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Thermal management of transverse magnetic source effects on nanofluid natural convection in a wavy porous enclosure

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Abstract

Thermal transport of nanofluid natural convection in a wavy porous enclosure exposed to an external and uniform magnetic source is investigated numerically. Numerous pertinent factors in terms of Darcy (Da = 10−4–10−2), Hartmann (Ha = 0–40), Rayleigh (Ra = 104–107), Prandtl (Pr = 0.71–7) and undulation (n = 3) numbers, in addition to wave amplitudes (A = 0.025–0.1) and particle volume concentration (\(\phi\) = 0, 2 and 4%) have been investigated. The Brinkmann–Forchheimer extended Darcy model is utilized, and the governing equations are solved by employing our own finite difference ADI-based program. Code accuracy was successfully validated with the open literature. The results revealed that for Ra > 105 and Da < 10−3, the magnetic field does not play a substantial role in the convective thermal energy, while at high Ha and low Ra, the intensity of conduction increases. The surface waviness and Darcy number both have significant effects on the heat transfer suppression if insulation is desired. Furthermore, a critical value of Ra = 105 is observed whereby the mean Nusselt number decreases despite particle volume concentration, particularly at high Hartmann values.

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Availability of data and material

The datasets during and/or analyzed during the current study available from the corresponding author on reasonable request.

Code availability

The implemented CFD code during the current study available from the corresponding author on reasonable request.

Abbreviations

A:

Amplitude of the wavy surface

B o :

External magnetic field, Tesla

C p :

Specific heat transfer, \( {\text{J}}{\text{kg}}^{-1}\,{\text{K}}^{-1} \)

Da :

Darcy number

g :

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

Ha :

Hartmann number

k :

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

K :

Porous media permeability, \( {\text{m}}^{2} \)

L :

Length and height of the enclosure, \( {\text{m}} \)

n :

Undulation number

Nu x :

Local Nusselt number

Nu m :

Mean Nusselt number

p :

Pressure, \( Pa \)

P :

Dimensionless pressure

Pr :

Prandtl number

Ra :

Rayleigh number

T :

Temperature, \( \text{K} \)

u, v :

Velocity components in x, y directions, \( {\text{m}}\,{\text{s}}^{-1} \)

U, V :

Dimensionless velocity components

x, y :

Cartesian coordinates, \( {\text{m}} \)

X, Y :

Dimensionless coordinates, \( {\text{m}} \)

\( \alpha \) :

Thermal diffusivity, \( {\text{m}}^{2}\,{\text{s}}^{-1}\)

\( \beta \) :

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

\( \phi \) :

Nanoparticles volume fraction

\( \mu \) :

Dynamic viscosity, \( \text{Pa s} \)

\( \upsilon \) :

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

\( \omega \) :

Dimensionless vorticity

\( \varepsilon \) :

Porosity

\( \theta \) :

Dimensionless temperature

\( \rho \) :

Density, \( {\text{kg}}\,{\text{m}}^{-3} \)

\( \sigma \) :

Electrical conductivity, \( {\text{S}}\,{\text{m}}^{-1} \)

\( \psi \) :

Dimensionless stream function

c:

Cold

bf:

Fluid

h:

Hot

m:

Mean

nf:

Nanofluid

p:

Particles

References

  1. 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. 2020. https://doi.org/10.1007/s10973-020-09832-3.

    Article  Google Scholar 

  2. Randall KR, Mitchell JW, El-Wakil MM. Natural convection heat transfer characteristics of flat plate enclosures. J Heat Transf Trans ASME. 1979;101:120–5.

    Google Scholar 

  3. Sunil, Varun, Sharma N. Experimental investigation of the performance of an indirect-mode natural convection solar dryer for drying fenugreek leaves. J Therm Anal Calorim. 2014;118:523–31.

    CAS  Google Scholar 

  4. Haghighi A, Albojamal A, Vafai K. Heat removal enhancement in a channel with a single or an array of metallic foam obstacles. Int J Therm Sci. 2019;149:106057.

