Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T08:54:01.403Z Has data issue: false hasContentIssue false
  • English
  • Français

Study of Heat Transfer Control with Magnetic Field Using Higher Order Finite Difference Scheme

Part of: Partial differential equations, boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  27 January 2016

R. Sivakumar ,
S. Vimala ,
S. Damodaran  and
T. V. S. Sekhar
R. Sivakumar
Affiliation:
Department of Physics, Pondicherry University, Puducherry-605 014, India
S. Vimala
Affiliation:
Department of Mathematics, Pondicherry Engineering College, Puducherry-605 014, India
S. Damodaran
Affiliation:
Department of Mathematics, Bharathidasan Govt. College for Women, Puducherry-605 003, India
T. V. S. Sekhar*
Affiliation:
School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-751 007, India
*
*Corresponding author., Email:rsk.phy@pondiuni.edu.in (R. Sivakumar), vimalaks@pec.edu (S. Vimala), sreedamo@gmail.com (S. Damodaran), sekhartvs@iitbbs.ac.in (T. V. S. Sekhar)
Get access

Abstract.

The control of convective heat transfer from a heated circular cylinder immersed in an electrically conducting fluid is achieved using an externally imposed magnetic field. A Higher Order Compact Scheme (HOCS) is used to solve the governing energy equation in cylindrical polar coordinates. The HOCS gives fourth order accurate results for the temperature field. The behavior of local Nusselt number, mean Nusselt number and temperature field due to variation in the aligned magnetic field is evaluated for the parameters 5≤Re≤40, 0≤N≤20 and 0.065≤Pr≤7. It is found that the convective heat transfer is suppressed by increasing the strength of the imposed magnetic field until a critical value of N, the interaction parameter, beyond which the heat transfer increases with further increase in N. The results are found to be in good agreement with recent experimental studies.

Keywords

Higher Order Compact Schemeforced convectionmagnetic fieldlow Rm approximation

MSC classification

Secondary: 76D05: Navier-Stokes equations 65N06: Finite difference methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 449 - 463
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Davidson, P. A., Magnetohydrodynamics in materials processing, Annu. Rev. Fluid Mech., 31 (1999), pp. 273–300.Google Scholar
[2]Boynton, J. H., Experimental study of an ablating sphere with hydromagnetic effect included, J. Aerosp. Sci., 27 (1960), pp. 306.Google Scholar
[3]Uda, N., Miyazawa, A., Inoue, S., Yamaoka, N., Horiike, H. and Miyazaki, K., Forced convection heat transfer and temperature fluctuations of Lithium under transverse magnetic fields, J. Nuc. Sci. Tech., 38 (2001), pp. 936–943.Google Scholar
[4]Yokomine, T., Takeuchi, J., Nakaharai, H., Satake, S., Kunugi, T., Morley, N. B., and Abdou, M. A., Experimental investigation of turbulent heat transfer of high Prandtl number fluid flow under strong magnetic field, Fusion Sci. Tech., 52 (2007), pp. 625–629.Google Scholar
[5]Kenjeres, S., Electromagnetic enhancement of turbulent heat transfer, Phys. Rev. E, 78 (2008), 066309.Google Scholar
[6]Hussam, W. K. and Sheard, G. J., Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder placed near the heated side-wall, Int. J. Heat Mass Transfer, 67 (2013), pp. 944–954.Google Scholar
[7]Chatterjee, D. and Chatterjee, K., Wall-bounded flow and heat transfer around a circular cylinder at low Reynolds and Hartmann numbers, Heat Transfer-Asian Research, 42 (2013), pp. 133–150.Google Scholar
[8]Ghadi, A. Z., Goodarzian, H., Bandpy, M. G. and Valipour, M. S., Numerical investigation of magnetic effect on forced convection around two-dimensional circular cylinder embedded in porous media, Eng. Appl. Comput. Fluid Mech., 6 (2012), pp. 395–402.Google Scholar
[9]Lahjomri, J., Caperan, P. and Alemany, A., The cylinder wake in a magnetic field aligned with the velocity, J. Fluid Mech., 253 (1993), pp. 421–448.Google Scholar
[10]Shatrov, V., Mutschke, G. and Gerbeth, G., Numerical simulation of the two-dimensional MHD-flow around a circular cylinder, Magnetohydrodynamics, 33 (1997), pp. 5–15.Google Scholar
[11]Mutschke, G., Gerbeth, G., Shatrov, V. and Tomboulides, A., Two- and three dimensional instabilities of the cylinder wake in an external magnetic field, Phys. Fluids, 9 (1997), pp. 3114–3116.Google Scholar
[12]Yoon, H. S., Chun, H. H., Ha, M. Y. and Lee, H. G., A numerical study on the fluid flow and heat transfer around a circular cylinder in an aligned magnetic field, Int. J. Heat Mass Trans., 47 (2004), pp. 4075–4087.Google Scholar
[13]Sanyasiraju, Y. V. S. S. and Manjula, V., Flow past an impulsively started circular cylinder using a higher-order semicompact scheme, Phys. Rev. E, 72 (2005), 016709.Google Scholar
[14]Sekhar, T. V. S. and Hema Sundar Raju, B., An efficient higher order compact scheme to capture heat transfer solutions in spherical geometry, Comput. Phys. Commun., 183 (2012), pp. 2337–2345.CrossRefGoogle Scholar
[15]Sekhar, T. V. S. and Hema Sundar Raju, B., Spherical geometry HOC scheme to capture low pressures within a wake, East Asian J. Appl. Math., 3 (2013), pp. 93–106.Google Scholar
[16]Bramely, J. S., Magnetohydrodynamic flow past a circular cylinder, J. Appl. Math. Phys., 25 (1974), pp. 409–416.Google Scholar
[17]Bramely, J. S., Magnetohydrodynamic flow past a circular cylinder-II, J. Appl. Math. Phys., 26 (1975), pp. 203–209.Google Scholar
[18]Sekhar, T. V. S., Sivakumar, R. and Ravi Kumar, T. V. R., Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers, J. Appl. Math., 2005 (2005), pp. 183–203.Google Scholar
[19]Juncu, G. H., Conjugate heat/mass transfer from a circular cylinder with an internal heat/ mass source in laminar cross flow at low Reynolds numbers, Int. J. Heat Mass Transfer, 48 (2005), pp. 419–424.Google Scholar
[20]Dennis, S. C. R., Hudson, J. D. and Smith, N., Steady laminar forced convection from a circular cylinder at low Reynolds numbers, Phys. Fluids, 11 (1968), pp. 933–940.CrossRefGoogle Scholar
[21]Kurdyumov, V. N. and Fernandez, E., Heat transfer from a circular cylinder at low Reynolds numbers, ASME J. Heat Transfer, 120 (1998), pp. 72–75.CrossRefGoogle Scholar