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Magnetohydrodynamic flow and heat transfer of ferrofluid in a channel with non-symmetric cavities

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Abstract

This paper explores the heat transfer characteristics and fluid flow of ferrofluid in a channel having non-symmetric cavities under the applied magnetic field. Bottom surface of the cavity is uniformly heated, whereas ceiling of the top cavity is cooled isothermally. The dimensionless governing equations for various physical parameters are computed via a higher-order and stable Galerkin-based finite element technique. Effective governing parameters are nanoparticle volume fraction; \((0 \le \phi \le 0.15\)), aspect ratio of the cavities; (\(0.2\le h/H \le 1.0\) ), Richardson number; (\(0.01\le \mathrm{Ri} \le 10\)), Hartmann number; (\(0 \le \mathrm{Ha} \le 100\) ); and Reynolds number; (\(1\le \mathrm{Re} \le 200\)). It is found that the most important parameter is the geometry such that there is an optimal value to maximize the heat transfer. Moreover, it is also noticed that the heat transfer is reduced with strong magnetic field, namely Hartmann number.

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Abbreviations

\(C_{\mathrm{p}}\) :

Specific heat (\(\hbox {J }\hbox {kg}^{-1}\hbox {K}^{-1}\))

H :

Channel height (m)

h :

Cavity height (m)

g :

Gravitational acceleration (\(\hbox {m }\hbox {s}^{-2}\))

k :

Thermal conductivity (\(\hbox {W }\hbox {m}^{-1}\hbox {K}^{-1}\))

Nu:

Nusselt number (local)

T :

Temperature (K)

p :

Pressure (\(\hbox {N }\hbox {m}^{-2}\))

P :

Dimensionless pressure

Ha:

Hartmann number \(B_{0}H\sqrt{\dfrac{\sigma _\mathrm{f}}{\mu _\mathrm{f}}}\),

\({\bar{u}}\) :

Average velocity (\(\hbox {m }\hbox {s}^{-1}\))

Pr:

Prandtl number \(\nu _\mathrm{f}/\alpha _\mathrm{f}\)

Re:

Reynolds number \({\bar{u}} H/\nu _\mathrm{f}\)

uv :

Velocity components (\(\hbox {m }\hbox {s}^{-1}\))

UV :

Velocity components (dimensionless)

XY :

Dimensionless space coordinates

\(\mathrm{Nu}_{\text {avg}}\) :

Average Nusselt number

xy :

Dimensional space coordinates (m)

\(\text {div}\) :

Divergence operator

\(\mathbf e\) :

Unit vector (0,1)

\(\mu\) :

Dynamic viscosity (\(\hbox {kg }\hbox {m}^{-1}\hbox {s}^{-1}\))

\(\phi\) :

Volume fraction of the nanoparticles

\(\beta\) :

Thermal expansion coefficient (\(\hbox {K}^{-1}\))

\(\rho\) :

Density (\(\hbox {kg }\hbox {m}^{-3}\))

\(\nu\) :

Kinematic viscosity (\(\hbox {m}^2\hbox { s}^{-1}\))

\(\theta\) :

Dimensionless temperature

\(\text {avg}\) :

Average

f:

Fluid

c:

Cold

h:

Hot

s:

Nanoparticles

ff:

Ferrofluid

References

  1. Abu-Nada E, Chamkha AJ. Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid. Eur J Mech B Fluids. 2010;29:472–82.

    Article  Google Scholar 

  2. Alinia M, Ganji DD, Gorji-Bandpy M. Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model. Int Commun Heat Mass Transf. 2011;38:1428–35.

    Article  CAS  Google Scholar 

  3. Alsabery A, Sheremet M, Chamkha A, Hashim I. Impact of nonhomogeneous nanofluid model on transient mixed convection in a double lid-driven wavy cavity involving solid circular cylinder. Int J Mech Sci. 2019;150:637–55. https://doi.org/10.1016/j.ijmecsci.2018.10.069.

    Article  Google Scholar 

  4. Alsabery AI, Armaghani T, Chamkha AJ, Hashim I. Conjugate heat transfer of al2o3-water nanofluid in a square cavity heated by a triangular thick wall using Buongiorno’s two-phase model. J Therm Anal Calorim. 2019;135(1):161–76. https://doi.org/10.1007/s10973-018-7473-7.

    Article  CAS  Google Scholar 

  5. Alsabery AI, Armaghani T, Chamkha AJ, Sadiq MA, Hashim I. Effects of two-phase nanofluid model on convection in a double lid-driven cavity in the presence of a magnetic field. Int J Numer Methods Heat Fluid Flow. 2019;29(4):1272–99. https://doi.org/10.1108/HFF-07-2018-0386.

    Article  Google Scholar 

  6. Alsabery AI, Ismael MA, Chamkha AJ, Hashim I. Effects of two-phase nanofluid model on mhd mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater. J Therm Anal Calorim. 2019;135(1):729–50. https://doi.org/10.1007/s10973-018-7377-6.

