Skip to main content
Log in

Ferrofluid non-Darcy heat transfer involving second law analysis: an application of CVFEM

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

Abstract

The non-Darcy heat transportation of the ferrofluid together with the entropy generation has been studied in a permeable zone under the role of magnetic force. To incorporate the permeable impact, the non-Darcy approach was utilized. CVFEM-based code is implemented to explore the entropy generation and heat transportation for the parametric ranges of Rayleigh (Ra), Darcy (Da) and Hartmann (Ha) numbers. The results demonstrate that here the conduction is the significant mode of transportation of heat at higher Ha; however, the increment in Ra and Da promotes the convection. The Bejan number increases at higher Ha and it decreases with the augmentation of Ra and Da. The enhancement of Ra and Da results in the declination of \(X_{{\rm d}}\), and it escalates under the impact of stronger Ha.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Rudraiah N, Barron RM, Venkatachalappa M, Subbaraya CK. Effect of a magnetic field on free convection in a rectangular enclosure. Int J Eng Sci. 1995;33:1075–84.

    Article  Google Scholar 

  2. Kakarantzas SC, Sarris IE, Grecos AP, Vlachos NS. Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature. Int J Heat Mass Transf. 2009;52:250–9.

    Article  Google Scholar 

  3. Öztop HF, Rahman MM, Ahsan A, Hasanuzzaman M, Saidur R, Al-Salem K, Rahim NA. MHD natural convection in an enclosure from two semi-circular heaters on the bottom wall. Int J Heat Mass Transf. 2012;55:1844–54.

    Article  Google Scholar 

  4. Sheikholeslami Mohsen. Magnetic field influence on CuO–H2O nanofluid convective flow in a permeable cavity considering various shapes for nanoparticles. Int J Hydrog Energy. 2017;42:19611–21.

    Article  CAS  Google Scholar 

  5. Astanina MS, Sheremet MA, Oztop HF, Abu-hamdeh N. MHD natural convection and entropy generation of ferrofluid in an open trapezoidal cavity partially filled with a porous medium. Int J Mech Sci. 2018;136:493–502.

    Article  Google Scholar 

  6. Mehryan SAM, Izadi M, Chamkha AJ, Sheremet MA. Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field. J Mol Liq. 2018;263:510–25.

    Article  CAS  Google Scholar 

  7. Selimefendigil F, Öztop HF. Numerical study and POD-based prediction of natural convection in a ferrofluids-filled triangular cavity with generalized neural networks. Numer Heat Transf Part A Appl. 2015;67(10):1136–61.

    Article  Google Scholar 

  8. Manh TD, Nam ND, Abdulrahman GK, Moradi R, Babazadeh H. Impact of MHD on hybrid nanomaterial free convective flow within a permeable region. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-09008-8.

    Article  Google Scholar 

  9. Li Y, Aski FS, Barzinjy AA, Dara RN, Shafee A, Tlili I. Nanomaterial thermal treatment along a permeable cylinder. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08706-7.

    Article  Google Scholar 

  10. Manh TD, Nam ND, Abdulrahman GK, Shafee A, Shamlooei M, Babazadeh H, Jilani AK, Tlili I. Effect of radiative source term on the behavior of nanomaterial with considering Lorentz forces. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-09077-9.

    Article  Google Scholar 

  11. Yang L, Du K. A comprehensive review on the natural, forced and mixed convection of non-Newtonian fluids (nanofluids) inside different cavities. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08987-y.

    Article  Google Scholar 

  12. Liu S, Yang B. Vibrations of flexible multistage rotor systems supported by water-lubricated rubber bearings. J Vib Acoust. 2017;139(2):021016.

    Article  Google Scholar 

  13. 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;146–147:9–24.

    Article  Google Scholar 

  14. 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.

    Article  CAS  Google Scholar 

  15. Selimefendigil F, Öztop HF. MHD Pulsating forced convection of nanofluid over parallel plates with blocks in a channel. Int J Mech Sci. 2019;157–158:726–40.

    Article  Google Scholar 

  16. Liu Z-H, Xiong J-G, Bao R. Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface. Int J Multiphase Flow. 2007;33(12):1284–95.

    Article  CAS  Google Scholar 

  17. Sheikholeslami M, Shehzad SA, Li Z, Shafee A. Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law. Int J Heat Mass Transf. 2018;127:614–22.

    Article  CAS  Google Scholar 

  18. Ganesh Kumar K. Scrutinization of 3D flow and nonlinear radiative heat transfer of non-Newtonian nanoparticles over an exponentially sheet. Int J Numer Methods Heat Fluid Flow. 2019. https://doi.org/10.1108/HFF-12-2018-0741.

    Article  Google Scholar 

  19. Sheikholeslami M, Darzi M, Sadoughi MK. Heat transfer improvement and pressure drop during condensation of refrigerant-based nanofluid; an experimental procedure. Int J Heat Mass Transf. 2018;122:643–50.

    Article  CAS  Google Scholar 

  20. Ganesh Kumar K. Exploration of flow and heat transfer of non-Newtonian nanofluid over a stretching sheet by considering slip factor. Int J Numer Methods for Heat Fluid Flow. 2019. https://doi.org/10.1108/HFF-11-2018-0687.

    Article  Google Scholar 

  21. Souayeh B, Kumar KG, Reddy MG, Rani S, Hdhiri N, Alfannakh H, Rahimi-Gorji M. Slip flow and radiative heat transfer behavior of titanium alloy and ferromagnetic nanoparticles along with suspension of dusty fluid. J Mol Liq. 2019;290:111223.

