Advertisement

Role of Suction/Injection on Natural Convection Flow of Magnetite \( ({\text{Fe}}_{ 3} {\text{O}}_{ 4} ) \) Nanoparticles in Vertical Porous Micro-annulus Between Two Concentric Tubes: A Purely Analytical Approach

  • Z. Abbas
  • I. Mehdi
  • J. HasnainEmail author
  • Shaban Aly
Research Article - Mechanical Engineering
  • 5 Downloads

Abstract

Natural convection heat transfer analysis was carried out to examine the flow of magnetite–water ferrofluid in an annular zone between a pair of vertical micro-cylindrical tubes under conditions of slip velocity and thermal jump at the porous wall of cylinders. The effects of radial magnetic field and thermal radiation are also considered along with suction/injection at the walls. Linear Rosseland approximation was employed to obtain the expression for thermal radiation. Similarity variables and non-dimensional parameters are introduced to express the resultant flow equations in term of continuity, momentum and energy in a dimensionless fashion. A closed-form solution of the problem was constructed in the form of modified Bessel functions of the first and second kind. The numerical values of the obtained expressions for fluid velocity, temperature profiles, volume flow rate, surface friction and Nusselt number were plotted to examine the significance of different flow parameters. It was found that the fluid velocity was reduced when injection parameter was increased, while it was augmented when the suction parameter was increased. In contrast to this, opposite effects were observed in the temperature distribution. Further, the suction parameter enhances the rate of heat transfer at the inner surface of outer porous cylinder, while the injection parameter has a decreasing effect on the same.

Keywords

Vertical mirco-annulus Ferrofluid Magnetic field Thermal radiation Suction/injection 

Notes

Acknowledgements

The authors thank the anonymous reviewers for their useful comments to improve the version of the paper. The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Research Groups Program under grant number (R.G.P2./00/40).

Compliance with Ethical Standards

Conflict of interest

The authors have declared that no conflict of interests exits.

