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Numerical study of the effect of magnetic field on Fe3O4 –water ferrofluid convection with thermal radiation

Mohsen Sheikholeslami (Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran)
Shirley Abelman (School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa)

Engineering Computations

ISSN: 0264-4401

Article publication date: 7 August 2018

Issue publication date: 5 September 2018



The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.


Viscosity of Fe3O4 ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe3O4–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nuave is extracted.


The inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψmax| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψmax| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing NNu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nuloc profile matches the existence of the thermal plume and the number of undulations. Nuave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nuave increases with increasing Ra.


Nanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe3O4–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe3O4–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 103, 104 and 105), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).



The authors thank the reviewers for their careful reading of the manuscript. Their useful comments and suggestions have resulted in an improved manuscript.


Sheikholeslami, M. and Abelman, S. (2018), "Numerical study of the effect of magnetic field on Fe3O4 –water ferrofluid convection with thermal radiation", Engineering Computations, Vol. 35 No. 5, pp. 1855-1872.



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