Second law analysis of MHD mixed convection heat transfer in a vented irregular cavity filled with Ag–MgO/water hybrid nanofluid

  • Mahdi BenzemaEmail author
  • Youb Khaled Benkahla
  • Nabila Labsi
  • Seif-Eddine Ouyahia
  • Mohammed El Ganaoui


The present paper investigates numerically the effect of an external magnetic field on heat transfer and entropy generation of Ag–MgO (50:50 vol%)/water hybrid nanofluid flow in a partially heated irregular ventilated cavity. A finite-volume FORTRAN code has been written to solve the governing partial differential equations. New empirical correlations specifically dedicated to predict the dynamic viscosity and the thermal conductivity of the considered hybrid nanofluid were employed. After validation of model, the analysis has been done for a wide range of Reynolds number (10 ≼ Re ≼ 600), Hartmann number (0 ≼ Ha ≼ 80) and total nanoparticle volume fraction (0 ≼ φ ≼ 0.02). The results are presented in terms of streamlines, isotherms and isentropic lines as well as the average Nusselt number (Num), the average entropy generation (Sgen,m) and the Bejan number (Beavg). The criterion ξ = Sgen,m/Num is adopted to discuss the thermal performances of the system. The results reveal that the intensification of the magnetic field tends to attenuate the heat transfer convection and to reduce the thickness of the thermal boundary layer, close to the active walls. Globally, adding nanoparticles to the base fluid improves the heat transfer but increases the total entropy generation.


Irregular ventilated cavity Entropy generation Magnetic field Mixed convection Ag–MgO/water hybrid nanofluid 

List of symbols


Magnetic induction (T)


Average Bejan number


Specific heat capacity (J kg−1 K−1)


Dimensional length of the heat source (m)


Dimensionless distance of heat source from the entrance e1/W


Distance of heat source from the entrance (m)


Distance of heat source from the right vertical wall (m)


Eckert number


Gravitational acceleration (m s2)


Grashof number


Opening width (m)


Height of the cavity (m)


Hartmann number


Thermal conductivity (W m−1 K−1)


Local Nusselt number


Average Nusselt number


Normalized Nusselt number


Pressure (Pa)


Dimensionless pressure


Prandtl number


Reynolds number


Richardson number


Dimensional local entropy generation (W K−1 m−3)


Dimensionless local entropy generation


Dimensionless average entropy generation due to heat transfer


Dimensionless average entropy generation due to fluid friction

Savg, Mag

Dimensionless average entropy generation due to magnetic field


Normalized entropy generation


Temperature (K)

u, v

Velocity components (m s−1)


Velocity of the flow at the inlet (m s−1)

U, V

Dimensionless velocity components

x, y

Dimensional Cartesian coordinates (m)

X, Y

Dimensionless Cartesian coordinates


Width of the cavity (m)

Greek letters


Thermal diffusivity (m2 s−1)


Thermal expansion coefficient (K−1)


Dimensionless length of the heat source d/W


Thermal performance criterion (Sgen,m/Num)


Nanoparticle volume fraction


Dynamic viscosity (kg m−1 s−1)


Kinematic viscosity (m2 s−1)


Dimensionless temperature


Density (kg m−3)


Fluid electrical conductivity (Ω−1 m−1)