    Google Scholar 

  5. Tong TW, Subramanian E. Natural Convection in Rectangular Enclosures Partially Filled With a Porous Medium. 1983;1:331–8.

    Google Scholar 

  6. Wu F, Lu D, Wang G. Numerical analysis of natural convection in a porous cavity with the sinusoidal thermal boundary condition using a thermal nonequilibrium model. Numer Heat Transf Part A Appl. 2016;69:1280–96.

    Google Scholar 

  7. Garandet JP, Alboussiere T, Moreau R. Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field. Int J Heat Mass Transf. 1992;35:741–8.

    CAS  Google Scholar 

  8. Daneshvar Garmroodi MR, Ahmadpour A, Hajmohammadi MR, Gholamrezaie S. Natural convection of a non-Newtonian ferrofluid in a porous elliptical enclosure in the presence of a non-uniform magnetic field. J Therm Anal Calorim. 2019;.

  9. 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.

    CAS  Google Scholar 

  10. Kumar BVR. A study of free convection induced by a vertical wavy surface with heat flux in a porous enclosure. Numer Heat Transf Part A Appl. 2000;37:493–510.

    CAS  Google Scholar 

  11. Das D, Biswal P, Roy M, Basak T. Role of the importance of “Forchheimer term” for visualization of natural convection in porous enclosures of various shapes. Int J Heat Mass Transf. 2016;97:1044–68.

    Google Scholar 

  12. Salari M, Rashidi MM, Malekshah EH, Malekshah MH. Numerical analysis of turbulent/transitional natural convection in trapezoidal enclosures. Int J Numer Methods Heat Fluid Flow. 2017;27:2902–23.

    Google Scholar 

  13. Albojamal A, Hamzah H, Haghighi A, Vafai K. Analysis of nanofluid transport through a wavy channel. Numer Heat Transf Part A Appl. 2017;72:869–90.

    CAS  Google Scholar 

  14. Hamzah H, Hasan SI, Küçüka S. Numerical study of thermal transport in a flat-plate solar collector using novel absorber plate. Green Energy Technol. 2020;32:649–62.

    Google Scholar 

  15. Khanafer K, Al-Azmi B, Marafie A, Pop I. Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure. Int J Heat Mass Transf. 2009;52:1887–96.

    CAS  Google Scholar 

  16. Sathiyamoorthy M, Basak T, Roy S, Pop I. Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall(s). Int J Heat Mass Transf. 2007;50:1892–901.

    Google Scholar 

  17. Basak T, Roy S, Paul T, Pop I. Natural convection in a square cavity filled with a porous medium: effects of various thermal boundary conditions. Int J Heat Mass Transf. 2006;49:1430–41.

    CAS  Google Scholar 

  18. Mahmud S, Das PK, Hyder N, Sadrul Islam AKM. Free convection in an enclosure with vertical wavy walls. Int J Therm Sci. 2002;41:440–6.

    Google Scholar 

  19. Choi SU, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Am Soc Mech Eng Fluids Eng Div FED. 1995;231:99–105.

    CAS  Google Scholar 

  20. 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.

    CAS  Google Scholar 

  21. Khanafer K, Vafai K. A critical synthesis of thermophysical characteristics of nanofluids. Nanotechnol Energy. 2018;54:279–332.

    Google Scholar 

  22. Jang SP, Choi SU. Role of Brownian motion in the enhanced thermal conductivity of nanofluids. Appl Phys Lett. 2004;84:4316–8.

    CAS  Google Scholar 

  23. Ho CJ, Chen MW, Li ZW. Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity. Int J Heat Mass Transf. 2008;51:4506–16.

    CAS  Google Scholar 

  24. Saleh H, Roslan R, Hashim I. Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure. Int J Heat Mass Transf. 2011;54:194–201.

    CAS  Google Scholar 

  25. Nasrin R, Alim MA, Chamkha AJ. Combined convection flow in triangular wavy chamber filled with water-CuO nanofluid: effect of viscosity models. Int Commun Heat Mass Transf. 2012;39:1226–36.

