Magnetic field effects on forced convection flow of a hybrid nanofluid in a cylinder filled with porous media: a numerical study

  • 77 Accesses


The magnetic field can serve as a proper controlling parameter for heat transfer and fluid flow; it can be also employed to maximize the thermodynamic efficiency in various fields. Nanofluids and porous inserts are among the conventional approaches of heat transfer enhancements. Porous media, in addition to improving the heat transfer, can enhance the pressure drop. This research presents a numerical investigation on the magnetohydrodynamics forced convection effects of Al2O3–CuO–water nanofluid inside a partitioned cylinder within a porous medium. The calculations were carried out for a broad range of governing parameters. The nanofluid flow is modeled as a two-phase flow using two-phase mixture model, and the Darcy–Brinkman–Forchheimer equation is employed to model fluid flow in porous media. Simulation was also conducted under the laminar flow regime by finite volume method. Furthermore, the thermal boundary condition of constant uniform heat flux was imposed on the cylinder walls. The average Nusselt number as well as the performance evaluation criteria (PEC) were examined for diverse Darcy numbers (0.0001 < Da < 0.1) and Hartmann numbers (0 < Ha < 40). The results indicate the significant impact of Hartmann and Darcy number enhancement on the elevation of heat transfer coefficient. Additionally, incorporation of nanoparticles to the base fluid increased the PEC in all cases. Moreover, the PEC reached to its maximum value in configurations involving permeable porous media (i.e., a medium with Da = 0.1 and Ha = 40).

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


B :

Intensity of the magnetic field

C :

Specific heat/J kg−1 K−1

g :

Gravity acceleration/m s−2

J :

Electric current density

K :

Permeability of porous medium/m2

k :

Thermal conductivity/W m−1 K−1

L :


P :

Dimensionless pressure

p :



Heat flux/W m−2

R :


T :


U, V :

Dimensionless velocity

u, v :

Velocity components/m s−1

X, Y :

Dimensionless cylindrical coordinates

x, y :

Cylindrical coordinates/m

α :

Thermal diffusivity/m2 s−1

β :

Thermal expansion coefficient/K−1

ε :


θ :

Dimensionless temperature

ϑ :

Kinematic viscosity/m2 s−1

μ :

Dynamic viscosity/kg m−1 s−1

ρ :

Density/kg m3

σ :

Electrical conductivity/Ω−1 m−1

φ :

Volume fraction

ψ :

Magnetic field angle








Hybrid nanofluid




Computational fluid dynamics


Carbon nanotubes


Darcy number


Hartmann number




Nusselt number


Prandtl number


Performance evaluation criteria


Reynolds number


Semi-implicit method for pressure-linked equations


  1. 1.

    Choi SU, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Lemont: Argonne National Lab; 1995.

  2. 2.

    Kasaeian A, Daviran S, Azarian RD, Rashidi A. Performance evaluation and nanofluid using capability study of a solar parabolic trough collector. Energy Convers Manag. 2015;89:368–75.

  3. 3.

    Shi L, He Y, Wang X, Hu Y. Recyclable photo-thermal conversion and purification systems via Fe3O4@ TiO2 nanoparticles. Energy Convers Manag. 2018;171:272–8.

  4. 4.

    Kherbeet AS, Mohammed H, Munisamy K, Salman B. The effect of step height of microscale backward-facing step on mixed convection nanofluid flow and heat transfer characteristics. Int J Heat Mass Transf. 2014;68:554–66.

  5. 5.

    Sharif M. Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Appl Therm Eng. 2007;27(5–6):1036–42.

  6. 6.

    Sajid MU, Ali HM. Thermal conductivity of hybrid nanofluids: a critical review. Int J Heat Mass Transf. 2018;126:211–34.

  7. 7.

    Yarmand H, et al. Graphene nanoplatelets–silver hybrid nanofluids for enhanced heat transfer. Energy Convers Manag. 2015;100:419–28.

  8. 8.