Irreversibility factor







Base fluid






Hybrid nanofluid


Reference state



  1. 1.
    Rashidi S, Bovand M, Abolfazli J, Ahmadi G. Discrete particle model for convective Al2O3-water nanofluid around a triangular obstacle. Appl Therm Eng. 2016;100:39–54. Scholar
  2. 2.
    Akbarzadeh M, Rashidi S, Karimi N, Omar N. First and second laws of thermodynamics analysis of nanofluid flow inside a heat exchanger duct with wavy walls and a porous insert. J Therm Anal Calorim. 2018. Scholar
  3. 3.
    Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2018;9:1–24. Scholar
  4. 4.
    Mahian O, Kolsi L, Amani M, et al. Recent advances in modeling and simulation of nanofluid flows-Part I: fundamental and theory. Phys Rep. 2018. Scholar
  5. 5.
    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. 2018;8:1–15. Scholar
  6. 6.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2017;131:2027–39. Scholar
  7. 7.
    Rahimi A, Sepehr M, Lariche MJ, Mesbah M, Kasaeipoor A, Malekshah EH. Analysis of natural convection in nanofluid-filled H-shaped cavity by entropy generation and heatline visualization using lattice Boltzmann method. Phys E Low Dimens Syst Nanostructures. 2018;97:347–62.CrossRefGoogle Scholar
  8. 8.
    Sidik NAC, Adamu IM, Jamil MM, Kefayati GHR, Mamat R, Najafi G. Recent progress on hybrid nanofluids in heat transfer applications: a comprehensive review. Int Commun Heat Mass Transf. 2016;78:68–79. Scholar
  9. 9.
    Esfe MH, Arani AAA, Rezaie M, Yan W-M, Karimipour A. Experimental determination of thermal conductivity and dynamic viscosity of Ag–MgO/water hybrid nanofluid. Int Commun Heat Mass Transf. 2015;66:189–95. Scholar
  10. 10.
    Kasaeipoor A, Malekshah EH, Kolsi L. Free convection heat transfer and entropy generation analysis of MWCNT-MgO (15%–85%)/water nanofluid using Lattice Boltzmann method in cavity with refrigerant solid body-Experimental thermo-physical properties. Powder Technol. 2017;322:9–23. Scholar
  11. 11.
    Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid. J Therm Anal Calorim. 2016;125:527–35. Scholar
  12. 12.
    Ismael MA, Abu-Nada E, Chamkha AJ. Mixed convection in a square cavity filled with CuO-Water nanofluid heated by corner heater. Int J Mech Sci. 2017;133:42–50. Scholar
  13. 13.
    Astanina MS, Sheremet MA, Oztop HF, Abu-Hamdeh N. Mixed convection of Al2O3-water nanofluid in a lid-driven cavity having two porous layers. Int J Heat Mass Transf. 2018;118:527–37. Scholar
  14. 14.
    Sun C, Yu B, Oztop HF, Wang Y, Wei J. Control of mixed convection in lid-driven enclosures using conductive triangular fins. 2011;54:894–909. Scholar
  15. 15.
    Akar S, Rashidi S, Esfahani AJ. Second law of thermodynamic analysis for nanofluid turbulent flow around a rotating cylinder. J Therm Anal Calorim. 2017;132:1189–200. Scholar
  16. 16.
    Shirejini ZS, Rashidi S, Esfahani JA. Recovery of drop in heat transfer rate for a rotating system by nanofluids. J Mol Liq. 2016;220:961–9. Scholar
  17. 17.
    Mansour MA, Siddiqa S, Gorla RSR, Rashad AM. Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3–Cu/water hybrid nanofluid filled with square porous cavity. Therm Sci Eng Prog. 2018;6:57–71. Scholar
  18. 18.
    Radhakrishnan TV, Verma AK, Balaji C, Venkateshan SP. An experimental and numerical investigation of mixed convection from a heat generating element in a ventilated cavity. 2007;32:502–20. Scholar
  19. 19.
    Tmartnhad I, El M, Najam M, Oubarra A. Numerical investigation on mixed convection flow in a trapezoidal cavity heated from below. Energy Convers Manag. 2008;49:3205–10. Scholar
  20. 20.
