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Research Papers: Porous Media

Thermal Nonequilibrium and Viscous Dissipation in the Thermal Entrance Region of a Darcy Flow With Streamwise Periodic Boundary Conditions

[+] Author and Article Information
A. Barletta

DIENCA, Alma Mater Studiorum—Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italyantonio.barletta@unibo.it

E. Rossi di Schio

DIENCA, Alma Mater Studiorum—Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italyeugenia.rossidischio@unibo.it

L. Selmi

DIENCA, Alma Mater Studiorum—Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italylorenzo.selmi@studio.unibo.it

J. Heat Transfer 133(7), 072602 (Apr 06, 2011) (7 pages) doi:10.1115/1.4003557 History: Received August 28, 2010; Revised January 11, 2011; Published April 06, 2011; Online April 06, 2011

The thermal entrance region in a plane-parallel channel filled by a fluid saturated porous medium is investigated with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the thermal entrance region are solved numerically by a finite element method and by the method of lines.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 6

Plots of Num(∞)/Br versus H for γ=0.1 (a), γ=0.8 (b), γ=2 (c), and γ=5 (d)

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Figure 7

Plots of L∗ versus Ω for γ=0.8 and Br=5 and for H=0.01 (a), H=0.5 (b), H=2 (c), and H=5 (d)

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Figure 1

Plots of Tf (upper frame) and of Ts (lower frame) versus x with y=0,0.6,0.8,1 for H=2, γ=0.8, Ω=1, and Br=5

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Figure 2

Plots of Tf (upper frame) and of Ts (lower frame) versus x with y=0 and for H=2, γ=0.8, Ω=1, and Br=5; comparison between the method of lines (solid line) and the finite element method (circles)

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Figure 3

Contour plots of the fluid phase (upper frame) and of the solid phase (lower frame) temperature distributions for H=2, γ=0.8, Ω=1, and Br=1

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Figure 4

Plots of Tf (upper frame) and of Ts (lower frame) versus x with y=0 and for H=2, γ=0.8, Ω=1, and Br=5; comparison between the numerical thermal entrance solution (a) and the analytical asymptotic solution (b)

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Figure 5

Plots of Tf (upper frame) and of Ts (lower frame) versus x with y=0 and for H=2, γ=0.8, Ω=10, and Br=5; comparison between the numerical thermal entrance solution (a) and the analytical asymptotic solution (b)

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