    Article  CAS  Google Scholar 

  22. Reddy MGG, Kumar KG, Shehzad SA, Javed T, Ambreen T. Thermal transportation analysis of nanoliquid squeezed flow past a sensor surface with MCWCNT and SWCNT. Heat Transf Asian Res. 2019;48(6):2262–75.

    Article  Google Scholar 

  23. Gireesha BJ, Ganesh Kumar K, Krishanamurthy MR, Rudraswamy NG. Enhancement of heat transfer in an unsteady rotating flow for the aqueous suspensions of single wall nanotubes under nonlinear thermal radiation: a numerical study. Colloid Polym Sci. 2018;296(9):1501–8.

    Article  CAS  Google Scholar 

  24. Qin Y, Zhang M, Hiller JE. Theoretical and experimental studies on the daily accumulative heat gain from cool roofs. Energy. 2017;129:138–47.

    Article  Google Scholar 

  25. Sheikholeslami M, Jafaryar M, Hedayat M, Shafee A, Li Z, Nguyen TK, Bakouri M. Heat transfer and turbulent simulation of nanomaterial due to compound turbulator including irreversibility analysis. Int J Heat Mass Transf. 2019;137:1290–300.

    Article  CAS  Google Scholar 

  26. Sureshkumar R, Mohideen ST, Nethaji N. Heat transfer characteristics of nanofluids in heat pipes: a review. Renew Sustain Energy Rev. 2013;20:397–410.

    Article  CAS  Google Scholar 

  27. Kole M, Dey TK. Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids. Appl Therm Eng. 2013;50(1):763–70.

    Article  CAS  Google Scholar 

  28. Sivaraj C, Sheremet MA. MHD natural convection and entropy generation of ferrofluids in a cavity with a non-uniformly heated horizontal plate. Int J Mech Sci. 2018;149:326–37.

    Article  Google Scholar 

  29. Sheikholeslami M. New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Comput Methods Appl Mech Eng. 2019;344:319–33.

    Article  Google Scholar 

  30. Gibanov NS, Sheremet MA, Oztop HF, Al-salem K. MHD natural convection and entropy generation in an open cavity having different horizontal porous blocks saturated with a ferrofluid. J Magn Magn Mater. 2018;452:193–204.

    Article  CAS  Google Scholar 

  31. Abbasi FM, Shanakhat I, Shehzad SA. Entropy generation analysis in peristalsis of nanofluid with Ohmic heating and Hall effects. Phys Scr. 2019;94:025001.

    Article  CAS  Google Scholar 

  32. Sheikholeslami M, Haq R, Shafee A, Li Z, Elaraki YG, Tlili I. Heat transfer simulation of heat storage unit with nanoparticles and fins through a heat exchanger. Int J Heat Mass Transf. 2019;135:470–8.

    Article  CAS  Google Scholar 

  33. Sheikholeslami M, Haq R, Shafee A, Li Z. Heat transfer behavior of Nanoparticle enhanced PCM solidification through an enclosure with V shaped fins. Int J Heat Mass Transf. 2019;130:1322–42.

    Article  CAS  Google Scholar 

  34. Qin Y, He Y, Hiller JE, Mei G. A new water-retaining paver block for reducing runoff and cooling pavement. J Clean Prod. 2018;199:948–56.

    Article  Google Scholar 

  35. Sheikholeslami M. Finite element method for PCM solidification in existence of CuO nanoparticles. J Mol Liq. 2018;265:347–55.

    Article  CAS  Google Scholar 

  36. Sheikholeslami M, Jafaryar M, Shafee A, Li Z, Haq R. Heat transfer of nanoparticles employing innovative turbulator considering entropy generation. Int J Heat Mass Transf. 2019;136:1233–40.

    Article  CAS  Google Scholar 

  37. Sheikholeslami M. Application of control volume based finite element method (CVFEM) for nanofluid flow and heat transfer. Amsterdam: Elsevier; 2019.

    Google Scholar 

  38. Sheikholeslami M, Bhatti MM. Active method for nanofluid heat transfer enhancement by means of EHD. Int J Heat Mass Transf. 2017;109:115–22.

    Article  CAS  Google Scholar 

  39. Sheikholeslami M, Shehzad SA. Thermal radiation of ferrofluid in existence of Lorentz forces considering variable viscosity. Int J Heat Mass Transf. 2017;109:82–92.

    Article  CAS  Google Scholar 

  40. Sheikholeslami M, Arabkoohsar A, Babazadeh H. Modeling of Nanomaterial treatment through a porous space including magnetic forces. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08878-2.

    Article  Google Scholar 

  41. Sheikholeslami M, Shehzad SA. CVFEM simulation for nanofluid migration in a porous medium using Darcy model. Int J Heat Mass Transf. 2018;122:1264–71.

    Article  CAS  Google Scholar 

  42. Sheikholeslami M, Shehzad SA. Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model. Int J Heat Mass Transf. 2018;120:1200–12.

    Article  CAS  Google Scholar 

  43. Vo DD, Hedayat M, Ambreen T, Shehzad SA, Sheikholeslami M, Shafee A, Nguyen TK. Effectiveness of various shapes of Al2O nanoparticles on the MHD convective heat transportation in porous medium: CVFEM modeling. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08501-4.

    Article  Google Scholar 

  44. Sheikholeslami M, Sheremet MA, Shafee A, Li Z. CVFEM approach for EHD flow of nanofluid through porous medium within a wavy chamber under the impacts of radiation and moving walls. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08235-3.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sabir A. Shehzad.

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

Babazadeh, H., Ambreen, T., Shehzad, S.A. et al. Ferrofluid non-Darcy heat transfer involving second law analysis: an application of CVFEM. J Therm Anal Calorim 143, 455–472 (2021). https://doi.org/10.1007/s10973-020-09264-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-09264-z

Keywords

Navigation