    Minaei A, Ashjaee M, Goharkhah M. Experimental and numerical study of mixed and natural convection in an enclosure with a discrete heat source and ventilation ports. Heat Transf Eng. 2014;35:63–73. Scholar
  21. 21.
    Parvin S, Chamkha AJ. An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid. Int Commun Heat Mass Transf. 2014;54:8–17. Scholar
  22. 22.
    Rehena N, Alim MA. Control volume finite element simulation of MHD forced and natural convection in a vertical channel with a heat-generating pipe. Int J Heat Mass Transf. 2012;55:2813–21. Scholar
  23. 23.
    Kalidasan K, Velkennedy R, Kanna PR. Laminar natural convection of Copper–Titania/Water hybrid nanofluid in an open ended C-shaped enclosure with an isothermal block. J Mol Liq. 2017;246:251–8. Scholar
  24. 24.
    Kalidasan K, Kanna PR. Natural convection on an open square cavity containing diagonally placed heaters and adiabatic square block and filled with hybrid nanofluid of nanodiamond-cobalt oxide/water. Int Commun Heat Mass Transf. 2017;81:64–71. Scholar
  25. 25.
    Kalidasan K, Kanna PR. Effective utilization of MWCNT-water nanofluid for the enhancement of laminar natural convection inside the open square enclosure. J Taiwan Inst Chem Eng. 2016;65:331–40. Scholar
  26. 26.
    Sourtiji E, Gorgi-Bandpy M, Ganji D, Hosseinizadeh SF. Numerical analysis of mixed convection heat transfer of Al2O3-water nanofluid in a ventilated cavity considering different positions of the outlet port. Powder Technol. 2014;262:71–81. Scholar
  27. 27.
    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 Commun Heat Mass Transf. 2012;39:1000–8. Scholar
  28. 28.
    Shahi M, Mahmoudi AH, Talebi F. Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid. Int Commun Heat Mass Transf. 2010;37:201–13. Scholar
  29. 29.
    Yousefi-Lafouraki B, Ramiar A, Mohsenian S. Entropy generation analysis of a confined slot impinging jet in a converging channel for a shear thinning nanofluid. Appl Therm Eng. 2016;105:675–85. Scholar
  30. 30.
    Rashidi S, Javadi P, Esfahani AJ. Second law of thermodynamics analysis for nanofluid turbulent flow inside a solar heater with the ribbed absorber plate. J Therm Anal Calorim. 2018. Scholar
  31. 31.
    Bejan A. A study of entropy generation in fundamental convective heat transfer. J Heat Transf. 1979;101:718–25.CrossRefGoogle Scholar
  32. 32.
    Biswal P, Basak T. Entropy generation vs energy efficiency for natural convection based energy flow in enclosures and various applications: a review. Renew Sustain Energy Rev. 2017;80:1412–57. Scholar
  33. 33.
    Kasaeipoor A, Ghasemi B, Aminossadati SM. Convection of Cu-water nanofluid in a vented T-shaped cavity in the presence of magnetic field. Int J Therm Sci. 2015;94:50–60. Scholar
  34. 34.
    Benzema M, Benkahla YK, Ouyahia S-E. Etude numérique de la convection mixte lors de l’écoulement d’un nanofluide hybride (Ag-MgO/Eau) dans une cavité trapézoïdale ventilée soumise à l’action d’un champ magnétique. In: 23th Congrès Fr. Mec. Lille, Fr. 28 Aout- 1 Sept.; 2017.Google Scholar
  35. 35.
    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
  36. 36.
    Mehrez Z, El Cafsi A, Belghith A, Le Quéré P. The entropy generation analysis in the mixed convective assisting flow of Cu-water nanofluid in an inclined open cavity. Adv Powder Technol. 2015;26:1442–51. Scholar
  37. 37.
    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
  38. 38.
    Mahmoudi HA, Hooman K. Effect of a discrete heat source location on entropy generation in mixed convective cooling of a nanofluid inside the ventilated cavity. Int J Exergy. 2013;13:299–319.CrossRefGoogle Scholar