    Sarkar J, Ghosh P, Adil A. A review on hybrid nanofluids: recent research, development and applications. Renew Sustain Energy Rev. 2015;43:164–77.

  9. 9.

    Ahmadi AA, Khodabandeh E, Moghadasi H, Malekian N, Akbari OA, Bahiraei M. Numerical study of flow and heat transfer of water–Al2O3 nanofluid inside a channel with an inner cylinder using Eulerian–Lagrangian approach. J Therm Anal Calorim. 2018;132(1):651–65.

  10. 10.

    Farhangmehr V, Moghadasi H, Asiaei S. A nanofluid MHD flow with heat and mass transfers over a sheet by nonlinear boundary conditions: heat and mass transfers enhancement. J Central South Univ. 2019;26(5):1205–17.

  11. 11.

    Malekian S, Fathi E, Malekian N, Moghadasi H, Moghimi M. Analytical and numerical investigations of unsteady graphene oxide nanofluid flow between two parallel plates. Int J Thermophys. 2018;39(9):100.

  12. 12.

    Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2019;137(1):267–87.

  13. 13.

    Siavashi M, Bahrami HRT, Aminian E. Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using nanofluid with gradient and multi-layered porous foams. Appl Therm Eng. 2018;138:465–74.

  14. 14.

    Siavashi M, Bahrami HRT, Aminian E, Saffari H. Numerical analysis on forced convection enhancement in an annulus using porous ribs and nanoparticle addition to base fluid. J Central South Univ. 2019;26(5):1089–98.

  15. 15.

    Siavashi M, Bahrami HRT, Saffari H. Numerical investigation of porous rib arrangement on heat transfer and entropy generation of nanofluid flow in an annulus using a two-phase mixture model. Numer Heat Transf Part A Appl. 2017;71(12):1251–73.

  16. 16.

    Selimefendigil F, Öztop HF. Numerical analysis and ANFIS modeling for mixed convection of CNT–water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction. Int J Heat Mass Transf. 2018;127:583–99.

  17. 17.

    Selimefendigil F, Öztop HF. Conjugate mixed convection of nanofluid in a cubic enclosure separated with a conductive plate and having an inner rotating cylinder. Int J Heat Mass Transf. 2019;139:1000–17.

  18. 18.

    Arshad W, Ali HM. Experimental investigation of heat transfer and pressure drop in a straight minichannel heat sink using TiO2 nanofluid. Int J Heat Mass Transf. 2017;110:248–56.

  19. 19.

    Khan MS, Abid M, Ali HM, Amber KP, Bashir MA, Javed S. Comparative performance assessment of solar dish assisted s-CO2 Brayton cycle using nanofluids. Appl Therm Eng. 2019;148:295–306.

  20. 20.

    Sajid MU, Ali HM. Recent advances in application of nanofluids in heat transfer devices: a critical review. Renew Sustain Energy Rev. 2019;103:556–92.

  21. 21.

    Xuan Y, Li Q. Investigation on convective heat transfer and flow features of nanofluids. J Heat Transf. 2003;125(1):151–5.

  22. 22.

    Sheikholeslami M, Gorji-Bandpy M, Seyyedi S, Ganji D, Rokni HB, Soleimani S. Application of LBM in simulation of natural convection in a nanofluid filled square cavity with curve boundaries. Powder Technol. 2013;247:87–94.

  23. 23.

    Sohel M, Khaleduzzaman S, Saidur R, Hepbasli A, Sabri M, Mahbubul I. An experimental investigation of heat transfer enhancement of a minichannel heat sink using Al2O3–H2O nanofluid. Int J Heat Mass Transf. 2014;74:164–72.

  24. 24.

    Ho C-J, Wei L, Li Z. An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluid. Appl Therm Eng. 2010;30(2–3):96–103.

  25. 25.

    Kasaeian A, et al. Nanofluid flow and heat transfer in porous media: a review of the latest developments. Int J Heat Mass Transf. 2017;107:778–91.

  26. 26.

