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Flow and heat over a rotating disk subject to a uniform horizontal magnetic field

  • Mustafa Turkyilmazoglu EMAIL logo
Published/Copyright: January 17, 2022
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 77 Issue 4

Abstract

Magnetic field is often applied to stabilize the flow field in real life applications of fluid mechanics problems. In the present work, it is employed a horizontal uniform magnetic field to regularize the flow field triggered due to a rotating disk. The energy equation is also studied subjected to such a horizontal magnetic field. The applied horizontal magnetic field is different from the well-known applied external vertical magnetic field. It is shown that the horizontal magnetic field leads to a similarity system of equations with the help of the traditional von Kármán similarity transformations. The effects of such a magnetic field on the development of velocity and temperature fields are then numerically investigated. The existence of exact series solutions in terms of decaying exponential functions is further discussed. The critical roles of horizontal magnetic field on the physical quantities involving the local wall shears, torque and the heat transfer rate are finally highlighted.

Keywords: exponential solutions; heat transfer; horizontal magnetic field; rotating disk; similarity equations; wall shears
Corresponding author: Mustafa Turkyilmazoglu, Department of Mathematics, Hacettepe University, Beytepe, Ankara 06532, Turkey; and Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, E-mail:

  1. Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author reports no conflict of interest.

References

[1] I. V. Shevchuk, Modelling of Convective Heat and Mass Transfer in Rotating Flows, Switzerland, Springer, 2016.10.1007/978-3-319-20961-6Search in Google Scholar

[2] T. von Kármán, “Uber laminare und turbulente reibung,” Z. Angew. Math. Mech., vol. 1, p. 233, 1921. https://doi.org/10.1002/zamm.19210010401.Search in Google Scholar

[3] W. G. Cochran, “The flow due to a rotating disk,” Proc. Camb. Phil. Soc., vol. 30, pp. 365–375, 1934. https://doi.org/10.1017/s0305004100012561.Search in Google Scholar

[4] E. M. Sparrow and J. L. Gregg, “Heat transfer from a rotating disk to fluids of any Prandtl number,” J. Heat Tran., vol. 81, pp. 249–251, 1959. https://doi.org/10.1115/1.4008195.Search in Google Scholar

[5] J. A. D. Ackroyd, “On the steady flow produced by a rotating disc with either surface suction or injection,” J. Eng. Phys., vol. 12, pp. 207–259, 1978. https://doi.org/10.1007/bf00036459.Search in Google Scholar

[6] M. R. Malik, “The neutral curve for stationary disturbances in rotating-disk flow,” J. Fluid Mech., vol. 164, pp. 275–287, 1986. https://doi.org/10.1017/s0022112086002550.Search in Google Scholar

[7] M. Turkyilmazoglu, J. W. Cole, and J. S. B. Gajjar, “Absolute and convective instabilities in the compressible boundary layer on a rotating disk,” Theor. Comput. Fluid Dynam., vol. 14, pp. 21–37, 2000. https://doi.org/10.1007/s001620050123.Search in Google Scholar

[8] C. Davies and P. W. Carpenter, “Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer,” J. Fluid Mech., vol. 486, pp. 287–329, 2003. https://doi.org/10.1017/s0022112003004701.Search in Google Scholar

[9] M. Turkyilmazoglu and N. Uygun, “Compressible modes of the rotating disk boundary layer flow leading to absolute instability,” Stud. Appl. Math., vol. 115, pp. 1–20, 2005. https://doi.org/10.1111/j.1467-9590.2005.01549.Search in Google Scholar

[10] M. Turkyilmazoglu and P. Senel, “Heat and mass transfer of the flow due to a rotating rough and porous disk,” Int. J. Therm. Sci., vol. 63, pp. 146–158, 2013. https://doi.org/10.1016/j.ijthermalsci.2012.07.013.Search in Google Scholar

[11] M. Turkyilmazoglu, “Nanofluid flow and heat transfer due to a rotating disk,” Comput. Fluids., vol. 94, pp. 139–146, 2014. https://doi.org/10.1016/j.compfluid.2014.02.009.Search in Google Scholar

[12] E. Appelquist, S. Imayama, P. H. Alfredsson, P. Schlatter, and R. J. Lingwood, “Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory,” Eur. J. Mech. B Fluid, vol. 55, pp. 170–181, 2016. https://doi.org/10.1016/j.euromechflu.2015.09.010.Search in Google Scholar

[13] H. P. Pao, “Magnetohydrodynamic flows over a rotating disk,” AIAA J., vol. 6, pp. 1285–1291, 1968. https://doi.org/10.2514/3.4735.Search in Google Scholar

[14] T. Watanabe and T. Oyama, “Magnetohydrodynamic boundary layer flow over a rotating disk,” Z. Angew. Math. Mech., vol. 71, pp. 522–524, 1992.10.1002/zamm.19910711217Search in Google Scholar

[15] P. D. Ariel, “On computation of MHD flow near a rotating-disk,” Z. Angew. Math. Mech., vol. 82, pp. 235–246, 2001.10.1002/1521-4001(200204)82:4<235::AID-ZAMM235>3.0.CO;2-LSearch in Google Scholar

[16] H. A. Jasmine and J. S. B. Gajjar, “Convective and absolute instability in the incompressible boundary layer on a rotating disk in the presence of a uniform magnetic field,” J. Eng. Math., vol. 52, pp. 337–353, 2005. https://doi.org/10.1007/s10665-005-2732-6.Search in Google Scholar

[17] M. Turkyilmazoglu, “Primary instability mechanisms on the magnetohydrodynamic boundary layer flow over a rotating disk subject to a uniform radial flow,” Phys. Fluids, vol. 21, p. 7, 2009. https://doi.org/10.1063/1.3177353.Search in Google Scholar

