Skip to main content
SpringerLink
Log in

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

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

\({\varvec{b}}\) :

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\(^{2}\))

0:

Reference value

c:

Hot

h:

Cold

References

  • Akamatsu, M., Higano, M., Takahashi, Y., et al.: Numerical computation on the control of aerial flow by the magnetizing force in gravitational and nongravitational fields. Numer. Heat Transf. A 43(1), 9–19 (2003)

    Article  Google Scholar 

  • Akamatsu, M., Higano, M., Takahashi, Y., et al.: Numerical prediction on heat transfer phenomenon in paramagnetic and diamagnetic fluids under a vertical magnetic field gradient. IEEE Trans. Appl. Supercond. 14(2), 1674–1681 (2004)

    Article  Google Scholar 

  • Bednarz, T., Tagawa, T., Kaneda, M., et al.: Magnetic and gravitational convection of air with a coil inclined around the X axis. Numer. Heat Transf. A 46(1), 99–113 (2004)

    Article  Google Scholar 

  • Bednarz, T., Tagawa, T., Kaneda, M., et al.: Convection of air in a cubic enclosure with an electric coil inclined in general orientations. Fluid Dyn. Res. 36(2), 91–106 (2005)

    Article  Google Scholar 

  • Bednarz, T., Fornalik, E., Ozoe, H., et al.: Influence of a horizontal magnetic field on the natural convection of paramagnetic fluid in a cube heated and cooled from two vertical side walls. Int. J. Therm. Sci. 47(6), 668–679 (2008)

    Article  Google Scholar 

  • Bednarz, T.P., Lei, C., Patterson, J.C., et al.: Effects of a transverse, horizontal magnetic field on natural convection of a paramagnetic fluid in a cube. Int. J. Therm. Sci. 48(1), 26–33 (2009)

    Article  Google Scholar 

  • Braithwaite, D., Beaugnon, E., Tournier, R.: Magnetically controlled convection in a paramagnetic fluid. Nature 354, 134–136 (1991)

    Article  Google Scholar 

  • Carruthers, J.R., Wolfe, R.: Magnetothermal convection in insulation paramagnetic fluids. J. Appl. Phys. 39(12), 5718–5722 (1968)

    Article  Google Scholar 

  • Filar, P., Fornalik, E., Kaneda, M.: Three-dimensional numerical computation for magnetic convection of air inside a cylinder heated and cooled isothermally from a side wall. Int. J. Heat Mass Transf. 48(9), 1858–1867 (2005)

    Article  Google Scholar 

  • Fornalik, E., Filar, P., Tagawa, T., et al.: Experimental study on the magnetic convection in a vertical cylinder. Exp. Therm. Fluid Sci. 29(8), 971–980 (2005)

    Article  Google Scholar 

  • Gray, D.D., Huang, J., Edwards, B.F.: Two dimensional magnetothermal plumes. Int. J. Eng. Sci. 39(16), 1837–1861 (2001)

    Article  Google Scholar 

  • Huang, J., Edwards, B.F., Gray, D.D.: Magnetic control of convection in nonconducting paramagnetic fluids. Phys. Rev. E 57(1), R29–E31 (1998a)

  • Huang, J., Gray, D.D., Edwards, B.F.: Thermoconvective instability of paramagnetic fluids in a nonuniform magnetic field. Phys. Rev. E 57(5), 5564–5571 (1998b)

  • Huang, J., Gray, D.D., Edwards, B.F.: Magnetic control of convection in nonconducting diamagnetic fluids. Phys. Rev. E 58(4), 5164–5167 (1998c)

  • Kaneda, M., Tagawa, T., Ozoe, H.: Convection induced by a cusp-shaped magnetic field for air in a cube heated from above and cooled from below. J. Heat Transf. 124(1), 17–25 (2002)

