Journal of Thermal Analysis and Calorimetry

, Volume 138, Issue 5, pp 3089–3108 | Cite as

Effect of magnetohydrodynamics on heat transfer intensification and entropy generation of nanofluid flow inside two interacting open rectangular cavities

  • B. FersadouEmail author
  • H. Kahalerras
  • W. Nessab
  • D. Hammoudi


MHD mixed convection heat transfer and entropy generation analysis for Cu–water nanofluid inside two interacting open cavities are numerically investigated. The right and the left walls of each cavity are heated or cooled at uniform but different heat flux densities. The nanofluid flow is described by the Buongiorno model in order to take into account the thermophoresis effect and the Brownian motion. The governing equations are solved using the finite volume method with the SIMPLE algorithm. The effects of relevant parameters including the Hartmann number (Ha), the Richardson number (Ri), the opening ratio (R), the heat flux ratio (Rq) and the nanoparticles volume fraction (ϕi) are analyzed. The results show that the flow pattern resulting from the simultaneous action of the magnetic field and the buoyancy force is heightened by the decrease in Ha and R and the increase in Ri and Rq. The heat transfer, which evolves in a non-monotonous way with the Hartmann number, is enhanced by the rise of the Richardson number, the heat flux ratio and the nanoparticles volume fraction, as well as by the reduction in the opening ratio. It is also observed that, overall, the thermodynamic disorder is dominated by the thermal irreversibility which decreases at high Ha with the augmentations of Ri and ϕi and the reductions in R and Rq.


MHD Mixed convection Entropy generation Nanofluid Open cavities 

List of symbols


Magnetic induction (T)


Specific heat at constant pressure (J kg−1 K−1)


Cavity opening width


Molecule diameter of the base fluid (m)


Nanoparticle diameter (m)


Brownian diffusion coefficient (m2 s−1)


Thermophoretic diffusion coefficient (m2 s−1 K−1)


Eckert number


Gravitational acceleration (m s−2)


Channel width (m)


Hartmann number


Thermal conductivity (W m−1 K−1)


Boltzmann’s constant (J K−1)

Channel length (m)


Lewis number


Brownian motion parameter


Entropy generation number


Thermophoresis parameter


Nusselt number


Pressure (Pa)


Prandtl number


Heat flux density (W m−2)


Opening ratio


Reynolds number


Richardson number


Heat flux ratio


Source width


Total entropy generation

\(S^{{{\prime \prime \prime }}}\)

Local entropy generation (W m−3 K−1)


Temperature (K)


Freezing point of the base fluid (K)


Axial velocity (m s−1)


Transverse velocity (m s−1)


Adiabatic zone width (m)


Axial coordinate (m)


Transverse coordinate (m)

Greek symbols


Irreversibility ratio


Thermal expansion coefficient (K−1)


Dimensionless temperature


Viscosity (kg m−1 s−1)


Density (kg m−3)


Channel volume (m3)