References

  1. 1.
    Choi, S.U.S.; Eastman J.A.: Enhancing thermal conductivity of fluids with nanoparticles. In: The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, ASME, San Francisco, USA, FED 231/MD 66 pp. 99–105 (1995).Google Scholar
  2. 2.
    Choi, S.U.S.; Zhang, Z.G.; Yu, W.; Lockwood, F.E.; Grulke, E.A.: Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001)CrossRefGoogle Scholar
  3. 3.
    Zeng, J.; Deng, Y.; Vedantam, P.; Tzeng, T.-R.; Xuan, X.: Magnetic separation of particles and cells in ferrofluid flow through a straight microchannel using two offset magnets. J. Magn. Magn. Mater. 346, 118–123 (2013)CrossRefGoogle Scholar
  4. 4.
    Seo, H.-S.; Lee, J.-C.; Hwang, I.-J.; Kim, Y.-J.: Flow characteristics of ferrofluid in a microchannel with patterned blocks. Mater. Res. Bull. 58, 10–14 (2014)CrossRefGoogle Scholar
  5. 5.
    Goharkhah, M.; Ashjaee, M.: Effect of an alternating nonuniform magnetic field on ferrofluid flow and heat transfer in a channel. J. Magn. Magn. Mater. 362, 80–89 (2014)CrossRefGoogle Scholar
  6. 6.
    Sheikholeslami, M.; Ganji, D.D.: Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer. Energy 75, 400–410 (2014)CrossRefGoogle Scholar
  7. 7.
    Aminfar, H.; Mohammadpourfard, M.; Maroofiazar, R.: Experimental study on the effect of magnetic field on critical heat flux of ferrofluid flow boiling in a vertical annulus. Exp. Thermal Fluid Sci. 58, 156–169 (2014)CrossRefGoogle Scholar
  8. 8.
    Ghasemian, M.; Najafian Ashrafi, Z.; Goharkhah, M.; Ashjaee, M.: Heat transfer characteristics of Fe3O4 ferrofluid flowing in a mini channel under constant and alternating magnetic fields. J. Magn. Magn. Mater. 381, 158–167 (2015)CrossRefGoogle Scholar
  9. 9.
    Sheikholeslami, M.; Ganji, D.D.; Rashidi, M.M.: Ferrofluid flow and heat transfer in a semi annulus enclosure in the presence of magnetic source considering thermal radiation. J. Taiwan Inst. Chem. Eng. 47, 6–17 (2015)CrossRefGoogle Scholar
  10. 10.
    Abbas, Z.; Hasnain, J.: Two-phase magnetoconvection flow of magnetite (Fe3O4) nanoparticles in a horizontal composite porous annulus. Results Phys. 7, 574–580 (2017)CrossRefGoogle Scholar
  11. 11.
    Biswal, L.; Som, S.K.; Chakraborty, S.: Effects of entrance region transport processes on free convection slip flow in vertical microchannels with isothermally heated walls. Int. J. Heat Mass Transf. 50, 1248–1254 (2007)CrossRefzbMATHGoogle Scholar
  12. 12.
    Chakraborty, S.; Som, S.K.; Rahul: A boundary layer analysis for entrance region heat transfer in vertical microchannels within the slip flow regime. Int. J. Heat Mass Transf. 51, 3245–3250 (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Avcı, M.; Aydın, O.: Laminar forced convection slip-flow in a micro-annulus between two concentric cylinders. Int. J. Heat Mass Transfer 51, 3460–3467 (2008)CrossRefzbMATHGoogle Scholar
  14. 14.
    Jha, B.K.; Aina, B.; Isa, S.: Fully developed MHD natural convection flow in a vertical annular microchannel: an exact solution. J. King Saud Univ. Sci. 27, 253–259 (2015)CrossRefGoogle Scholar
  15. 15.
    Jha, B.K.; Oni, M.O.; Aina, B.: Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: an exact solution. Ain Shams Eng. J. (2016).  https://doi.org/10.1016/j.asej.2016.08.005 Google Scholar
  16. 16.
    Jha, B.K.; Aina, B.: Magnetohydrodynamic natural convection flow in a vertical micro-porous-annulus in the presence of radial magnetic field. J. Nanofluids 5, 292–301 (2016)CrossRefGoogle Scholar
  17. 17.
    Jha, B.K.; Aina, B.: Role of suction/injection on steady fully developed mixed convection flow in a vertical parallel plate microchannel. Ain Shams Eng. J. (2016).  https://doi.org/10.1016/j.asej.2016.05.001 Google Scholar
  18. 18.
    Sarris, I.E.; Zikos, G.K.; Grecos, A.P.; Vlachos, N.S.: On the limits of validity of the low magnetic Reynolds approximation in MHD natural convection heat transfer. Numer. Heat Transfer B 50, 157–180 (2006)CrossRefGoogle Scholar
  19. 19.
    Rosseland, S.: Astrophysics and nuclear-theoretical foundations, pp. 41–44. Springer, Berlin (1931)Google Scholar
  20. 20.
    Weng, H.C.; Chen, C.O.-K.: Drag reduction and heat transfer enhancement over a heated wall of a vertical annular microchannel. Int. J. Heat Mass Transfer 52, 1075–1079 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    Avcı, M.; Aydın, O.: Mixed convection in a vertical microannulus between two concentric microtubes. J. Heat Transfer 131, 014502 (2009)CrossRefGoogle Scholar
  22. 22.
    Arpaci, V.S.: Conduction Heat Transfer, pp. 135–136. Addision Weslay, Reading (1966)zbMATHGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe Islamia University of BahawalpurBahawalpurPakistan
  2. 2.Department of Computer SciencesBahria University Islamabad CampusIslamabadPakistan
  3. 3.Department of Mathematics, Faculty of ScienceKing Khalid UniversityAbhaKingdom of Saudi Arabia

Personalised recommendations