Skip to main content
SpringerLink
Log in

Effects of half-sinusoidal nonuniform heating during MHD thermal convection in Cu–Al2O3/water hybrid nanofluid saturated with porous media

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

Abstract

The intent of this study is to demonstrate an approach for augmenting heat transfer through porous media subjected to nonuniform heating during the magnetohydrodynamic flow of a hybrid nanofluid of Cu–Al2O3/water. The efficacy of such a heating technique is examined utilizing a classical flow geometry consisting of a square cavity. The heating is made at the bottom following a half-sinusoidal function of different frequencies, along with the presence of a uniform magnetic field. The thermal conditions of the cavity, particularly at the bottom wall, drive thermo-hydrodynamics and associated heat transfer. Furthermore, the addition of different types of nanoparticles to the base liquid in order to boost the thermal performance of conventional fluids and mono-nanofluids is a current technique. The coupled nonlinear governing equations are solved numerically in dimensionless forms adapting the finite volume approach, the Brinkman–Forchheimer–Darcy model, local thermal equilibrium and single-phase model. The study is conducted for wide ranges of parametric impacts to analyze global heat transfer performance. The results of this study reveal that the multi-frequency spatial heating during hybrid nanofluid flow can be utilized as a powerful means to improve the thermal performance of a system operating under different ranges of parameters, even with the presence of porous media and magnetic fields. In addition to different heating frequencies, the variations in amplitude (I) and superposed uniform temperature (\(\theta_{\text{os}}\)) to half-sinusoidal heating are also examined thoughtfully in the analysis for different concentrations of Cu–Al2O3 nanoparticles. Compared to the base liquid, the hybrid nanofluid can contribute toward higher heat transfer.

Graphic abstract

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

Similar content being viewed by others

Abbreviations

B :

Magnetic field (Tesla, N A−1 m−2)

Da:

Darcy number

F c :

Forchheimer coefficient

g :

Acceleration due to gravity (m s−2)

H :

Height of the cavity/length scale (m)

Ha:

Hartmann number

K :

Permeability of porous medium (m2)

L :

Length of the cavity (m)

Nu:

Average Nusselt number

P :

Dimensionless pressure

Pr:

Prandtl number

Ra:

Fluid Rayleigh number

Ram :

Darcy–Rayleigh number

T :

Temperature (K)

u, v :

Velocity components (m s−1)

U, V :

Dimensionless velocity components

x, y :

Cartesian coordinates (m)

X, Y :

Dimensionless coordinates

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

ε :

Porosity

η :

Heat transfer parameter

θ :

Dimensionless temperature

μ :

Dynamic viscosity (Ns m−2)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Electrical conductivity (μ Scm−1)

ϕ :

Volume fraction of nanoparticles

ψ :

Dimensionless stream function

Π :

Dimensionless heat function

c:

Cold

f:

Base fluid/liquid

h:

Hot

nf:

Nanofluid

hnf:

Hybrid nanofluid

max:

Maximum

os:

Offset temperature

s:

Solid

References

  1. Nield DA, Bejan A. Convection in porous media. 3rd ed. Berlin: Springer; 2006.

    Google Scholar 

  2. Manna NK, Biswas N, Mahapatra PS. Convective heat transfer enhancement: effect of multi-frequency heating. Int J Numer Methods Heat Fluid Flow. 2019;29(10):3822–56.

    Google Scholar 

  3. Garimella SV, Persoons T, Weibel JA, Gektin V. Electronics thermal management in information and communications technologies: challenges and future directions. IEEE Trans Comp Pack Manufac Technol. 2016;PP:1–15.

    Google Scholar 

  4. Incropera FP. Convection heat transfers in electronic equipment cooling. J Heat Transf. 1988;110:1097–111.

    Google Scholar 

  5. Remsburg R. Thermal design of electronic equipment. Boca Raton: CRC Press LLC; 2001.

    Google Scholar 

  6. Çebi A, Celen A, Donmez AH, Karakoyun Y, Celen P, Cellek MS, Dalkiliç AS, Taner T, Wongwises S. A review of flow boiling in mini and microchannel for enhanced geometries. J Thermal Eng. 2018;4(3):2037–74.

    Google Scholar 

  7. Dalkiliç AS, Çelen A, Çebi A, Taner T, Wongwises S. Parametric study of energy, exergy and thermoeconomic analyses on vapor compression system cascaded with Libr/Water and NH3/Water absorbtion cascade refrigeration cycle. Anadolu Univ J Sci Technol A Appl Sci Eng. 2017;18(1):78–96.

