Skip to main content
SpringerLink
Log in

Transient magneto-buoyant convection of a magnetizable nanofluid inside a circle sensible storage subjected to double time-dependent thermal sources

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

Abstract

Thermal and flow behaviors of sensible heat energy storage unit subjected to uniform and nonuniform magnetic field effects and to double time dependent heat sources were numerically investigated. The sensible heat energy storage unit is occupied with the nanofluid consisting in Cu nanoparticles dispersed into water and subjected to two variable magnetic sources. The dimensionless governing equations are established and solved via finite element numerical approach. An excellent consistency with published data has been observed during validation of the results. The influence of a certain range of key nondimensional parameters on the transient problem including the frequency of sinusoidal time-dependent temperature imposed from heat sources (λ = 0.1–50), temperature-dependent amplitude of sinusoidal fluctuations (Λ = 0–1), the magnetic number (Mn = 0–5000) and Hartmann number (Ha = 0–50) for two separate Rayleigh number (Ra = 104 and 106) was considered. According to the findings, temperature-varying boundaries affect convective flow, heat exchange, thermal stratification, and total heat content. The oscillations amplitudes for the average time-dependent Nusselt number grow as Ra, Λ and λ increase and Ha decreases. Total heat content in the storage unit is found to have higher mean values at steady development for higher Ra values when Ha = 0. Mn values slightly enhance the mean values of heat content.

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

Similar content being viewed by others

Data availability

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.]

Abbreviations

g:

Gravitational acceleration (m s−2)

Cp :

Specific heat (J kg−1 K−1)

D:

Cavity size (m)

V :

Velocity vector (m s−1)

Ec:

Eckert number

x, y:

Cartesian coordinates (m)

u, v:

Components of velocity in x and y directions, respectively (m s−1)

T:

Temperature (k)

B :

Magnetic induction vector

H * :

Magnetic field vector

M :

Magnetization vector

Da :

Darcy number

Ha :

Hartmann number

a :

Dimensional amplitude

a i, b i :

Coordinates of the magnetic sources

f :

Dimensional frequency

k :

Thermal conductivity (W m−1 K−1)

n :

Normal direction to the semi-cylinders

Nu a :

Average Nusselt number

p :

Pressure (Pa)

\(\dot{r}\) :

Distance to the magnetic source

Pr :

Prandtl number

Mn :

Magnetism Numbers

Ra :

Rayleigh number

K′:

Constant

T c′:

Curie temperature

S :

Thermal stratification

Q:

Total heat content

t:

Dimensional time (s)

λ :

Frequency of sinusoidal time-dependant temperature imposed from heat sources

Λ:

Temperature-dependent amplitude of sinusoidal fluctuations

α :

Thermal diffusivity coefficient, m−2 s−1

β :

Thermal expansion coefficient (1/K)

Ω:

Strength of the magnetic source

Ωr :

Strength ratio of the two magnetic sources #1 and #2

μ :

Dynamic viscosity (kg m−1 s−1)

μ 0 :

Permeability of vacuum

φ :

Volume fraction of nanoparticles

ρ :

Density (kg m−3)

σ :

Electrical conductivity (S m−1)

θ :

Non-dimensional temperature

τ:

Non-dimensional time

ff :

Ferro fluid

r :

The relative properties of the ferrofluid to the base fluid

x, y:

In x and y directions

1, 2:

Refer to the magnetic sources #1 and #2, respectively

i:

Initial

-:

Dimensionless variables

~ :

Dimensional variables

References

  1. Suri ARS, Kumar A, Maithani R. Convective heat transfer enhancement techniques of heat exchanger tubes: A review. Int J Ambient Energy. 2018;39:649–70. https://doi.org/10.1080/01430750.2017.1324816.

    Article  CAS  Google Scholar 

  2. Singh H, Eames PC. Correlations for natural convective heat exchange in CPC solar collector cavities determined from experimental measurements. Sol Energy. 2012;86:2443–57. https://doi.org/10.1016/j.solener.2012.05.014.

    Article  Google Scholar 

  3. Laguerre O, Ben Amara S, Flick D. Experimental study of heat transfer by natural convection in a closed cavity: Application in a domestic refrigerator. J Food Eng. 2005;70:523–37. https://doi.org/10.1016/j.jfoodeng.2004.10.007.

    Article  Google Scholar 

  4. El Omari K, Kousksou T, Le Guer Y. Impact of shape of container on natural convection and melting inside enclosures used for passive cooling of electronic devices. Appl Therm Eng. 2011;31:3022–35. https://doi.org/10.1016/j.applthermaleng.2011.05.036.

