Heat transfer in magnetohydrodynamic free convection flow of generalized ferrofluid with magnetite nanoparticles

  • Kashif Ali Abro
  • Ilyas Khan
  • J. F. Gómez-AguilarEmail author


This article investigates the effects of magnetite \( {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} \) nanoparticles on free convection flow of nanofluid with magnetohydrodynamics. The magnetite \( {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} \) nanoparticles that have been dispersed in water are taken as a conventional base fluid. In order to compare newly fractional derivatives, the governing equations have been fractionalized via Atangana–Baleanu and Caputo–Fabrizio fractional operators. The resulting partial differential equations are solved by employing Laplace transforms. Exact solutions have been investigated for temperature and velocity field via Atangana–Baleanu and Caputo–Fabrizio fractional operators and then expressed in Mittag–Leffler function \( {\mathbf{M}}_{{\upbeta,\upgamma}}^{\rm{y}} \left( W \right) \) and M-function \( {\mathbf{M}}_{\text{q}}^{\rm{p}} \left( W \right) \). The enhancement of heat transfer and effects in the natural convection flows are analyzed graphically by Atangana–Baleanu and Caputo–Fabrizio fractional operators. Graphical comparison has been depicted via Atangana–Baleanu and Caputo–Fabrizio derivatives for four types of models, i.e., (1) fractionalized nanofluid with magnetic field, (2) ordinary nanofluid with magnetic field, (3) fractionalized nanofluid without magnetic field and (4) ordinary nanofluid without magnetic field on fluid flows.


Nanofluid and nanoparticles Atangana–Baleanu derivative Caputo–Fabrizio derivative Laplace transform Special functions 



The author Kashif Ali Abro is highly thankful and grateful to Mehran university of Engineering and Technology, Jamshoro, Pakistan for generous support and facilities of this research work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

Authors’ contribution

All authors contributed equally to the writing of this paper. All authors read and approved the final paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2020

Authors and Affiliations

  1. 1.Department of Basic Sciences and Related StudiesMehran University of Engineering TechnologyJamshoroPakistan
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.CONACyT-Tecnológico Nacional de México/CENIDETCuernavacaMexico

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