    Article  CAS  Google Scholar 

  7. Alsarraf J, Rahmani R, Shahsavar A, Afrand M, Wongwises S, Tran MD. Effect of magnetic field on laminar forced convective heat transfer of MWCNT-\(Fe_3O_4\)/water hybrid nanofluid in a heated tube. J Therm Anal Calorim. 2019;. https://doi.org/10.1007/s10973-019-08078-y.

    Article  Google Scholar 

  8. Aminossadati SM, Ghasemi B. A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity. Eur J Mech B Fluids. 2009;28(4):590–8. https://doi.org/10.1016/j.euromechflu.2009.01.001.

    Article  Google Scholar 

  9. Asadi A, Nezhad AH, Sarhaddi F, Keykha T. Laminar ferrofluid heat transfer in presence of non-uniform magnetic field in a channel with sinusoidal wall: A numerical study. J Magn Magn Mater. 2019;471:56–63. https://doi.org/10.1016/j.jmmm.2018.09.045.

    Article  CAS  Google Scholar 

  10. Bahiraei M, Hangi M, Rahbari A. A two-phase simulation of convective heat transfer characteristics of water-\(Fe_3O_4\) ferrofluid in a square channel under the effect of permanent magnet. Appl Therm Eng. 2019;147:991–7. https://doi.org/10.1016/j.applthermaleng.2018.11.011.

    Article  CAS  Google Scholar 

  11. Berger P, Adelman NB, Beckman KJ, Campbell DJ, Ellis AB, Lisensky GC. Preparation and properties of an aqueous ferrofluid. J Chem Educ. 1999;76(7):943. https://doi.org/10.1021/ed076p943.

    Article  CAS  Google Scholar 

  12. Evcin C, Uğur O, Tezer-Sezgin M. Determining the optimal parameters for the MHD flow and heat transfer with variable viscosity and hall effect. Comput Math Appl. 2018;76(6):1338–55. https://doi.org/10.1016/j.camwa.2018.06.027.

    Article  Google Scholar 

  13. Hussain S, Ahmed S, Mehmood K, Sagheer M. Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources. Int J Heat Mass Transf. 2017;106:847–60.

    Article  CAS  Google Scholar 

  14. Hussain S, Mehmood K, Sagheer M, Farooq A. Entropy generation analysis of mixed convective flow in an inclined channel with cavity with \(Al_2O_3\)-water nanofluid in porous medium. Int Commun Heat Mass Transf. 2017;89:198–210. https://doi.org/10.1016/j.icheatmasstransfer.2017.10.009.

    Article  CAS  Google Scholar 

  15. Hussain S, Schieweck F, Turek S. Efficient Newton multigrid solution techniques for higher order space time Galerkin discretizations of incompressible flow. Appl Numer Math. 2014;83:51–71.

    Article  Google Scholar 

  16. Jhumur NC, Bhattacharjee A. Unsteady MHD mixed convection inside l-shaped enclosure in the presence of ferrofluid (\(Fe_3O_4\)). In: In 10th international conference on marine technology procedia engineering. 2017;194:494–501. https://doi.org/10.1016/j.proeng.2017.08.176, MARTEC 2016.

  17. Job VM, Gunakala SR. Mixed convective ferrofluid flow through a corrugated channel with wall-mounted porous blocks under an alternating magnetic field. Int J Mech Sci. 2018;144:357–81. https://doi.org/10.1016/j.ijmecsci.2018.05.054.

    Article  Google Scholar 

  18. Karimipour A, Esfe MH, Safaei MR, Semiromi DT, Jafari S, Kazi SN. Mixed convection of copper-water nanofluid in a shallow inclined lid driven cavity using the Lattice Boltzmann Method. Physica A: Stat Mech Appl. 2014;402:150–68. https://doi.org/10.1016/j.physa.2014.01.057.

    Article  CAS  Google Scholar 

  19. Khosravi A, Malekan M, Assad ME. Numerical analysis of magnetic field effects on the heat transfer enhancement in ferrofluids for a parabolic trough solar collector. Renew Energy. 2019;134:54–63. https://doi.org/10.1016/j.renene.2018.11.015.

    Article  CAS  Google Scholar 

  20. Ma Y, Mohebbi R, Rashidi MM, Yang Z. MHD forced convection of MWCNT-\(Fe_3O_4\)/water hybrid nanofluid in a partially heated \(\uptau\)-shaped channel using LBM. J Therm Anal Calorim. 2019;136(4):1723–35. https://doi.org/10.1007/s10973-018-7788-4.

    Article  CAS  Google Scholar 

  21. Manca O, Nardini S, Khanafer K, Vafai K. Effect of heat wall position on mixed convection in a channel with an open cavity. Numer Heat Transf. 2003;43:259–82.

    Article  Google Scholar 

  22. Maxwell JC. A treatise on electricity and magnetism. Cambridge: Oxford University Press; 1873.

    Google Scholar 

  23. Mehrez Z, Bouterra M, Cafsi A, Belghith A. Heat transfer and entropy generation analysis of nanofluid flow in an open cavity. Comput Fluids. 2013;88:363–73.