    Article  CAS  Google Scholar 

  5. Choi, S. E. J. In: Enhancing Thermal Conductivity of Fluids with Nanoparticles CONF-951135-29 (1995).

  6. Izadi S, Armaghani T, Ghasemiasl R, Chamkha AJ, Molana M. A comprehensive review on mixed convection of nanofluids in various shapes of enclosures. Powder Technol. 2019;343:880–907. https://doi.org/10.1016/j.powtec.2018.11.006.

    Article  CAS  Google Scholar 

  7. Basak T, Chamkha AJ. Heatline analysis on natural convection for nanofluids confined within square cavities with various thermal boundary conditions. Int J Heat Mass Transf. 2012;55:5526–43. https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.025.

    Article  CAS  Google Scholar 

  8. Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46:3639–53. https://doi.org/10.1016/S0017-9310(03)00156-X.

    Article  CAS  Google Scholar 

  9. Sadeghi MS, Anadalibkhah N, Ghasemiasl R, Armaghani T, Dogonchi AS, Chamkha AJ, Ali H, Asadi A. On the natural convection of nanofluids in diverse shapes of enclosures: An exhaustive review. J Therm Anal Calorim. 2022;147:1–22. https://doi.org/10.1007/s10973-020-10222-y.

    Article  CAS  Google Scholar 

  10. Giwa SO, Sharifpur M, Ahmadi MH, Meyer JP. A review of magnetic field influence on natural convection heat transfer performance of nanofluids in square cavities. J Therm Anal Calorim. 2021;145:2581–623. https://doi.org/10.1007/s10973-020-09832-3.

    Article  CAS  Google Scholar 

  11. Rostami S, Aghakhani S, Hajatzadeh Pordanjani A, Afrand M, Cheraghian G, Oztop HF, Shadloo MS. A review on the control parameters of natural convection in different shaped cavities with and without nanofluid. Processes. 2020;8:1011. https://doi.org/10.3390/pr8091011.

    Article  CAS  Google Scholar 

  12. Abouali O, Ahmadi G. Computer simulations of natural convection of single phase nanofluids in simple enclosures: A critical review. Appl Therm Eng. 2012;36:1–13. https://doi.org/10.1016/j.applthermaleng.2011.11.065.

    Article  CAS  Google Scholar 

  13. Haddad Z, Oztop HF, Abu-Nada E, Mataoui A. A review on natural convective heat transfer of nanofluids. Renew Sustain Energy Rev. 2012;16:5363–78. https://doi.org/10.1016/j.rser.2012.04.003.

    Article  CAS  Google Scholar 

  14. Saha A, Chakravarty A, Ghosh K, Biswas N, Manna NK. Role of obstructing block on enhanced heat transfer in a concentric annulus. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2106386.

    Article  Google Scholar 

  15. Saha A, Manna NK, Ghosh K, Biswas N. Analysis of geometrical shape impact on thermal management of practical fluids using square and circular cavities. Eur Phys J Spec Top. 2022;231:2509–37. https://doi.org/10.1140/epjs/s11734-022-00593-8.

    Article  CAS  Google Scholar 

  16. Khoshvaght-Aliabadi M, Alizadeh A. An experimental study of Cu–water nanofluid flow inside serpentine tubes with variable straight-section lengths. Exp Therm Fluid Sci. 2015;61:1–11. https://doi.org/10.1016/j.expthermflusci.2014.09.014.

    Article  CAS  Google Scholar 

  17. Khoshvaght-Aliabadi M, Davoudi S, Dibaei MH. Performance of agitated-vessel U tube heat exchanger using spiky twisted tapes and water based metallic nanofluids. Chem Eng Res Des. 2018;133:26–39. https://doi.org/10.1016/j.cherd.2018.02.030.

    Article  CAS  Google Scholar 

  18. M’hamed B, Sidik NAC, Yazid MNAWM, Mamat R, Najafi G, Kefayati GHR. A review on why researchers apply external magnetic field on nanofluids. Int Commun Heat Mass Transf. 2016;78:60–7. https://doi.org/10.1016/j.icheatmasstransfer.2016.08.023.

    Article  CAS  Google Scholar 

  19. Nkurikiyimfura I, Wang Y, Pan Z. Heat transfer enhancement by magnetic nanofluids—A review. Renew Sustain Energy Rev. 2013;21:548–61. https://doi.org/10.1016/j.rser.2012.12.039.