Nanoparticles volume fraction


Irreversibility coefficient





Base fluid


Fluid friction



















  1. 1.
    Mousavi SS, Hooman K. Heat and fluid flow in entrance region of a channel with staggered baffles. Energy Convers Manag. 2006;47:2011–9. Scholar
  2. 2.
    Wu W, Ching CY. Laminar natural convection in an air-filled square cavity with partitions on the top wall. Int J Heat Mass Transf. 2010;53:1759–72. Scholar
  3. 3.
    Deng QH, Zhou J, Mei C, Shen YM. Fluid, heat and contaminant transport structures of laminar double-diffuse mixed convection in a two-dimensional ventilated enclosure. Int J Heat Mass Transf. 2004;47:5257–69. Scholar
  4. 4.
    Bahlaoui A, Raji A, Hasnaoui M, Naimi M, Makayssi T, Lamsaadi M. Mixed convection cooling combined with surface radiation in a partitioned rectangular cavity. Energy Convers Manag. 2009;50:626–35. Scholar
  5. 5.
    Naphon P, Nakharintr L, Wiriyasart S. Continuous nanofluids jet impingement heat transfer and flow in a micro-channel heat sink. Int J Heat Mass Transf. 2018;126:924–32. Scholar
  6. 6.
    Choi SUS. Enhancing thermal conductivity of fluids with nano-particles. Trans ASME J Heat Transf. 1995;66:99–105.Google Scholar
  7. 7.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems: a review. J Therm Anal Calorim. 2018;131:2027–39. Scholar
  8. 8.
    Rashidi S, Karimi N, Mahian O, Esfahani JA. A concise review on the role of nanoparticles upon the productivity of solar desalination systems. J Therm Anal Calorim. 2019;135:1145–59. Scholar
  9. 9.
    Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, Marshall JS, Siavashi M, Taylor RA, Niazmand H, Wongwises S, Hayat T, Kolanjiyil A, Kasaeian A, Pop I. Recent advances in modeling and simulation of nanofluid flows-part I: fundamental and theory. Phys Rep. 2019;790:1–48. Scholar
  10. 10.
    Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, Marshall JS, Taylor RA, Abu-Nada E, Rashidi S, Niazmand H, Wongwises S, Hayat T, Kasaeian A, Pop I. Recent advances in modeling and simulation of nanofluid flows-part II: applications. Phys Rep. 2019;791:1–59. Scholar
  11. 11.
    Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement: gaps and challenges. J Therm Anal Calorim. 2019;135:437–60. Scholar
  12. 12.
    Sourtiji E, Hosseinizadeh SF, Gorji-Bandpy M, Ganji DD. Effect of water-based Al2O3 nanofluids on heat transfer and pressure drop in periodic mixed convection inside a square ventilated cavity. Int Comm Heat Mass Transf. 2011;38:1125–34. Scholar
  13. 13.
    Mehrizi AA, Farhadi M, Afroozi HH, Sedighi K, Darz AAR. Mixed convection heat transfer in a ventilated cavity with hot obstacle: effect of nanofluid and outlet port location. Int Comm Heat Mass Transf. 2012;39:1000–8. Scholar
  14. 14.
    Mehrez Z, Bouterra M, El Cafsi A, Belghith A. Heat transfer and entropy generation analysis of nanofluids flow in an open cavity. Comput Fluids. 2013;88:363–73. Scholar
  15. 15.
    Mohammed HA, Alawi OA, Wahid MA. Mixed convective nanofluids flow in a channel having backward-facing step with a baffle. Powder Technol. 2015;275:329–43. Scholar
  16. 16.
    Fazeli H, Madani S, Mashaei PR. Nanofluid forced convection in entrance region of a baffled channel considering nanoparticle migration. Appl Therm Eng. 2016;106:293–306. Scholar
  17. 17.
    Mashaei PR, Taheri-Ghazvini M, Shabanpour Moghadam R, Madani S. Smart role of Al2O3-water suspension on laminar heat transfer in entrance region of a channel with transverse in-line baffles. Appl Therm Eng. 2017;112:450–63. Scholar
  18. 18.
    Mashaei PR, Hosseinalipour SM, Bagheri N, Taheri-Ghazvini M, Madani S. Simultaneous effect of staggered baffles and dispersed nanoparticles on thermal performance of a cooling channel. Appl Therm Eng. 2017;120:748–62. Scholar
  19. 19.
    Siavashi M, Yousofvand R, Rezanejad S. Nanofluid and porous fins effects on natural convection and entropy generation of flow inside a cavity. Adv Powder Technol. 2018;29:142–56. Scholar
  20. 20.
    Sheremet MA, Roşca NC, Roşca AV, Pop I. Mixed convection heat transfer in a square porous cavity filled with a nanofluid with suction/injection effect. Comput Math Appl. 2018;76:2665–77. Scholar
  21. 21.
    Rashidi S, Esfahani JA. The effect of magnetic field on instabilities of heat transfer from an obstacle in a channel. J Magn Magn Mater. 2015;391:5–11. Scholar
  22. 22.
