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Research Papers: Porous Media

Forced Convection in a Bidisperse Porous Medium Embedded in a Circular Pipe

[+] Author and Article Information
Keyong Wang, Peichao Li

School of Mechanical Engineering,
Shanghai University of Engineering Science,
Shanghai 201620, China

Kambiz Vafai

Fellow ASME
Department of Mechanical Engineering,
University of California,
Riverside, CA 92521

Hao Cen

Office of Campus Construction,
Tianjin Foreign Studies University,
Tianjin 300204, China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 17, 2017; final manuscript received March 8, 2017; published online June 1, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(10), 102601 (Jun 01, 2017) (12 pages) Paper No: HT-17-1029; doi: 10.1115/1.4036574 History: Received January 17, 2017; Revised March 08, 2017

Compared to the regular (monodisperse) porous medium (MDPM) with one porosity scale, the bidisperse porous medium (BDPM) has two porosity scales, which may enhance the heat transfer capability. This work investigates the forced convective heat transport through a circular pipe filled with a BDPM. The two-velocity two-temperature model is utilized to describe the flow and temperature fields for both the fracture phase (macropores) and the porous phase (the matrix with micropores). The bidispersion effect is taken into account by altering the permeability of the porous phase in the medium. Analytical solutions of the velocities and temperatures for both phases are derived under the constant wall heat flux boundary condition. The local Nusselt number and heat transfer performance (HTP) are also developed to investigate how the bidispersivity affects the thermal characteristics over a wide range of parameter space.

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Figures

Grahic Jump Location
Fig. 1

Configuration of a circular pipe filled with a bidisperse porous medium

Grahic Jump Location
Fig. 2

Comparison of the present analytical dimensionless temperature distributions with those obtained by Dukhan et al. [40]

Grahic Jump Location
Fig. 3

Dimensionless temperature distributions at (Daf, DaP)=(10−2, 10−3) and ψ=1: (a) κ=0.1, Bi=0.5; (b) κ=0.1, Bi=10; (c) κ=10, Bi=0.5; and (d) κ=10, Bi=10

Grahic Jump Location
Fig. 4

Dimensionless temperature distributions at (Daf, DaP)=(1, 0.1) and ψ=1: (a) κ=0.1, Bi=0.5; (b) κ=0.1, Bi=10; (c) κ=10, Bi=0.5; and (d) κ=10, Bi=10

Grahic Jump Location
Fig. 5

Variation of the Nusselt number with the Biot number for different Darcy numbers: (a) κ=0.1, ψ=1; (b) κ=10, ψ=1; (c) κ=0.1, ψ=100; and (d) κ=10, ψ=100

Grahic Jump Location
Fig. 6

Variation of the Nusselt number with the Biot number for very high Darcy numbers: (a) κ=0.1, ψ=1; (b) κ=10, ψ=1; (c) κ=0.1, ψ=100; and (d) κ=10, ψ=100

Grahic Jump Location
Fig. 7

Variation of the Nusselt number with the effective thermal conductivity ratio for different Darcy numbers: (a) Bi=0.5, ψ=1; (b) Bi=10, ψ=1; (c) Bi=0.5, ψ=100; and (d) Bi=10, ψ=100

Grahic Jump Location
Fig. 8

Variation of the Nusselt number with the effective thermal conductivity ratio for very high Darcy numbers: (a) Bi=0.5, ψ=1; (b) Bi=10, ψ=1; (c) Bi=0.5, ψ=100; and (d) Bi=10, ψ=100

Grahic Jump Location
Fig. 9

Variation of the Nusselt number with the dimensionless momentum transfer coefficient for different combinations of Darcy numbers: (a) κ=0.1, Bi=0.5; (b) κ=0.1, Bi=10; (c) κ=10, Bi=0.5; and (d) κ=10, Bi=10

Grahic Jump Location
Fig. 10

Effect of Darcy numbers on the contours of HTP: (a) ψ=1, (Daf, Dap)=(10−2, 10−4); (b) ψ=1, (Daf, DaP)=(10−2, 10−3); (c) ψ=100, (Daf, Dap)=(10−2, 10−4); and (d) ψ=100, (Daf, DaP)=(10−2, 10−3)

Grahic Jump Location
Fig. 11

Effect of very high Darcy numbers on the contours of HTP: (a) ψ=1, (Daf, Dap)=(1, 0.01); (b) ψ=1, (Daf, DaP)=(1, 0.1); (c) ψ=100, (Daf, Dap)=(1, 0.01); and (d) ψ=100, (Daf, DaP)=(1, 0.1)

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