    Google Scholar 

  8. Khanafer K, Vafai K. Applications of nanofluids in porous medium. J Therm Anal Calorim. 2019;135:1479–92.

    CAS  Google Scholar 

  9. Babar H, Ali HM. Airfoil shaped pin-fin heat sink: potential evaluation of ferric oxide and titania nanofluids. Energy Conv Manag. 2019;202:112194-1–-19.

    Google Scholar 

  10. Sajid MU, Ali HM, Sufyan A, Rashid D, Zahid SU, Rehman WU. Experimental investigation of TiO2-water nanofluid flow and heat transfer inside wavy minichannel heat sinks. J Therm Anal Calorim. 2019;137:1279–94.

    Article  CAS  Google Scholar 

  11. Kasaeian A, Daneshazarian R, Mahian O, Kolsi L, Chamkha AJ, Wongwises S, Pop I. Nanofluid flow and heat transfer in porous media: a review of the latest developments. Int J Heat Mass Transf. 2017;107:778–91.

    CAS  Google Scholar 

  12. Rahimi A, Saee AD, Kasaeipoor A, Malekshah EH. A comprehensive review on natural convection flow and heat transfer: the most practical geometries for engineering applications. Int J Numer Method Heat Fluid Flow. 2018;29(3):834–77.

    Google Scholar 

  13. Nazari MA, Ghasempour R, Ahmadi MH. A review on using nanofluids in heat pipes. J Therm Anal Calorim. 2019;137:1847–55.

    Google Scholar 

  14. Sarkar J, Ghosh P, Adil A. A review on hybrid nanofluids: recent research, development and applications. Renew Sustain Energy Rev. 2015;43:164–77.

    CAS  Google Scholar 

  15. Bhosale GH, Borse SL, Pool Boiling CHF. Enhancement with Al2O3–CuO/H2O hybrid nanofluid. Int J Eng Res Technol. 2013;2(10):946–50.

    Google Scholar 

  16. Selvakumar P, Suresh S. Use of Al2O3–Cu/water hybrid nanofluid in an electronic heat sink. IEEE Trans Compon Packag Manuf Technol. 2012;2(10):1600–7.

    CAS  Google Scholar 

  17. Ghalambaz M, Mehryan SAM, Izadpanahi E, Chamkha AJ, Wen D. MHD natural convection of Cu–Al2O3 water hybrid nanofluids in a cavity equally divided into two parts by a vertical flexible partition membrane. J Therm Anal Calorim. 2019;138:1723–43.

    CAS  Google Scholar 

  18. Chamkha AJ, Sazegar S, Jamesahar E, Ghalambaz M. Thermal non-equilibrium heat transfer modeling of hybrid nanofluids in a structure composed of the layers of solid and porous media and free nanofluids. Energies. 2019;12:541.

    CAS  Google Scholar 

  19. Ghalambaz M, Sheremet MA, Mehryan SAM, Kashkooli FM, Pop I. Local thermal non-equilibrium analysis of conjugate free convection within a porous enclosure occupied with Ag–MgO hybrid nanofluid. J Therm Anal Calorim. 2019;135:1381–98.

    CAS  Google Scholar 

  20. Al-Srayyih BM, Gao S, Hussain SH. Natural convection flow of a hybrid nanofluid in a square enclosure partially filled with a porous medium using a thermal non-equilibrium model. Phys Fluids. 2019;31:043609.

    Google Scholar 

  21. Suresh S, Venkitaraj K, Selvakumar P, Chandrasekar M. Effect of Al2O3–Cu/water hybrid nanofluid in heat transfer. Exp Therm Fluid Sci. 2012;38:54–60.

    CAS  Google Scholar 

  22. Mehryan SAM, Sheremet MA, Soltani M, Izadi M. Natural convection of magnetic hybrid nanofluid inside a double-porous medium using two-equation energy model. J Mol Liq. 2019;277:959–70.

    CAS  Google Scholar 

  23. Izadi M, Mohebbi R, Delouei AA, Sajjadi H. Natural convection of a magnetizable hybrid nanofluid inside a porous enclosure subjected to two variable magnetic fields. Int J Mech Sci. 2018;151:154–69.

    Google Scholar 

  24. 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.

    Google Scholar 

  25. Ghadikolaei SS, Hosseinzadeh Kh, Hatami M, Ganji DD. MHD boundary layer analysis for micropolar dusty fluid containing Hybrid nanoparticles (Cu Al2O3) over a porous medium. J Mol Liq. 2018;268:813–23.

    CAS  Google Scholar 

  26. Ghadikolaei SS, Gholinia M. Terrific effect of H2 on 3D free convection MHD flow of C2H6O2–H2O hybrid base fluid to dissolve Cu nanoparticles in a porous space considering the thermal radiation and nanoparticle shapes effects. Int J Hydrog Energy. 2019;44:17072–83.