  39. 39.
    Al-Rashed AAAA, Kalidasan K, Kolsi L, Velkennedy R, Aydi A, Hussein AK, Malekshah EH. Mixed convection and entropy generation in a nanofluid filled cubical open cavity with a central isothermal block. Int J Mech Sci. 2018;135:362–75. Scholar
  40. 40.
    Zamzari F, Mehrez Z, El Cafsi A, Belghith A, Le Quéré P. Numerical investigation of entropy generation and heat transfer of pulsating flow in a horizontal channel with an open cavity. J. Hydrodyn. 2017;29:632–46. Scholar
  41. 41.
    Benzema M, Benkahla YK, Labsi N, Brunier E, Ouyahia S. Numerical mixed convection heat transfer analysis in a ventilated irregular enclosure crossed by Cu-water nanofluid. Arab J Sci Eng. 2017;42:4575–86. Scholar
  42. 42.
    Öztop HF, Estellé P, Yan W-M, Al-Salem K, Orfi J, Mahian O. A brief review of natural convection in enclosures under localized heating with and without nanofluids. Int Commun Heat Mass Transf. 2015;60:37–44. Scholar
  43. 43.
    Biswas N, Manna NK, Datta P, Mahapatra PS. Analysis of heat transfer and pumping power for bottom-heated porous cavity saturated with Cu-water nanofluid. Powder Technol. 2018;326:356–69. Scholar
  44. 44.
    Garoosi F, Bagheri G, Talebi F. Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside. Int J Heat Mass Transf. 2013;67:362–76. Scholar
  45. 45.
    Mahian O, Pop I, Sahin AZ, Oztop HF, Wongwises S. Irreversibility analysis of a vertical annulus using TiO2/water nanofluid with MHD flow effects. Int J Heat Mass Transf. 2013;64:671–9. Scholar
  46. 46.
    Davarnejad R, Jamshidzadeh M. CFD modeling of heat transfer performance of MgO-water nanofluid under turbulent flow. Eng Sci Technol Int J. 2015;18:536–42. Scholar
  47. 47.
    Smith DK, Leider HR. Low-temperature thermal expansion of LiH, MgO and CaO. J Appl Cryst. 1968;246:246–9. Scholar
  48. 48.
    Kolsi L, Mahian O, Öztop HF, Aich W, Borjini MN, Abu-Hamdeh N, Ben Aissia H. 3D Buoyancy-induced flow and entropy generation of nanofluid-filled open cavities having adiabatic diamond shaped obstacles. Entropy. 2016. Scholar
  49. 49.
    Mahian O, Oztop H, Pop I, Mahmud S, Wongwises S. Entropy generation between two vertical cylinders in the presence of MHD flow subjected to constant wall temperature. Int Commun Heat Mass Transf. 2013;44:87–92. Scholar
  50. 50.
    Mahian O, Kolsi L, Amani M, et al. Recent advances in modeling and simulation of nanofluid flows-part II: applications. Phys Rep. 2018. Scholar
  51. 51.
    Patankar SV. Numerical heat transfer and fluid flow. New York: McGraw-Hil; 1980.Google Scholar
  52. 52.
    Ouyahia S, Benkahla YK, Labsi N. Numerical study of the hydrodynamic and thermal proprieties of titanium dioxide nanofluids trapped in a triangular geometry. Arab J Sci Eng. 2016;41:1995–2009. Scholar
  53. 53.
    Ismael MA, Armaghani T, Chamkha AJ. Conjugate heat transfer and entropy generation in a cavity filled with a nanofluid-saturated porous media and heated by a triangular solid. J Taiwan Inst Chem Eng. 2015;59:138–51. Scholar
  54. 54.
    Mahmoudi HA, Pop I, Shahi M, Talebi F. MHD natural convection and entropy generation in a trapezoidal enclosure using Cu–water nanofluid. Comput Fluids. 2013;72:46–62. Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Mahdi Benzema
    • 1
    Email author
  • Youb Khaled Benkahla
    • 1
  • Nabila Labsi
    • 1
  • Seif-Eddine Ouyahia
    • 1
  • Mohammed El Ganaoui
    • 2
  1. 1.Laboratory of Transport Phenomena, Faculty of Mechanical and Process EngineeringUSTHBAlgiersAlgeria
  2. 2.LERMAB, IUT LongwyUniversité de LorraineCosnes et RomainFrance

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