Advertisement

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

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

References

  1. 1.
    Raptis A. Unsteady free convection flow through a porous medium. Int J Eng Sci. 1983;21:345–8.CrossRefGoogle Scholar
  2. 2.
    Kim SJ, Vafai K. Analysis of natural convection about a vertical plate embedded in a porous medium. Int J Heat Mass Transf. 1989;32:665–77.CrossRefGoogle Scholar
  3. 3.
    Narasimha K, Pop I. Transient free convection in a fluid saturated porous media with temperature dependent viscosity. Int Commun Heat Mass Transf. 1994;21:573–81.CrossRefGoogle Scholar
  4. 4.
    Zhang C, Zheng L, Zhang X, Chen G. MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl Math Model. 2015;39:165–81.CrossRefGoogle Scholar
  5. 5.
    Abd Elazem N, Ebaid A, Aly H. Radiation effect of MHD on Cu-water and Ag-water nanofluids flow over a stretching sheet: numerical study. J Appl Computat Math. 2015;4:1000235–43.Google Scholar
  6. 6.
    Bianco V, Manca O, Nardini S, Vafai K. Heat transfer enhancement with nanofluids. London: CRC Press; 2015.CrossRefGoogle Scholar
  7. 7.
    Khan W, Aziz A. Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux. Int J Therm Sci. 2011;50:1207–14.CrossRefGoogle Scholar
  8. 8.
    Turkyilmazoglu M. Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. Chem Eng Sci. 2012;84:182–7.CrossRefGoogle Scholar
  9. 9.
    Mohankrishna P, Sugunamma V, Sandeep N. Radiation and magnetic field effects on unsteady natural convection flow of a nanofluid past an infinite vertical plate with heat source. Chem Process Eng Res. 2014;25:39–52.Google Scholar
  10. 10.
    Ellahi R. The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions. Appl Math Model. 2013;37:1451–7.CrossRefGoogle Scholar
  11. 11.
    Rizwan U, Khan Z, Hussain S, Hammouch Z. Flow and heat transfer analysis of water and ethylene glycol based Cu nanoparticles between two parallel disks with suction/injection effects. J Mol Liq. 2016;221:298–304.CrossRefGoogle Scholar
  12. 12.
    Sheikholeslami M, Zaigham Q, Ellahi R. Influence of induced magnetic field on free convection of nanofluid considering Koo–Kleinstreuer–Li (KKL) correlation. Appl Sci. 2016;324:1–13.Google Scholar
  13. 13.
    Sekrani G, Poncet S. Further investigation on laminar forced convection of nanofluid flows in a uniformly heated pipe using direct numerical simulations. Appl Sci. 2016;332:1–24.Google Scholar
  14. 14.
    Ibrahim W, Haq R. Magnetohydrodynamic (MHD) stagnation point flow of nanofluid past a stretching sheet with convective boundary condition. J Braz Soc Mech Sci Eng. 2016;38:1155–64.CrossRefGoogle Scholar
  15. 15.
    Akbar N, Raza M, Ellahi R. Copper oxide nanoparticles analysis with water as base fluid for peristaltic flow in permeable tube with heat transfer. Comput Methods Programs Biomed. 2016;130:22–30.PubMedCrossRefPubMedCentralGoogle Scholar
  16. 16.
    Tateishi AA, Ribeiro HV, Lenzi EK. The role of fractional time-derivative operators on anomalous diffusion. Front Phys. 2017;5:1–21.CrossRefGoogle Scholar
  17. 17.
    Kashif AA, Ilyas K, Asifa T. Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate. Math Model Nat Phenom. 2018;13:1–16.CrossRefGoogle Scholar
  18. 18.
    Sheikholeslami M, Ellahi R. Electrohydrodynamic nanofluid hydrothermal treatment in an enclosure with sinusoidal upper wall. Appl Sci. 2015;5:294–306.CrossRefGoogle Scholar
  19. 19.
    Abro KA, Memon AA, Uqaili MA. A comparative mathematical analysis of RL and RC electrical circuits via Atangana–Baleanu and Caputo–Fabrizio fractional derivatives. Eur Phys J Plus. 2018;33:1–13.Google Scholar
  20. 20.
    Ilyas K, Kashif AA. Thermal analysis in Stokes’ second problem of nanofluid: applications in thermal engineering. Case Stud Therm Eng. 2018;1:1–15.Google Scholar
