Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

B 0 :

Magnetic induction (T)

C p :

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

d :

Cavity opening width

d f :

Molecule diameter of the base fluid (m)

d p :

Nanoparticle diameter (m)

D B :

Brownian diffusion coefficient (m2 s−1)

D T :

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

Ec :

Eckert number

g :

Gravitational acceleration (m s−2)

H :

Channel width (m)

Ha :

Hartmann number

k :

Thermal conductivity (W m−1 K−1)

k B :

Boltzmann’s constant (J K−1)

ℓ :

Channel length (m)

Le :

Lewis number

N B :

Brownian motion parameter

Ns :

Entropy generation number

N T :

Thermophoresis parameter

Nu :

Nusselt number

p :

Pressure (Pa)

Pr :

Prandtl number

q :

Heat flux density (W m−2)

R :

Opening ratio

Re :

Reynolds number

Ri :

Richardson number

R q :

Heat flux ratio

s :

Source width

S :

Total entropy generation

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

Local entropy generation (W m−3 K−1)

T :

Temperature (K)

T fr :

Freezing point of the base fluid (K)

u :

Axial velocity (m s−1)

v :

Transverse velocity (m s−1)

w :

Adiabatic zone width (m)

x :

Axial coordinate (m)

y :

Transverse coordinate (m)

α :

Irreversibility ratio

β :

Thermal expansion coefficient (K−1)

θ :

Dimensionless temperature

μ :

Viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

ϑ :

Channel volume (m3)

ϕ :

Nanoparticles volume fraction

δ :

Irreversibility coefficient

c:

Cooled

f:

Base fluid

Frt:

Fluid friction

h:

Heated

i:

Inlet

m:

Mean

Mag:

Hydromagnetic

nf:

Nanofluid

p:

Nanoparticles

Th:

Thermal

W:

Wall

References

  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. https://doi.org/10.1016/j.enconman.2005.12.018.

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.014.

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2004.06.025.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.enconman.2008.10.001.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.101.

    Article  CAS  Google Scholar 

  6. Choi SUS. Enhancing thermal conductivity of fluids with nano-particles. Trans ASME J Heat Transf. 1995;66:99–105.

    Google Scholar 

  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. https://doi.org/10.1007/s10973-017-6773-7.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1007/s10973-018-7500-8.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.physrep.2018.11.004.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.physrep.2018.11.003.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1007/s10973-018-7070-9.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.icheatmasstransfer.2011.05.009.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.icheatmasstransfer.2012.04.002.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.compfluid.2013.09.026.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.powtec.2014.09.046.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.applthermaleng.2016.06.010.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.applthermaleng.2016.10.061.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.applthermaleng.2017.03.142.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.apt.2017.10.021.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.camwa.2018.08.069.

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.jmmm.2015.04.095.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1140/epjp/i2016-16194-3.

    Article  Google Scholar 

  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. https://doi.org/10.1140/epjp/i2016-16423-9.

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.jmmm.2017.05.014.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.jmmm.2014.08.010.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2015.08.042.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.055.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.jmmm.2016.04.061.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.006.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1007/s40430-016-0578-7.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.molliq.2015.12.034.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.021.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.135.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijmecsci.2017.08.034.

    Article  Google Scholar 

  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. https://doi.org/10.2514/1.T4907.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.112.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.072.

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1007/s10973-018-7975-3.

    Article  Google Scholar 

  39. Buongiorno J. Convective transports in nanofluids. Trans ASME J Heat Transf. 2006;128:240–50. https://doi.org/10.1115/1.2150834.

    Article  Google Scholar 

  40. Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Ener Conver Manage. 2011;52:789–93. https://doi.org/10.1016/j.enconman.2010.06.072.

    Article  CAS  Google Scholar 

  41. Bejan A. Second-law analysis in heat transfer and thermal design. Adv Heat Transf. 1982;52:1–58. https://doi.org/10.1016/S0065-2717(08)70172-2.

    Article  Google Scholar 

  42. Bejan A. Entropy generation minimization. Boca Taron: CRC Press; 1996.

    Google Scholar 

  43. Patankar SV. Numerical heat transfer and fluid flow. New York: Mc Graw-Hill; 1980.

    Google Scholar 

  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. https://doi.org/10.1016/j.icheatmasstransfer.2010.04.004.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP), University of Sciences and Technology Houari Boumediene (USTHB), BP 32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria

    B. Fersadou, H. Kahalerras, W. Nessab & D. Hammoudi

Authors
  1. B. Fersadou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Kahalerras
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Nessab
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Hammoudi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Fersadou.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fersadou, B., Kahalerras, H., Nessab, W. et al. Effect of magnetohydrodynamics on heat transfer intensification and entropy generation of nanofluid flow inside two interacting open rectangular cavities. J Therm Anal Calorim 138, 3089–3108 (2019). https://doi.org/10.1007/s10973-019-08343-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-019-08343-0

Keywords

Search

Navigation