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Heat and Mass Transfer into a Porous Annulus Found Between Two Horizontal Concentric Circular Cylinders

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Applied Mechanics, Behavior of Materials, and Engineering Systems

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

This numerical work refers to the study of natural convection driven by cooperating thermal and solutal buoyancy forces, into a porous annulus found between a cold (less concentric) outer circular enclosure and a hot (concentric) inner cylinder. The physical model for the momentum conservation equation makes use of the Brinkman extension of the classical Darcy equation, the set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. To account for the effects of the main parameters such the Lewis number, the buoyancy ratio and the cylinders aspect ratio as well, heat and mass transfer characteristics are inspected. Summarizing the numerical predictions, the dynamic, thermal and solutal fields are found strongly dependent on the governing studied parameters. It is to note that the validity of the computing code used was ascertained by comparing our results with the numerical ones already available in the literature.

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Abbreviations

C:

Dimensional mass fraction

D:

Mass diffusivity, m2 s−1

Dint :

Inner cylinder diameter, m

Dext :

Outer cylinder diameter, m

Da:

Darcy number, (K/D 2ext )

K:

Porous medium permeability, m2

Le:

Lewis number

N:

Buoyancy ratio, (βC/βT)

p*:

Pressure, Pa

P:

Dimensionless pressure

Pr:

Prandtl number (ν/α)

Ra:

Thermal Rayleigh number (g βT ∆T D 3ext / ν2)

Ra*:

Porous thermal Rayleigh number (Ra Da)

T:

Dimensional Temperature, K

u:

V, Velocity components, m s−1

U:

V, Dimensionless velocity components

x:

Y, Cartesian coordinates, m

X:

Y, Dimensionless Cartesian coordinates

α:

Thermal diffusivity, m2 s−1

βT :

Thermal expansion coefficient, K−1

βC :

Solutal expansion coefficient

ε:

Porosity of the porous medium

ν:

Kinematic viscosity, m2 s−1

Ï•:

Dimensionless concentration

θ:

Dimensionless temperature

Ψ:

Stream function

h:

Hot

c:

Cold

+:

Concentric

–:

Less concentric

References

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Author information

Authors and Affiliations

  1. Laboratory of Transport Phenomena, USTHB, 16111, Algiers, Algeria

    Karim Ragui, Abdelkader Boutra & Youb Khaled Benkahla

  2. Preparatory School of Science and Technology, 16111, Algiers, Algeria

    Abdelkader Boutra

  3. LMT, Superior Normal School Cachan, 94235, Cedex, France

    Rachid Bennacer

Authors
  1. Karim Ragui
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  2. Abdelkader Boutra
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  3. Rachid Bennacer
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  4. Youb Khaled Benkahla
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Corresponding author

Correspondence to Karim Ragui .

Editor information

Editors and Affiliations

  1. Lab for Advanced Mechanics, USTHB, Bab-Ezzouar, Algeria

    Taoufik Boukharouba

  2. Metz, France

    Guy Pluvinage

  3. Laboratoire de Mécanique Avancée (LMA), (USTHB), Bab-Ezzouar, Algeria

    Krimo Azouaoui

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Ragui, K., Boutra, A., Bennacer, R., Benkahla, Y.K. (2017). Heat and Mass Transfer into a Porous Annulus Found Between Two Horizontal Concentric Circular Cylinders. In: Boukharouba, T., Pluvinage, G., Azouaoui, K. (eds) Applied Mechanics, Behavior of Materials, and Engineering Systems. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-41468-3_43

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  • DOI: https://doi.org/10.1007/978-3-319-41468-3_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41467-6

  • Online ISBN: 978-3-319-41468-3

  • eBook Packages: EngineeringEngineering (R0)

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