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


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.


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



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.


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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

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