  21. 21.
    Scerer C, Figueiredo N. Ferrofluids: properties and applications. Braz J Phys. 2005;35:718–27.CrossRefGoogle Scholar
  22. 22.
    Aaiza G, Ilyas K, Sharidan S, Asma K, Arshad K. Heat transfer in MHD mixed convection flow of a ferrofluid along a vertical channel. PLoS ONE. 2015;10(11):1–14.Google Scholar
  23. 23.
    Ram P, Kumar V. Heat transfer in FHD boundary layer flow with temperature dependent viscosity over a rotating disk. Fluid Dyn Mater Process. 2014;10(2):179–96.Google Scholar
  24. 24.
    Colla L, Fedele L, Scattolini M, Bobbo S. Water-based Fe2O3 nanofluid characterization: thermal conductivity and viscosity measurements and correlation. Adv Mech Eng. 2012;8:1–16.Google Scholar
  25. 25.
    Abareshi M, Goharshiadi K, Zebarjad M, Fadafan K, Youssefi A. Fabrication, characterization and measurement of thermal conductivity of Fe3O4 nanofluids. J Magn Magn Mater. 2010;322(24):3895–901.CrossRefGoogle Scholar
  26. 26.
    Borglin E, Moridis J, Oldenburg M. Experimental studies of the flow of the ferrofluid of porous media. Transp Porous Media. 2000;41:61–80.CrossRefGoogle Scholar
  27. 27.
    Ali-Abro K, Mohammad MR, Khan I, Irfan AA, Tassadiq A. Analysis of Stokes’ second problem for nanofluids using modern fractional derivatives. J Nanofluids. 2018;7:738–47.CrossRefGoogle Scholar
  28. 28.
    Ali-Abro K, Mukarrum H, Mirza Mahmood B. A mathematical analysis of magnetohydrodynamic generalized burger fluid for permeable oscillating plate. Punjab Univ J Math. 2018;50(2):97–111.Google Scholar
  29. 29.
    Ali-Abro K, Mukarrum H, Mirza Mahmood B. An analytic study of molybdenum disulfide nanofluids using modern approach of Atangana–Baleanu fractional derivatives. Eur Phys J Plus. 2017;132:1–19.CrossRefGoogle Scholar
  30. 30.
    Atangana A, Qureshi S. Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Chaos Solitons Fractals. 2019;123:320–37.CrossRefGoogle Scholar
  31. 31.
    Ali-Abro K, Ilyas K, Gómez-Aguilar JF. Thermal effects of magnetohydrodynamic micropolar fluid embedded in porous medium with Fourier sine transform technique. J Braz Soc Mech Sci Eng. 2019;41:174–81.CrossRefGoogle Scholar
  32. 32.
    Yusuf A, Qureshi S, Inc M, Aliyu AI, Baleanu D, Shaikh AA. Two-strain epidemic model involving fractional derivative with Mittag–Leffler kernel. Chaos Interdiscip J Nonlinear Sci (AIP). 2018;28(12):1–11.Google Scholar
  33. 33.
    Ali-Abro K, Yildirim A. Fractional treatment of vibration equation through modern analogy of fractional differentiations using integral transforms. Iran J Sci Technol Trans A Sci. 2019;43:1–8.CrossRefGoogle Scholar
  34. 34.
    Saad K, Atangana A, Baleanu D. New fractional derivatives with non-singular kernel applied to the Burgers equation. Chaos Interdiscip J Nonlinear Sci (AIP). 2018;28:1–8.Google Scholar
  35. 35.
    Ali-Abro K, Ali AM, Anwer AM. Functionality of circuit via modern fractional differentiations. Analog Integr Circuits Signal Process Int J. 2019;99(1):11–21.CrossRefGoogle Scholar
  36. 36.
    Baleanu D, Jajarmi A, Hajipour M. On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dyn. 2018;94(1):397–414.CrossRefGoogle Scholar
  37. 37.
    Ali-Abro K, Gómez-Aguilar JF. Dual fractional analysis of blood alcohol model via non-integer order derivatives. In: Gómez J, Torres L, Escobar R, editors. Fractional derivatives with Mittag–Leffler Kernel. Studies in systems, decision and control, vol. 194. Cham: Springer; 2019.Google Scholar
  38. 38.
    Atangana A, Owolabi KM. New numerical approach for fractional differential equations. Math Model Nat Phenom. 2018;13(1):1–8.CrossRefGoogle Scholar
  39. 39.
