Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 3, pp 1407–1416 | Cite as

Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure

  • Akram Jahanbakhshi
  • Afshin Ahmadi Nadooshan
  • Morteza Bayareh


The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n < 1) and increases for shear-thickening fluids (n > 1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure α < 60° and α > 60°, respectively.


Magnetohydrodynamics (MHD) Natural convection Newtonian fluid Non-Newtonian fluid Enclosure 

List of symbols


Aspect ratio


Magnetic induction (T)


Gravitational acceleration (m s−2)


Hartmann number


Thermal conductivity (W m−1 K−1)


Specific length (m)


Power-law index


Local Nusselt number


Pressure (Pa)


Prandtl number


Rayleigh number


Reynolds number


Wall temperature (K)


Velocity in x-direction (m s−1)


Velocity in y-direction (m s−1)


Dimensionless velocity in x-direction


Dimensionless velocity in y-direction


Distance along x-coordinate


Distance along y-coordinate

Greek letters


Thermal expansion coefficient (k−1)


Dynamic viscosity (kg m−1 s−1)


Density (kg m−3)


Dimensionless temperature


  1. 1.
    Moldoveanu GM, Ibanescu C, Danu M, Minea AA. Viscosity estimation of Al2O3, SiO2 nanofluids and their hybrid: an experimental study. J Mol Liq. 2018;253:188–96.CrossRefGoogle Scholar
  2. 2.
    Moldoveanu GM, Minea AA, Jacob M, Ibanescu C. Experimental study on viscosity of stabilized Al2O3, TiO2 nanofluids and their hybrid. Thermochimia Acta. 2018;659:203–12.CrossRefGoogle Scholar
  3. 3.
    Minea AA, El-Maghlany WM. Influence of hybrid nanofluids on the performance of parabolic trough collectors in solar thermal systems: recent findings and numerical comparison. Renew Energy. 2018;120:350–64.CrossRefGoogle Scholar
  4. 4.
    Akilu S, Tesfamicheael A, Said MAM, Minea AA, Sharma KV. Properties of glycerol and ethylene glycol mixture based SiO2–CuO/C hybrid nanofluid for enhanced solar energy transport. Sol Energy Mater Sol Cells. 2018;179:118–28.CrossRefGoogle Scholar
  5. 5.
    Akilu S, Baheta AT, Minea AA, Sharma KV. Rheology and thermal conductivity of non-porous silica (SiO2) in viscous glycerol and ethylene glycol based nanofluids. Int Commun Heat Mass Transf. 2017;88:245–53.CrossRefGoogle Scholar
  6. 6.
    Minea AA. Hybrid nanofluids based on Al2O3, TiO2 and SiO2: numerical evaluation of different approaches. Int J Heat Mass Transf. 2017;104:852–60.CrossRefGoogle Scholar
  7. 7.
    Minea AA. Challenges in hybrid nanofluids behavior in turbulent flow: recent research and numerical comparison. Renew Sustain Energy Rev. 2017;71:426–34.CrossRefGoogle Scholar
  8. 8.
    Minea AA. Numerical simulation of nanoparticles concentration effect on forced convection in a tube with nanofluids. Heat Transf Eng. 2015;36:1144–53.CrossRefGoogle Scholar
  9. 9.
    Minea AA. Comparative study of turbulent heat transfer of nanofluids. J Therm Anal Calorim. 2016;124:407–16.CrossRefGoogle Scholar
  10. 10.
    Minea AA. Numerical studies on heat transfer enhancement in different closed enclosures heated symmetrically. J Therm Anal Calorim. 2015;121:711–20.CrossRefGoogle Scholar
  11. 11.
    Minea AA, El-Maghlany WM. Natural convection heat transfer utilizing ionic nanofluids with temperature-dependent thermophysical properties. Chem Eng Sci. 2017;174:13–24.CrossRefGoogle Scholar
  12. 12.
    Jhumur NC, Bhattacharjee A. Unsteady MHD mixed convection inside L-shaped enclosure in the presence of ferrofluid (Fe3O4). Proc Eng. 2017;194:494–501.CrossRefGoogle Scholar
  13. 13.
    Yadollahi Farsani R, Raisi A, Nadooshan AA, Vanapalli S. The effect of a magnetic field on the melting of gallium in a rectangular cavity. Heat Transf Eng. 2017. Scholar
  14. 14.
    Hajatzadeh Pordanjani A, Jahanbakhshi A, Nadooshan AA, Afrand M. Effect of two isothermal obstacles on the natural convection of nanofluid in the presence of magnetic field inside an enclosure with sinusoidal wall temperature distribution. Int J Heat Mass Transf. 2018;121:565–78.CrossRefGoogle Scholar
  15. 15.
    Zadhoush M, Nadooshan AA, Afrand M, Ghafori H. Constructal optimization of longitudinal and latitudinal rectangular fins used for cooling a plate under free convection by the intersection of asymptotes method. Int J Heat Mass Transf. 2017;112:441–53.CrossRefGoogle Scholar
  16. 16.