    Hajipour M, Dehkordi AM. Analysis of nanofluid heat transfer in parallel-plate vertical channels partially filled with porous medium. Int J Therm Sci. 2012;55:103–13.

  27. 27.

    Servati AA, Javaherdeh K, Ashorynejad HR. Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method. Adv Powder Technol. 2014;25(2):666–75.

  28. 28.

    Targui N, Kahalerras H. Analysis of a double pipe heat exchanger performance by use of porous baffles and nanofluids. Int J Mech Aerosp Ind Mechatron Manuf Eng. 2014;8(9):1581–6.

  29. 29.

    Cimpean DS, Pop I. Fully developed mixed convection flow of a nanofluid through an inclined channel filled with a porous medium. Int J Heat Mass Transf. 2012;55(4):907–14.

  30. 30.

    Qi C, Wang G, Ma Y, Guo L. experimental research on stability and natural convection of TiO2–Water nanofluid in enclosures with different rotation angles. Nanoscale Res Lett. 2017;12(1):396.

  31. 31.

    Sheikholeslami M, Gorji-Bandpy M, Ganji D. Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid. Powder Technol. 2014;254:82–93.

  32. 32.

    Bahiraei M, Hangi M. Flow and heat transfer characteristics of magnetic nanofluids: a review. J Magn Magn Mater. 2015;374:125–38.

  33. 33.

    Nkurikiyimfura I, Wang Y, Pan Z. Heat transfer enhancement by magnetic nanofluids—a review. Renew Sustain Energy Rev. 2013;21:548–61.

  34. 34.

    Selimefendigil F, Öztop HF. Magnetic field effects on the forced convection of CuO–water nanofluid flow in a channel with circular cylinders and thermal predictions using ANFIS. Int J Mech Sci. 2018;146:9–24.

  35. 35.

    Selimefendigil F, Öztop HF. Forced convection in a branching channel with partly elastic walls and inner L-shaped conductive obstacle under the influence of magnetic field. Int J Heat Mass Transf. 2019;144:118598.

  36. 36.

    Selimefendigil F, Öztop HF. MHD Pulsating forced convection of nanofluid over parallel plates with blocks in a channel. Int J Mech Sci. 2019;157:726–40.

  37. 37.

    Selimefendigil F, Öztop HF. Effects of conductive curved partition and magnetic field on natural convection and entropy generation in an inclined cavity filled with nanofluid. Phys A Stat Mech Its Appl. 2020;540:123004.

  38. 38.

    Sureshkumar S, Muthukumar S, Doh DH, Prem E. Effects of magnetic field inclination on tilted square cavity filled with a nanofluid saturated porous medium. Int J Ambient Energy. 2018.

  39. 39.

    Zhang T, Che D, Zhu Y, Shi H, Chen D. Effects of magnetic field and inclination on natural convection in a cavity filled with nanofluids by a double multiple-relaxation-time thermal lattice boltzmann method. Heat Transf Eng. 2019;41:1–19.

  40. 40.

    Al-Rashed AA, et al. 3D magneto-convective heat transfer in CNT-nanofluid filled cavity under partially active magnetic field. Phys E. 2018;99:294–303.

  41. 41.

    Sheremet MA, Oztop H, Pop I, Al-Salem K. MHD free convection in a wavy open porous tall cavity filled with nanofluids under an effect of corner heater. Int J Heat Mass Transf. 2016;103:955–64.

  42. 42.

    Hatami M, Nouri R, Ganji D. Forced convection analysis for MHD Al2O3–water nanofluid flow over a horizontal plate. J Mol Liq. 2013;187:294–301.

  43. 43.

    Sheikholeslami M, Rashidi M, Ganji D. Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4–water nanofluid. Comput Methods Appl Mech Eng. 2015;294:299–312.

  44. 44.

    Aminossadati S, Raisi A, Ghasemi B. Effects of magnetic field on nanofluid forced convection in a partially heated microchannel. Int J Non-Linear Mech. 2011;46(10):1373–82.

  45. 45.

