plots of sr versus Λ with B1=1, B2=1, and different values of σ and P = 1. Each frame displays six curves characterized by different values of k: from the top k = 0,1,2,3,4,5.

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