    Article  Google Scholar 

  • Lu, S.S., Lee, C.H.: Enhancement of heat transfer and flow rates of air flow in a pipe with an application of magnetic field. J. Enhanc. Heat Transf. 10(1), 45–60 (2003)

    Article  Google Scholar 

  • Qi, J.: Wakayama, N.I., Yabe, A.: Attenuation of natural convection by magnetic force in electro-nonconducting fluids media. J. Cryst. Growth 204(3), 408–412 (1999)

    Article  Google Scholar 

  • Qi, J., Wakayama, N.I., Yabe, A.: Magnetic control of thermal convection in electrically non-conducting or low conducting paramagnetic fluids. Int. J. Heat Mass Transf. 44(16), 3043–3052 (2001)

    Article  Google Scholar 

  • Shigemitsu, R., Tagawa, T., Ozoe, H.: Numerical computation for natural convection of air in a cubic enclosure under combination of magnetizing and gravitational forces. Numer. Heat Transf. A 43(5), 449–463 (2003)

    Article  Google Scholar 

  • Tagawa, T., Ozoe, H.: Convective and diffusive phenomena of air in a vertical cylinder under strong magnetic field. Numer. Heat Transf. B Fundam. 41(3), 1–14 (2002)

    Google Scholar 

  • Vafai, K.: Handbook of porous media, 2nd edn. Taylor & Francis, New York (2005)

    Book  Google Scholar 

  • Wakayama, N.I.: Use of magnetic force to control convection. Proc. SPIE 3792, 48–55 (1999)

    Article  Google Scholar 

  • Wakayama, N.I., Yabe, A.: Magnetic control of thermal convection in electrically non-conducting or low conducting paramagnetic fluids. Int. J. Heat Mass Transf. 44(16), 3043–3052 (2001)

    Article  Google Scholar 

  • Wang, L.B., Wakayama, N.I.: Control of natural convection in non- and low-conducting diamagnetic fluids in a cubical enclosure using inhomogeneous magnetic fields with different directions. Chem. Eng. Sci. 57(11), 1867–1876 (2002)

    Article  Google Scholar 

  • Wang, Q., Zeng, M., Huang, Z., et al.: Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field. Int. J. Heat Mass Transf. 50(17–18), 3684–3689 (2007)

    Article  Google Scholar 

  • Yang, L., Ren, J., Song, Y., et al.: Free convection of a gas induced by a magnetic quadruple field. J. Magn. Magn. Mater. 261(3), 377–384 (2003)

    Article  Google Scholar 

  • Yang, L., Ren, J., Song, Y., et al.: Convection heat transfer enhancement of air in a rectangular duct by application of a magnetic quadrupole field. Int. J. Eng. Sci. 42(5–6), 491–507 (2004)

    Article  Google Scholar 

  • Zeng, M., Wang, Q., Huang, Z., et al.: Numerical investigation of natural convection in an enclosure filled with porous medium under magnetic field. Numer. Heat Transf. A 52(10), 959–971 (2007)

    Article  Google Scholar 

  • Zeng, M., Wang, Q., Ozoe, H., et al.: Natural convection of diamagnetic fluid in an enclosure filled with porous medium under magnetic field. Prog. Comput. Fluid Dyn. 9(2), 77–85 (2009)

    Article  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha , 410114, China

    Changwei Jiang, Wei Feng, Hui Zhong, Qiangming Zhu & Junyong Zeng

  2. Key Laboratory of Efficient and Clean Energy Utilization, College of Hunan Province, Changsha , 410114, China

    Changwei Jiang, Wei Feng, Hui Zhong, Qiangming Zhu & Junyong Zeng

Authors
  1. Changwei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiangming Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Junyong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changwei Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, C., Feng, W., Zhong, H. et al. Magnetic and Gravitational Convection of Air in a Porous Cubic Enclosure with a Coil Inclined Around the Y Axis. Transp Porous Med 102, 167–183 (2014). https://doi.org/10.1007/s11242-014-0270-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-014-0270-2

Keywords

Search

Navigation