    Article  CAS  Google Scholar 

  24. Mehrez Z, Cafsi AE, Belghith A, Quéré PL. The entropy generation analysis in the mixed convective assisting flow of \(cu\)-water nanofluid in an inclined open cavity. Adv Powder Technol. 2015;26(5):1442–51. https://doi.org/10.1016/j.apt.2015.07.020.

    Article  CAS  Google Scholar 

  25. Mousavi SM, Jamshidi N, Rabienataj-Darzi AA. Numerical investigation of the magnetic field effect on the heat transfer and fluid flow of ferrofluid inside helical tube. J Therm Anal Calorim. 2019;137(5):1591–601. https://doi.org/10.1007/s10973-019-08066-2.

    Article  CAS  Google Scholar 

  26. Nessab W, Kahalerras H, Fersadou B, Hammoudi D. Numerical investigation of ferrofluid jet flow and convective heat transfer under the influence of magnetic sources. Appl Therm Eng. 2019;150:271–84. https://doi.org/10.1016/j.applthermaleng.2018.12.164.

    Article  CAS  Google Scholar 

  27. Rabbi KM, Saha S, Mojumder S, Rahman M, Saidur R, Ibrahim TA. Numerical investigation of pure mixed convection in a ferrofluid-filled lid-driven cavity for different heater configurations. Alex Eng J. 2016;55(1):127–39. https://doi.org/10.1016/j.aej.2015.12.021.

    Article  Google Scholar 

  28. Rahman M, Öztop HF, Rahim N, Saidur R, Al-Salem K, Amin N, Mamun M, Ahsan A. Computational analysis of mixed convection in a channel with a cavity heated from different sides. Int Commun Heat Mass Transf. 2012;39(1):78–84. https://doi.org/10.1016/j.icheatmasstransfer.2011.09.006.

    Article  Google Scholar 

  29. Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131(3):2027–39. https://doi.org/10.1007/s10973-017-6773-7.

    Article  CAS  Google Scholar 

  30. Reddy GJ, Raju RS, Rao JA. Influence of viscous dissipation on unsteady MHD natural convective flow of Casson fluid over an oscillating vertical plate via FEM. Ain Shams Eng J. 2018;9(4):1907–15. https://doi.org/10.1016/j.asej.2016.10.012.

    Article  Google Scholar 

  31. Salehpour A, Salehi S, Salehpour S, Ashjaee M. Thermal and hydrodynamic performances of MHD ferrofluid flow inside a porous channel. Exp Therm Fluid Sci. 2018;90:1–13. https://doi.org/10.1016/j.expthermflusci.2017.08.032.

    Article  Google Scholar 

  32. Selimefendigil F, Öztop HF. Effect of a rotating cylinder in forced convection of ferrofluid over a backward facing step. Int J Heat Mass Transf. 2014;71:142–8. https://doi.org/10.1016/j.ijheatmasstransfer.2013.12.042.

    Article  Google Scholar 

  33. Selimefendigil F, Öztop HF, Al-Salem K. Natural convection of ferrofluids in partially heated square enclosures. J Magn Magn Mater. 2014;372:122–33. https://doi.org/10.1016/j.jmmm.2014.07.058.

    Article  CAS  Google Scholar 

  34. Shahsavar A, Godini A, Sardari PT, Toghraie D, Salehipour H. Impact of variable fluid properties on forced convection of \(Fe_3O_4\)/CNT/water hybrid nanofluid in a double-pipe mini-channel heat exchanger. J Therm Anal Calorim. 2019;. https://doi.org/10.1007/s10973-018-07997-6.

    Article  Google Scholar 

  35. Shahsavar A, Saghafian M, Salimpour M, Shafii M. Experimental investigation on laminar forced convective heat transfer of ferrofluid loaded with carbon nanotubes under constant and alternating magnetic fields. Exp Therm Fluid Sci. 2016;76:1–11. https://doi.org/10.1016/j.expthermflusci.2016.03.010.

    Article  CAS  Google Scholar 

  36. Sheikholeslami M, Bandpy MG, Ganji D. Numerical investigation of MHD effects on \({A}l_{2}{O}_{3}\)-water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM. Energy. 2013;60:501–10.

    Article  CAS  Google Scholar 

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Acknowledgements

Calculations have been carried out on the LiDOng cluster at Technische Universität, Dortmund, Germany. The support by the LiDOng team at the ITMC at TU Dortmund is gratefully acknowledged. We would like to thank the LiDOng cluster team for their help and support. We also used FeatFlow (www.featflow.de) solver package and would like to acknowledge the support by the FeatFlow team. Second and last authors extend their appreciation to the International Scientific Partnership Program (ISPP) at King Saud University for funding this research work through ISPP#131.

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Hussain, S., Öztop, H.F., Qureshi, M.A. et al. Magnetohydrodynamic flow and heat transfer of ferrofluid in a channel with non-symmetric cavities. J Therm Anal Calorim 140, 811–823 (2020). https://doi.org/10.1007/s10973-019-08943-w

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