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Transport in Porous Media

, Volume 102, Issue 2, pp 167–183 | Cite as

Magnetic and Gravitational Convection of Air in a Porous Cubic Enclosure with a Coil Inclined Around the Y Axis

  • Changwei JiangEmail author
  • Wei Feng
  • Hui Zhong
  • Qiangming Zhu
  • Junyong Zeng
Article

Abstract

The natural convection heat transfer of air in a porous media can be controlled by gradient magnetic field. Thermomagnetic convection of air in a porous cubic enclosure with an electric coil inclined around the \(Y\) axis was numerically investigated. The Biot–Savart law was used to calculate the magnetic field. The governing equations in primitive variables were discretized by the finite-volume method and solved by the SIMPLE algorithm. The flow and temperature fields for the air natural convection were presented and the mean Nusselt number on the hot wall was calculated and compared. The results show that both the magnetic force and coil inclination have significant effect on the flow field and heat transfer in a porous cubic enclosure, the natural convection heat transfer of air can be enhanced or controlled by applying gradient magnetic field.

Keywords

Thermomagnetic convection Numerical simulation Magnetic force  Inclined electric coil Porous media 

List of Symbols

Variables

\({\varvec{b}}\)

Magnetic flux density (T)

\(b_{0}\)

Reference magnetic flux density, \(b_0 =\frac{\mu _\mathrm{m} i}{L}\) (T)

\({\varvec{B}}\)

Dimensionless magnetic flux

C

\(C=1+\frac{1}{T_0 \beta }\)

Da

Darcy number, \(\frac{\kappa }{L^{2}}\)

\(g\)

Gravitational acceleration (m s\(^{-2}\))

\(i\)

Electric current in a coil (A)

k

Thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

\(L\)

Length of a cubic enclosure (m)

\(Nu_{m}\)

Average Nusselt number

Pr

Prandtl number, \(Pr=\frac{\nu }{\alpha }\)

\(p\)

Pressure (Pa)

\(P\)

Dimensionless pressure

\(r\)

Radius of the coil (m)

\({\varvec{r}}\)

Position vector (m)

\({\varvec{R}}\)

Dimensionless position vector

Ra

Rayleigh number, \(Ra=\frac{g\beta (T_\mathrm{h} -T_\mathrm{c} )L^{3}}{\alpha \nu }\)

\({\varvec{s}}\)

Tangential element of a coil (m)

\({\varvec{S}}\)

Dimensionless tangential element of a coil

\(T_{0}\)

\(T_0 =\frac{T_\mathrm{h} +T_\mathrm{c} }{2}\) (K)

\(T_\mathrm{c}\)

Cold wall temperature (K)

\(T\)

Temperature (K)

\(T_\mathrm{h}\)

Hot wall temperature (K)

\(u,v,w\)

Velocity components (m s\(^{-1}\))

\(U,V,W\)

Dimensionless velocity components

\(y_\mathrm{euler}\)

Rotation angle around the \(Y\) axis (\(^{\circ }\))

\(x,y,z\)

Cartesian coordinates

\(X,Y,Z\)

Dimensionless Cartesian coordinates

\(\alpha \)

Thermal diffusivity (m s\(^{-1}\))

\(\beta \)

Thermal expansion coefficient (K\(^{-1}\))

\(\gamma \)

Dimensionless magnetic strength parameter, \(\gamma =\frac{\chi _0 b_0^2 }{\mu _\mathrm{m} gL}\)

\(\theta \)

Dimensionless temperature, \(\theta _f =\frac{T-T_0 }{T_\mathrm{h} -T_\mathrm{c}}\)

\(\mu _{0}\)

Magnetic permeability of vacuum (H m\(^{-1}\))

\(\mu _\mathrm{m}\)

Magnetic permeability (H m\(^{-1}\))

\(\nu \)

Kinematic viscosity (m\(^{2}\) s\(^{-1}\))

\(\rho \)

Density (kg m\(^{-3}\))

\(\chi \)

Magnetic susceptibility (m\(^{3}\) kg\(^{-1}\))

\(\chi _{0}\)

Reference mass magnetic susceptibility (m\(^{3}\) kg\(^{-1}\))

\(\upkappa \)

Permeability (m\(^{2}\))

Subscripts

0

Reference value

c

Hot

h

Cold

Notes

Acknowledgments

This work was financially supported by the Scientific Research Fund of Hunan Provincial Science and Technology Department (2013GK3063).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Changwei Jiang
    • 1
    • 2
    Email author
  • Wei Feng
    • 1
    • 2
  • Hui Zhong
    • 1
    • 2
  • Qiangming Zhu
    • 1
    • 2
  • Junyong Zeng
    • 1
    • 2
  1. 1.School of Energy and Power EngineeringChangsha University of Science and TechnologyChangsha China
  2. 2.Key Laboratory of Efficient and Clean Energy UtilizationCollege of Hunan ProvinceChangsha China

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