[18] M. Turkyilmazoglu, “Unsteady mhd flow with variable viscosity: applications of spectral scheme,” Int. J. Therm. Sci., vol. 49, pp. 563–570, 2010. https://doi.org/10.1016/j.ijthermalsci.2009.10.007.Search in Google Scholar

[19] M. Turkyilmazoglu, “Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field,” Acta Mech., vol. 218, pp. 237–245, 2011. https://doi.org/10.1007/s00707-010-0416-4.Search in Google Scholar

[20] M. Turkyilmazoglu, “Heat and mass transfer on the MHD fluid flow due to a porous rotating disk with hall current and variable properties,” J. Heat Tran., vol. 133, 2011. https://doi.org/10.1115/1.4002634.Search in Google Scholar

[21] T. Fang, “Flow over a stretchable disk,” Phys. Fluids, vol. 19, pp. 128105.1–128105.4, 2007. https://doi.org/10.1063/1.2823572.Search in Google Scholar

[22] M. Turkyilmazoglu, “Wall stretching in magnetohydrodynamics rotating flows in inertial and rotating frames,” J. Thermophys. Heat Tran., vol. 25, pp. 606–613, 2011. https://doi.org/10.2514/1.t3750.Search in Google Scholar

[23] M. Turkyilmazoglu, “MHD fluid flow and heat transfer due to a stretching rotating disk,” Int. J. Therm. Sci., vol. 51, pp. 195–201, 2012. https://doi.org/10.1016/j.ijthermalsci.2011.08.016.Search in Google Scholar

[24] M. Turkyilmazoglu, “Three dimensional MHD stagnation flow due to a stretchable rotating disk,” Int. J. Heat Mass Tran., vol. 55, pp. 6959–6965, 2012. https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.089.Search in Google Scholar

[25] M. Turkyilmazoglu, “MHD fluid flow and heat transfer due to a shrinking rotating disk,” Comput. Fluids., vol. 90, pp. 51–56, 2014. https://doi.org/10.1016/j.compfluid.2013.11.005.Search in Google Scholar

[26] M. Sheikholeslami and D. D. Ganji, “Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet,” J. Mol. Liq., vol. 194, pp. 13–19, 2014. https://doi.org/10.1016/j.molliq.2014.01.003.Search in Google Scholar

[27] T. Hayat, T. Muhammad, S. A. Shehzad, and A. Alsaedi, “On magnetohydrodynamic flow of nanofluid due to a rotating disk with slip effect: a numerical study,” Comput. Methods Appl. Mech. Eng., vol. 315, pp. 467–477, 2017. https://doi.org/10.1016/j.cma.2016.11.002.Search in Google Scholar

[28] M. Imtiaz, T. Hayat, A. Alsaedi, and S. Asghar, “Slip flow by a variable thickness rotating disk subject to magnetohydrodynamics,” Results Phys., vol. 7, pp. 503–509, 2017. https://doi.org/10.1016/j.rinp.2016.12.021.Search in Google Scholar

[29] M. Mustafa, “MHD nanofluid flow over a rotating disk with partial slip effects: Buongiorno model,” Int. J. Heat Mass Tran., vol. 108, pp. 1910–1916, 2017. https://doi.org/10.1016/j.ijheatmasstransfer.2017.01.064.Search in Google Scholar

[30] M. Turkyilmazoglu, “Flow and heat due to a surface formed by a vortical source,” Eur. J. Mech. B Fluid, vol. 68, pp. 76–84, 2018. https://doi.org/10.1016/j.euromechflu.2017.11.010.Search in Google Scholar

[31] T. Hayat, S. Ahmad, M. I. Khan, and A. Alsaedi, “Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source,” Phys. B Condens. Matter, vol. 537, pp. 116–126, 2018. https://doi.org/10.1016/j.physb.2018.01.052.Search in Google Scholar

[32] A. Mehmood, A. Zameer, and M. A. Z. Raja, “Intelligent computing to analyze the dynamics of magnetohydrodynamic flow over stretchable rotating disk model,” Appl. Soft Comput., vol. 67, pp. 8–28, 2018. https://doi.org/10.1016/j.asoc.2018.02.024.Search in Google Scholar
Received: 2021-11-26
Revised: 2021-12-28
Accepted: 2021-12-30
Published Online: 2022-01-17
Published in Print: 2022-04-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

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  2. Dynamical Systems & Nonlinear Phenomena
  3. Investigation of the non-linear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam
  4. Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp
  5. Flow and heat over a rotating disk subject to a uniform horizontal magnetic field
  6. Hydrodynamics
  7. The effect of surfactant on the drag and wall correction factor of a drop in a bounded medium
  8. The effect of second order slip condition on MHD nanofluid flow around a semi-circular cylinder
  9. Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary
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https://doi.org/10.1515/zna-2021-0350
Keywords for this article
exponential solutions; heat transfer; horizontal magnetic field; rotating disk; similarity equations; wall shears

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Investigation of the non-linear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam
  4. Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp
  5. Flow and heat over a rotating disk subject to a uniform horizontal magnetic field
  6. Hydrodynamics
  7. The effect of surfactant on the drag and wall correction factor of a drop in a bounded medium
  8. The effect of second order slip condition on MHD nanofluid flow around a semi-circular cylinder
  9. Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary
  10. Thermodynamics & Statistical Physics
  11. A self-similar solution for shock waves in conducting rotating non-ideal dusty gas medium with monochromatic radiation and magnetic field
  12. Analysis of the second virial coefficient, and application to rare gas mixtures
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