    Bovand M, Rashidi S, Esfahani JA, Masoodi R. Control of wake destructive behavior for different bluff bodies in channel flow by magnetohydrodynamics. Eur Phys J Plus. 2016;131:194. Scholar
  23. 23.
    Rashidi S, Bovand M, Esfahani JA. Application of magnetohydrodynamics for suppressing the fluctuations in the unsteady flow around two side-by-side circular obstacles. Eur Phys J Plus. 2016;131:423. Scholar
  24. 24.
    Rashidi S, Esfahani JA, Maskaniyan M. Applications of magnetohydrodynamics in biological systems-A review on the numerical studies. J Magn Magn Mater. 2017;439:358–72. Scholar
  25. 25.
    Mehrez Z, El Cafsi A, Belghith A, Le Quéré P. MHD effects on heat transfer and entropy generation of nanofluid flow in an open cavity. J Magn Magn Mater. 2015;374:214–24. Scholar
  26. 26.
    Chen CK, Chen BS, Liu CC. Entropy generation in mixed convection magnetohydrodynamic nanofluid flow in vertical channel. Int J Heat Mass Transf. 2015;91:1026–33. Scholar
  27. 27.
    Bondareva NS, Sheremet MA, Oztop HF, Abu-Hamdeh N. Heatline viualization of MHD natural convection in an inclined wavy open porous cavity filled with a nanofluid with a local heater. Int J Heat Mass Transf. 2016;99:872–81. Scholar
  28. 28.
    Sheremet MA, Oztop HF, Pop I. MHD natural convection in an inclined wavy cavity with corner heater filled with a nanofluid. J Magn Magn Mater. 2016;416:37–47. Scholar
  29. 29.
    Sheremet MA, Oztop HF, 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. Scholar
  30. 30.
    Abbaszadeh M, Ababaei A, Arani AAA, Sharifabadi AA. MHD forced convection and entropy generation of CuO-water nanofluid in a microchannel considering slip velocity and temperature jump. J Braz Soc Mech Sci Eng. 2016;39:775–90. Scholar
  31. 31.
    Rashidi S, Bovand M, Esfahani JA. Opposition of magnetohydrodynamics and Al2O3-water nanofluid flow around a vertex facing triangular obstacle. J Mol Liq. 2016;215:276–84. Scholar
  32. 32.
    Job VM, Gunakala SR. Mixed convection nanofluid flows through a grooved channel with internal heat generating solid cylinders in the presence of an applied magnetic field. Int J Heat Mass Transf. 2017;107:133–45. Scholar
  33. 33.
    Hussain S, Ahmed SE, Akbar T. Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle. Int J Heat Mass Transf. 2017;114:1054–66. Scholar
  34. 34.
    Yousofvand R, Derakhshan S, Ghasem K, Siavashi M. MHD transverse mixed convection and entropy generation study of electromagnetic pump including a nanofluid using 3D LBM simulation. Int J Mech Sci. 2017;133:73–90. Scholar
  35. 35.
    Bovand M, Rashidi S, Esfahani JA. Optimum interaction between magnetohydrodynamics and nanofluid for thermal and drag management. J Therm Heat Transf. 2017;31:218–29. Scholar
  36. 36.
    Job VM, Gunakala SR. Unsteady hydromagnetic mixed convection nanofluid flows through an L-shaped channel with a porous inner layer and heat-generating components. Int J Heat Mass Transf. 2018;120:970–86. Scholar
  37. 37.
    Ma Y, Mohebbi R, Rashidi MM, Yang Z, Sheremet MA. Numerical study of MHD nanofluid natural convection in a baffled U-shaped enclosure. Int J Heat Mass Transf. 2019;130:123–34. Scholar
  38. 38.
    Akar S, Rashidi S, Esfahani JA, Karimi N. Targeting a channel coating by using magnetic field and magnetic nanofluids. J Therm Anal Calorim. 2019. Scholar
  39. 39.
    Buongiorno J. Convective transports in nanofluids. Trans ASME J Heat Transf. 2006;128:240–50. Scholar
  40. 40.
    Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Ener Conver Manage. 2011;52:789–93. Scholar
  41. 41.
    Bejan A. Second-law analysis in heat transfer and thermal design. Adv Heat Transf. 1982;52:1–58. Scholar
  42. 42.
    Bejan A. Entropy generation minimization. Boca Taron: CRC Press; 1996.Google Scholar
  43. 43.
    Patankar SV. Numerical heat transfer and fluid flow. New York: Mc Graw-Hill; 1980.Google Scholar
  44. 44.
    Mahmoudi AH, Shahi M, Talebi F. Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid. Int Comm Heat Mass Transf. 2010;37:1158–73. Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • B. Fersadou
    • 1
    Email author
  • H. Kahalerras
    • 1
  • W. Nessab
    • 1
  • D. Hammoudi
    • 1
  1. 1.Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP)University of Sciences and Technology Houari Boumediene (USTHB)Bab Ezzouar, AlgiersAlgeria

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