    Ali-Abro KA, Gómez-Aguilar JF. A comparison of heat and mass transfer on a Walter’s-B fluid via Caputo–Fabrizio versus Atangana–Baleanu fractional derivatives using the Fox H function. Eur Phys J Plus. 2019;134:1–10.CrossRefGoogle Scholar
  40. 40.
    Goufo EFD, Kumar S, Mugisha SB. Similarities in a fifth-order evolution equation with and with no singular kernel. Chaos Solitons Fractals. 2020;130:1–10.Google Scholar
  41. 41.
    Odibat Z, Kumar S. A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations. J Comput Nonlinear Dyn. 2019;14(8):1–8.Google Scholar
  42. 42.
    El-Ajou A, Oqielat MAN, Al-Zhour Z, Kumar S, Momani S. Solitary solutions for time-fractional nonlinear dispersive PDEs in the sense of conformable fractional derivative. Chaos Interdiscip J Nonlinear Sci. 2019;29(9):1–9.CrossRefGoogle Scholar
  43. 43.
    Kumar S, Kumar A, Momani S, Aldhaifallah M, Nisar KS. Numerical solutions of nonlinear fractional model arising in the appearance of the stripe patterns in two-dimensional systems. Adv Differ Equ. 2019;2019(1):1–13.CrossRefGoogle Scholar
  44. 44.
    Aliyu AI, Inc M, Yusuf A, Baleanu D. A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives. Chaos Solitons Fractals. 2018;116:268–77.CrossRefGoogle Scholar
  45. 45.
    Khan W, Khan Z, Rahi M. Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary. Appl Nanosci. 2013;1:1–9.Google Scholar
  46. 46.
    Rosensweig R. Heating magnetic fluid with alternating magnetic field. J Magn Magn Mater. 2002;252:370–4.CrossRefGoogle Scholar
  47. 47.
    Ambreen S, Ali-Abro K, Muhammad AS. Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium: applications to thermal science. J Therm Anal Calorim. 2018.  https://doi.org/10.1007/s10973-018-7897-0.CrossRefGoogle Scholar
  48. 48.
    Turkyilmazoglu M, Pop I. Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect. Int J Heat Mass Transf. 2013;59:167–71.CrossRefGoogle Scholar
  49. 49.
    Tiwari R, Das M. Heat transfer argument in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf. 2007;50:2002–18.CrossRefGoogle Scholar
  50. 50.
    Oztop H, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow. 2008;29:1326–36.CrossRefGoogle Scholar
  51. 51.
    Kakac S, Pramuanjaroenkij A. Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf. 2009;52:3187–96.CrossRefGoogle Scholar
  52. 52.
    Atangana A. On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation. Appl Math Comput. 2016;273:948–56.Google Scholar
  53. 53.
    Ali-Abro K, Mukarrum H, Mahmood M. Slippage of magnetohydrodynamic fractionalized Oldroyd-B fluid in porous medium. Int J Prog Fract Differ Appl. 2017;3(1):69–80.CrossRefGoogle Scholar
  54. 54.
    Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl. 2015;1(2):1–13.Google Scholar
  55. 55.
    Al-Mdallal Q, Ali-Abro K, Khan I. Analytical solutions of fractional Walter’s-B fluid with applications. Complexity. 2018;1:1–19.CrossRefGoogle Scholar
  56. 56.
    Atangana A. Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties. Physica A. 2018;505:688–706.CrossRefGoogle Scholar
  57. 57.
    Atangana A, Gómez-Aguilar JF. Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena. Eur Phys J Plus. 2018;133(4):1–21.CrossRefGoogle Scholar
  58. 58.
    Atangana A. Blind in a commutative world: simple illustrations with functions and chaotic attractors. Chaos Solitons Fractals. 2018;114:347–63.CrossRefGoogle Scholar
  59. 59.
    Atangana A, Gómez-Aguilar JF. Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons Fractals. 2018;114:516–35.CrossRefGoogle Scholar
  60. 60.
    Ali-Abro K, Khan I. Analysis of heat and mass transfer in MHD flow of generalized Casson fluid in a porous space via non-integer order derivative without singular kernel. Chin J Phys. 2017;55(4):1583–95.CrossRefGoogle Scholar

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

Personalised recommendations