    Article  CAS  Google Scholar 

  20. Manna NK, Biswas N. Magnetic force vectors as a new visualization tool for magnetohydrodynamic convection. Int J Therm Sci. 2021;167:107004. https://doi.org/10.1016/j.ijthermalsci.2021.107004.

    Article  CAS  Google Scholar 

  21. Hemmat Esfe M, Afrand M, Esfandeh S. Investigation of the effects of various parameters on the natural convection of nanofluids in various cavities exposed to magnetic fields: A comprehensive review. J Therm Anal Calorim. 2020;140:2055–75. https://doi.org/10.1007/s10973-019-08939-6.

    Article  CAS  Google Scholar 

  22. Ghasemi B, Aminossadati SM, Raisi A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int J Therm Sci. 2011;50:1748–56. https://doi.org/10.1016/j.ijthermalsci.2011.04.010.

    Article  CAS  Google Scholar 

  23. Kefayati GR. Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method. Int Commun Heat Mass Transf. 2013;40:67–77. https://doi.org/10.1016/j.icheatmasstransfer.2012.10.024.

    Article  CAS  Google Scholar 

  24. Mahmoudi AH, Pop I, Shahi M. Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid. Int J Therm Sci. 2012;59:126–40. https://doi.org/10.1016/j.ijthermalsci.2012.04.006.

    Article  CAS  Google Scholar 

  25. Sheikholeslami M, Bandpy MG, Ellahi R, Zeeshan A. Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces. J Magn Magn Mater. 2014;369:69–80. https://doi.org/10.1016/j.jmmm.2014.06.017.

    Article  CAS  Google Scholar 

  26. Sheikholeslami M, Vajravelu K. Nanofluid flow and heat transfer in a cavity with variable magnetic field. Appl Math Comput. 2017;298:272–82. https://doi.org/10.1016/j.amc.2016.11.025.

    Article  Google Scholar 

  27. Sreedevi P, Sudarsana Reddy P. Effect of magnetic field and thermal radiation on natural convection in a square cavity filled with TiO2 nanoparticles using Tiwari–Das nanofluid model. Alex Eng J. 2022;61:1529–41. https://doi.org/10.1016/j.aej.2021.06.055.

    Article  Google Scholar 

  28. Bondareva NS, Sheremet MA, Pop I. Magnetic field effect on the unsteady natural convection in a right-angle trapezoidal cavity filled with a nanofluid. Int J Numer Methods Heat Fluid Flow. 2015;25:1924–46. https://doi.org/10.1108/HFF-07-2014-0236.

    Article  Google Scholar 

  29. Al-Zamily AMJ. Effect of magnetic field on natural convection in a nanofluid-filled semi-circular enclosure with heat flux source. Comput Fluids. 2014;103:71–85. https://doi.org/10.1016/j.compfluid.2014.07.013.

    Article  Google Scholar 

  30. Sheremet MA, Pop I, Roşca NC. Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno’s mathematical model. J Taiwan Inst Chem Eng. 2016;61:211–22. https://doi.org/10.1016/j.jtice.2015.12.015.

    Article  CAS  Google Scholar 

  31. Manna NK, Biswas N, Mandal DK, Sarkar UK, Öztop HF, Abu-Hamdeh N. Impacts of heater-cooler position and Lorentz force on heat transfer and entropy generation of hybrid nanofluid convection in quarter-circular cavity. Int J Numer Methods Heat Fluid Flow. 2023;33:1249–86. https://doi.org/10.1108/HFF-07-2022-0402.

    Article  Google Scholar 

  32. Chatterjee D, Biswas N, Manna NK, Sarkar S. Effect of discrete heating-cooling on magneto-thermal-hybrid nanofluidic convection in cylindrical system. Int J Mech Sci. 2023;238:107852. https://doi.org/10.1016/j.ijmecsci.2022.107852.

    Article  Google Scholar 

  33. Alsabery AI, Tayebi T, Chamkha AJ, Hashim I. Effects of two-phase nanofluid model on natural convection in a square cavity in the presence of an adiabatic inner block and magnetic field. Int J Numer Methods Heat Fluid Flow. 2018;28:1613–47. https://doi.org/10.1108/HFF-10-2017-0425.

    Article  Google Scholar 

  34. Sheikholeslami M, Rokni HB. Nanofluid two phase model analysis in existence of induced magnetic field. Int J Heat Mass Transf. 2017;107:288–99. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.130.

    Article  CAS  Google Scholar 

  35. Loenko DS, Shenoy A, Sheremet MA. Effect of time-dependent wall temperature on natural convection of a non-Newtonian fluid in an enclosure. Int J Therm Sci. 2021;166:106973. https://doi.org/10.1016/j.ijthermalsci.2021.106973.