    Rashidi MM, Nasiri M, Khezerloo M, Laraqi N. Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. J Magn Magn Mater. 2016;401:159–68.

  46. 46.

    Sheikholeslami M, Bandpy MG, Ellahi R, Hassan M, Soleimani S. Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM. J Magn Magn Mater. 2014;349:188–200.

  47. 47.

    Sheikholeslami M, Ziabakhsh Z, Ganji D. Transport of magnetohydrodynamic nanofluid in a porous media. Colloids Surf A. 2017;520:201–12.

  48. 48.

    Selimefendigil F, Öztop HF. Numerical study of MHD mixed convection in a nanofluid filled lid driven square enclosure with a rotating cylinder. Int J Heat Mass Transf. 2014;78:741–54.

  49. 49.

    Larimi M, Ghanaat A, Ramiar A, Ranjbar A. Forced convection heat transfer in a channel under the influence of various non-uniform transverse magnetic field arrangements. Int J Mech Sci. 2016;118:101–12.

  50. 50.

    Geridonmez BP, Oztop HF. Natural convection in a cavity filled with porous medium under the effect of a partial magnetic field. Int J Mech Sci. 2019;161:105077.

  51. 51.

    Ashorynejad HR, Shahriari A. MHD natural convection of hybrid nanofluid in an open wavy cavity. Res Phys. 2018;9:440–55.

  52. 52.

    Han W-S, Rhi S-H. Thermal characteristics of grooved heat pipe with hybrid nanofluids. Therm Sci. 2011;15(1):195–206.

  53. 53.

    Kamble D, Gadhave P, Anwar M. Enhancement of thermal performance of heat pipe using hybrid nanofluid. Int J Eng Trends Technol. 2014;17(9):425–8.

  54. 54.

    Pordanjani AH, Vahedi SM, Aghakhani S, Afrand M, Öztop HF, Abu-Hamdeh N. Effect of magnetic field on mixed convection and entropy generation of hybrid nanofluid in an inclined enclosure: sensitivity analysis and optimization. Eur Phys J Plus. 2019;134(8):412.

  55. 55.

    Ramachandran R, Ganesan K, Rajkumar M, Asirvatham L, Wongwises S. Comparative study of the effect of hybrid nanoparticle on the thermal performance of cylindrical screen mesh heat pipe. Int Commun Heat Mass Transf. 2016;76:294–300.

  56. 56.

    Tahat MS, Benim AC. Experimental analysis on thermophysical properties of Al2O3/CuO hybrid nano fluid with its effects on flat plate solar collector. Defect Diffus Forum. 2017;374:148–56.

  57. 57.

    Mahdavi M, Saffar-Avval M, Tiari S, Mansoori Z. Entropy generation and heat transfer numerical analysis in pipes partially filled with porous medium. Int J Heat Mass Transf. 2014;79:496–506.

  58. 58.

    Pavel BI, Mohamad AA. An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media. Int J Heat Mass Transf. 2004;47(23):4939–52.

  59. 59.

    Sutton GW, Sherman A. Engineering magnetohydrodynamics. New York: McGraw-Hill; 1965.

  60. 60.

    Alkam M, Al-Nimr M, Hamdan M. Enhancing heat transfer in parallel-plate channels by using porous inserts. Int J Heat Mass Transf. 2001;44(5):931–8.

  61. 61.

    Siavashi M, Bahrami HRT, Saffari H. Numerical investigation of flow characteristics, heat transfer and entropy generation of nanofluid flow inside an annular pipe partially or completely filled with porous media using two-phase mixture model. Energy. 2015;93:2451–66.

Download references

Author information

Correspondence to Hamid Saffari.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Aminian, E., Moghadasi, H. & Saffari, H. Magnetic field effects on forced convection flow of a hybrid nanofluid in a cylinder filled with porous media: a numerical study. J Therm Anal Calorim (2020).

Download citation


  • Forced convection
  • Nanofluid
  • MHD
  • Porous media
  • PEC