    CAS  Google Scholar 

  27. Mehryan SAM, Izadi M, Namazian Z, Chamkha AJ. Natural convection of multi-walled carbon nanotube–Fe3O4/water magnetic hybrid nanofluid flowing in porous medium considering the impacts of magnetic field-dependent viscosity. J Therm Anal Calorim. 2019;138:1541–55.

    CAS  Google Scholar 

  28. Biswas N, Mahapatra PS, Manna NK. Merit of non-uniform over uniform heating in a porous cavity. Int J Heat Mass Transf. 2016;78:135–44.

    Google Scholar 

  29. Khandelwal MK, Bera P, Chakrabarti A. Influence of periodicity of sinusoidal bottom boundary condition on natural convection in porous enclosure. Int J Heat Mass Transf. 2012;55:2889–900.

    Google Scholar 

  30. Saeid NF. Natural convection in porous cavity with sinusoidal bottom wall temperature variation. Int Commun Heat Mass Transf. 2005;32:454–63.

    Google Scholar 

  31. Chandra H, Bera P, Sharma AK. Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls. Numer Heat Transf A. 2020;77(3):317–41.

    CAS  Google Scholar 

  32. Cimpean DS, Revnic C, Pop I. Natural convection in a square inclined cavity filled with a porous medium with sinusoidal temperature distribution on both side walls. Transp Porous Med. 2019;130:391–404.

    Google Scholar 

  33. Wu F, Wang G, Zhou W. Buoyancy induced convection in a porous cavity with sinusoidally and partially thermally active sidewalls under local thermal non-equilibrium condition. Int Commun Heat Mass Transf. 2016;75:100–14.

    Google Scholar 

  34. Mikhailenko SA, Sheremet MA, Pop I. Convective heat transfer in a rotating nanofluid cavity with sinusoidal temperature boundary condition. J Therm Anal Calorim. 2019;137:799–809.

    CAS  Google Scholar 

  35. Oztop HF, Abu-Nada E, Varol Y, Al-Salem K. Computational analysis of nonisothermal temperature distribution on natural convection in nanofluid filled enclosures. Super Micro. 2011;49:453–67.

    CAS  Google Scholar 

  36. Alsabery AI, Chamkha AJ, Saleh H, Hashim I, Chanane B. Effects of finite wall thickness and sinusoidal heating on convection in nanofluid saturated local thermal non-equilibrium porous cavity. Phys A. 2017;470:20–38.

    CAS  Google Scholar 

  37. Arasteh H, Mashayekhi R, Goodarzi M, Motaharpour SH, Dahari M, Toghraie D. Heat and fluid flow analysis of metal foam embedded in a doublelayered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid. J Therm Anal Calorim. 2019;138:1461–76.

    CAS  Google Scholar 

  38. Li Z, Shehzad SA, Sheikholeslami M. An application of CVFEM for nanofluid heat transfer intensification in a porous sinusoidal cavity considering thermal non-equilibrium model. Comput Methods Appl Mech Eng. 2018;339:663–80.

    Google Scholar 

  39. Al-Amir QR, Ahmed SY, Hamzah HK, Ali FH. Effects of Prandtl number on natural convection in a cavity filled with Silver/Water nanofulid-saturated porous medium and non-Newtonian fluid layers separated by sinusoidal vertical interface. Arab J Sci Eng. 2019;44:10339–54.

    CAS  Google Scholar 

  40. Aly AM, Ahmed SE, Raizah ZAS. Double-diffusive natural convection in a square porous cavity with sinusoidal distributions sidewalls filled with a nanofluid. J Porous Media. 2018;21(2):101–22.

    Google Scholar 

  41. Aly AM, Raizah ZAS. Incompressible smoothed particle hydrodynamics method for natural convection of a ferrofluid in a partially layered porous cavity containing a sinusoidal wave rod under the effect of a variable magnetic field. AIP Adv. 2019;9:105210-1–-21.

    Google Scholar 

  42. Malik S, Nayak AK. MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transf. 2017;111:329–45.

    CAS  Google Scholar 

  43. Nazeer M, Ali N, Javed T. Numerical simulation of MHD flow of micropolar fluid inside a porous inclined cavity with uniform and non-uniform heated bottom wall. Can J Phys. 2018;96:576–93.

    CAS  Google Scholar 

  44. Javaherdeh K, Najjarnezami A. Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution. Appl Math Mech Engl Ed. 2018;39(8):1187–200.