    Article  Google Scholar 

  36. Hussam WK, Khanafer K, Salem HJ, Sheard GJ. Natural convection heat transfer utilizing nanofluid in a cavity with a periodic side-wall temperature in the presence of a magnetic field. Int Commun Heat Mass Transf. 2019;104:127–35. https://doi.org/10.1016/j.icheatmasstransfer.2019.02.018.

    Article  CAS  Google Scholar 

  37. Biswas N, Sarkar UK, Chamkha AJ, Manna NK. Magneto-hydrodynamic thermal convection of Cu–Al2O3/water hybrid nanofluid saturated with porous media subjected to half-sinusoidal nonuniform heating. J Therm Anal Calorim. 2021;143:1727–53. https://doi.org/10.1007/s10973-020-10123-0.

    Article  CAS  Google Scholar 

  38. Biswas N, Manna NK, Chamkha AJ. Effects of half-sinusoidal nonuniform heating during MHD thermal convection in Cu–Al2O3/water hybrid nanofluid saturated with porous media. J Therm Anal Calorim. 2021;143:1665–88. https://doi.org/10.1007/s10973-020-10109-y.

    Article  CAS  Google Scholar 

  39. Mondal MK, Biswas N, Datta A, Mandal DK, Manna NK. Magneto-hydrothermal convective dynamics of hybrid nanofluid-packed partially cooled porous cavity: Effect of half-sinusoidal heating. J Therm Anal Calorim. 2023. https://doi.org/10.1007/s10973-023-11959-y.

    Article  Google Scholar 

  40. Tzirtzilakis EE. A mathematical model for blood flow in magnetic field. Phys Fluids. 2005;17:77103.

    Article  Google Scholar 

  41. Tzirtzilakis EE, Xenos MA. Biomagnetic fluid flow in a driven cavity. Meccanica. 2013;48:187–200.

    Article  Google Scholar 

  42. Sheikholeslami M, Ganji DD. Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer. Energy. 2014;75:400–10. https://doi.org/10.1016/j.energy.2014.07.089.

    Article  CAS  Google Scholar 

  43. Kargarsharifabad H. Experimental and numerical study of natural convection of Cu-water nanofluid in a cubic enclosure under constant and alternating magnetic fields. Int Commun Heat Mass Transf. 2020;119:104957. https://doi.org/10.1016/j.icheatmasstransfer.2020.104957.

    Article  CAS  Google Scholar 

  44. Corvaro F, Paroncini M. Experimental analysis of natural convection in square cavities heated from below with 2D-PIV and holographic interferometry techniques. Exp Therm Fluid Sci. 2007;31:721–39.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Lorestan University, P.O. Box 68151-44316, Khorramabad, Iran

    Mohsen Izadi

  2. Department of Mechanical Engineering, Faculty of Sciences and Technology, Mohamed El Bachir El Ibrahimi University, 34030, El-Anasser, Bordj Bou Arreridj, Algeria

    Tahar Tayebi

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21521, Saudi Arabia

    Hashim M. Alshehri

  4. Materials and Structures Department, ECAM Lyon, Université de Lyon, Lyon, France

    Ahmad Hajjar

  5. College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

    Mohamed Bechir Ben Hamida

  6. Research Laboratory of Ionized Backgrounds and Reagents Studies (EMIR), Preparatory Institute for Engineering Studies of Monastir (IPEIM), University of Monastir, Monastir City, Tunisia

    Mohamed Bechir Ben Hamida

  7. Higher School of Sciences and Technology of Hammam Sousse (ESSTHS), University of Sousse, Sousse, Tunisia

    Mohamed Bechir Ben Hamida

  8. Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam bin Abdulaziz University, Wadi Alddawasir, Saudi Arabia

    Ahmed M. Galal

  9. Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O 35516, Mansoura, Egypt

    Ahmed M. Galal

Authors
  1. Mohsen Izadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tahar Tayebi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hashim M. Alshehri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmad Hajjar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mohamed Bechir Ben Hamida
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ahmed M. Galal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohsen Izadi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Izadi, M., Tayebi, T., Alshehri, H.M. et al. Transient magneto-buoyant convection of a magnetizable nanofluid inside a circle sensible storage subjected to double time-dependent thermal sources. J Therm Anal Calorim 148, 8511–8531 (2023). https://doi.org/10.1007/s10973-023-12242-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-023-12242-w

Keywords

Search

Navigation