    Bayareh M, Hajatzadeh Pordanjani A, Nadooshan AA, Dehkordi KS. Numerical study of the effects of stator boundary conditions and blade geometry on the efficiency of a scraped surface heat exchanger. Appl Therm Eng. 2017;113:1426–36.CrossRefGoogle Scholar
  17. 17.
    Ozoe H, Churchill SW. Hydrodynamic stability and natural convection In Ostwald–de Waele and Ellis fluids: the development of numerical solution. AIChE J. 1972;18:1196–207.CrossRefGoogle Scholar
  18. 18.
    Kim GB, Hyun JM, Kwak HS. Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure. Int J Heat Mass Transf. 2003;64:3605–17.Google Scholar
  19. 19.
    Kefayati GR. Simulation of heat transfer and entropy generation of MHD natural convection of non-Newtonian nanofluid in an enclosure. Int J Heat Mass Transf. 2016;92:1066–89.CrossRefGoogle Scholar
  20. 20.
    Zhang T, Che D. Double MRT thermal lattice Boltzmann simulation for MHD natural convection of nanofluids in an inclined cavity with four square heat sources. Int J Heat Mass Transf. 2016;94:87–100.CrossRefGoogle Scholar
  21. 21.
    Ghasemi B, Aminossadati SM, Raisi A. Magnetic field effect on natural convection in Nanofluid-filled square enclosure. Int J Therm Sci. 2013;50:1748–56.CrossRefGoogle Scholar
  22. 22.
    Mirabdoli Lavasani A, Farhadi M, Rabienataj Darzi AA. Study of convection heat transfer enhancement inside lid driven cavity utilizing fins and nanofluid. Int J Therm Sci. 2015;53:158–71.Google Scholar
  23. 23.
    Jamesahar E, Ghalambaz M, Chamkha AJ. Fluid–solid interaction in natural convection heat transfer in a square cavity with a perfectly thermal-conductive flexible diagonal partition. Int J Heat Mass Transf. 2016;100:303–19.CrossRefGoogle Scholar
  24. 24.
    Ohta M, Akiyoshi M, Obata E. A numerical study on natural convective heat transfer of pseudoplastic fluids in a square cavity. Numer. Heat Transf Part A Appl. 2002;41:357–72.CrossRefGoogle Scholar
  25. 25.
    Zablotsky D, Mezulis A, Blums E. Surface cooling based on the thermomagnetic convection: numerical simulation and experiment. Int J Heat Mass Transf. 2009;52:5302–8.CrossRefGoogle Scholar
  26. 26.
    Kefayati GHR. FDLBM simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a linearly heated cavity. Powder Technol. 2014;256:87–99.CrossRefGoogle Scholar
  27. 27.
    Lamsaadi M, Naimi M, Hasnaoui M, Mamou M. Natural convection in tilted rectangular slot containing non-newtonian power-law fluids and subject to longitudinal thermal gradient. Numer Heat Transf A Appl. 2006;50:561–83.CrossRefGoogle Scholar
  28. 28.
    Raisi A. The influence of pair constant temperature baffles on power-law fluids natural convection in square enclosure. Modares Mech Eng. 2015;15(11):215–24 (in Persian).Google Scholar
  29. 29.
    Shahmardan MM, Norouzi M. Numerical simulation of non-Newtonian fluid flows through a channel with a cavity. Modares Mech Eng. 2014;14:35–40 (in Persian).Google Scholar
  30. 30.
    Turan O, Sachdeva A, Chakraborty N, Poole RJ. Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant temperatures. J Non-Newton Fluid Mech. 2011;166:1049–63.CrossRefGoogle Scholar
  31. 31.
    Kasaeipoor Ghasemi B, Raisi A. Magnetic field on nanofluid water–Cu natural convection in an inclined shape cavity. Modares Mech Eng J. 2014 (in Persian).Google Scholar
  32. 32.
    Guha A, Pradhan K. Natural convection of non-Newtonian power-law fluids on a horizontal plate. Int J Heat Mass Transf. 2014;70:930–8.CrossRefGoogle Scholar
  33. 33.
    Kefayati GHR. Simulation of non-Newtonian molten polymer on natural convection in a sinusoidal heated cavity using FDLBM. J Mol Liq. 2014;195:165–74.CrossRefGoogle Scholar
  34. 34.
    Vinogradov I, Khezzar L, Siginer D. Heat transfer of non-Newtonian dilatant power law fluids in square and rectangular cavities. J Appl Fluid Mech. 2011;4:37–42.Google Scholar
  35. 35.
    Chhabra RP. Bubbles, drops, and particles in non-Newtonian fluids. Boca Raton: CRC Press; 2006.CrossRefGoogle Scholar
  36. 36.
    Pittman FFT, Richardson JF, Sherrard CP. An experimental study of heat transfer by laminar natural convection between an electrically heated vertical plate and both Newtonian and non-Newtonian fluids. Int J Heat Mass Transf. 1999;42:657–71.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Akram Jahanbakhshi
    • 1
  • Afshin Ahmadi Nadooshan
    • 1
  • Morteza Bayareh
    • 1
  1. 1.Department of Mechanical EngineeringShahrekord UniversityShahrekordIran

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