    Google Scholar 

  45. Sheremet MA, Pop I. Natural convection in a square porous cavity with sinusoidal temperature distributions on both side walls filled with a nanofluid: buongiorno’s mathematical model. Transp Porous Med. 2014;105:411–29.

    Google Scholar 

  46. Pordanjani AH, Jahanbakhshi A, Nadooshan AA, Afrand M. Effect of two isothermal obstacles on the natural convection of nanofluid in the presence of magnetic field inside an enclosure with sinusoidal wall temperature distribution. Int J Heat Mass Transf. 2018;121:565–78.

    CAS  Google Scholar 

  47. Vo DD, Shah Z, Sheikholeslami M, Shafee A, Nguyen TK. Numerical investigation of MHD nanomaterial convective migration and heat transfer within a sinusoidal porous cavity. Phys Scr. 2019;94:115225-1–-10.

    Google Scholar 

  48. Tayebi T, Chamkha AJ. Buoyancy-driven heat transfer enhancement in a sinusoidally heated enclosure utilizing hybrid nanofluid. Comput Therm Sci. 2017;9(5):405–21.

    Google Scholar 

  49. Takabi B, Salehi S. Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Adv Mech Eng. 2014;6:147059.

    Google Scholar 

  50. Ashorynejad HR, Shahriari A. MHD natural convection of hybrid nanofluid in an open wavy cavity. Results Phys. 2018;9:440–55.

    Google Scholar 

  51. Ghalambaz M, Doostani A, Izadpanahi E, Chamkha AJ. Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity. J Therm Anal Calorim. 2020;139:2321–36.

    CAS  Google Scholar 

  52. Almeshaal MA, Kalidasan K, Askri F, Velkennedy R, Alsagri AS, Kolsi L. Three-dimensional analysis on natural convection inside a T-shaped cavity with water-based CNT–aluminum oxide hybrid nanofluid. J Therm Anal Calorim. 2020;139:2089–98.

    CAS  Google Scholar 

  53. Tayebi T, Chamkha AJ. Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder. J Therm Anal Calorim. 2020;139:2165–79.

    CAS  Google Scholar 

  54. Ali A, Saleem S, Mumraiz S, Saleem A, Awais M, Marwat DNK. Investigation on TiO2–Cu/H2O hybrid nanofluid with slip conditions in MHD peristaltic flow of Jefrey material. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09648-1.

    Article  Google Scholar 

  55. Shafee A, Bhatti MM, Muhammad T, Kumar R, Nam ND, Babazadeh H. Simulation of convective MHD flow with inclusion of hybrid powders. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09601-2.

    Article  Google Scholar 

  56. Abdel-Nour Z, Aissa A, Mebarek-Oudina F, Rashad AM, Ali HM, Sahnoun M, Ganaoui ME. Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09690-z.

    Article  Google Scholar 

  57. Babazadeh H, Shah Z, Ullah I, Kumam P, Shafee A. Analysis of hybrid nanofulid behavior within a porous cavity including Lorentz forces and radiation impacts. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09416-1.

    Article  Google Scholar 

  58. 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. 2020;140:2865–73.

    CAS  Google Scholar 

  59. Biswas N, Manna NK. Enhanced convective heat transfer in lid-driven porous cavity with aspiration. Int J Heat Mass Transf. 2019;114:430–52.

    Google Scholar 

  60. 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.

    CAS  Google Scholar 

  61. Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20(4):571.

    CAS  Google Scholar 

  62. Incropera FP, DeWitt DP. Introduction to heat transfer. New York: Wiley; 2002.

    Google Scholar 

  63. Maxwell JC. A treatise on electricity and magnetism. Oxford: Clarendon Press; 1881.

    Google Scholar 

  64. Suresh S, Venkitaraj K, Selvakumar P, Chandrasekar M. Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids Surf A. 2011;388(1–3):41–8.

    CAS  Google Scholar 

  65. Patankar SV. Numerical heat transfer and fluid flow. New York: Hemisphere; 1980.

    Google Scholar 

  66. 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.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Power Engineering, Jadavpur University, Salt Lake, Kolkata, 700106, India

    Nirmalendu Biswas

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Nirmal K. Manna

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Ali J. Chamkha

  4. Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi, 100000, Vietnam

    Ali J. Chamkha

Authors
  1. Nirmalendu Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nirmal K. Manna
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali J. Chamkha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali J. Chamkha.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Biswas, N., Manna, N.K. & Chamkha, A.J. Effects of half-sinusoidal nonuniform heating during MHD thermal convection in Cu–Al2O3/water hybrid nanofluid saturated with porous media. J Therm Anal Calorim 143, 1665–1688 (2021). https://doi.org/10.1007/s10973-020-10109-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-10109-y

Keywords

Search

Navigation