    CAS  Google Scholar 

  26. Albojamal A, Vafai K. Analysis of single phase, discrete and mixture models, in predicting nanofluid transport. Int J Heat Mass Transf. 2017;114:225–37. https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.030.

    Article  CAS  Google Scholar 

  27. Sheikholeslami M, Ellahi R, Hassan M, Soleimani S. A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder. Int J Numer Methods Heat Fluid Flow. 2014;24:1906–27.

    Google Scholar 

  28. Shafahi M, Bianco V, Vafai K, Manca O. An investigation of the Thermal Performance of Cylindrical Heat Pipes using Nanofluids. Nanotechnol Energy. 2018;53:257–78.

    Google Scholar 

  29. Nemati H, Farhadi M, Sedighi K, Ashorynejad HR, Fattahi E. Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann model. Sci Iran. 2012;19:303–10.

    Google Scholar 

  30. 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.

    CAS  Google Scholar 

  31. Zhou WN, Yan YY. Numerical investigation of the effects of a magnetic field on nanofluid flow and heat transfer by the lattice Boltzmann method. Numer Heat Transf Part A Appl. 2015;68:1–16.

    CAS  Google Scholar 

  32. Xu HJ, Xing ZB, Wang FQ, Cheng ZM. Review on heat conduction, heat convection, thermal radiation and phase change heat transfer of nanofluids in porous media: fundamentals and applications. Chem Eng Sci. 2019;195:462–83.

    CAS  Google Scholar 

  33. Sheremet MA, Grosan T, Pop I. Free Convection in a Square Cavity Filled with a Porous Medium Saturated by Nanofluid Using Tiwari and Das’ Nanofluid Model. Transp Porous Media. 2015;106:595–610.

    CAS  Google Scholar 

  34. Rashidi S, Bovand M, Esfahani JA. Opposition of Magnetohydrodynamic and AL2O3-water nanofluid flow around a vertex facing triangular obstacle. J Mol Liq. 2016;215:276–84.

    CAS  Google Scholar 

  35. Vafai K, Tien CL. Boundary and inertia effects on convective mass transfer in porous media. Int J Heat Mass Transf. 1982;25:1183–90.

    Google Scholar 

  36. Amiri A, Vafai K. Transient analysis of incompressible flow through a packed bed. Int J Heat Mass Transf. 1998;41:4259–79.

    CAS  Google Scholar 

  37. Vafai K. Convective flow and heat transfer in variable-porosity media. J Fluid Mech. 1984;147:233–59.

    Google Scholar 

  38. Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf. 2000;43:3701–7.

    CAS  Google Scholar 

  39. Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20:571.

    CAS  Google Scholar 

  40. James Clerk M. A treatise on electricity and magnetism. A Treatise Electr Magn. 2010;9781108014:1–442.

    Google Scholar 

  41. Kollmann W. Computational fluid dynamics. Volume 2. 2000.

  42. Lauriat G, Prasad V. Natural Convection in a Vertical Porous Cavity: a Numerical Study for Brinkman-Extended Darcy Formulation. Am Soc Mech Eng Heat Transf Div HTD. 1986;56:13–22.

    CAS  Google Scholar 

  43. Nithiarasu P, Seetharamu KN, Sundararajan T. Natural convective heat transfer in a fluid saturated variable porosity medium. Int J Heat Mass Transf. 1997;40:3955–67.

    CAS  Google Scholar 

  44. 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 

  45. Sparrow EM, Abraham JP. A new buoyancy model replacing the standard pseudo-density difference for internal natural convection in gases. Int J Heat Mass Transf. 2003;46:3583–91.

    CAS  Google Scholar 

Download references

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Departmentt of Mechanical Engineering, College of Engineering, Cukurova University, Adana, 01330, Turkey

    Hudhaifa Hamzah & Besir Sahin

  2. Departmentt of Mechanical Engineering, College of Engineering, University of California-Riverside, Riverside, CA, 92521, USA

    Ahmed Albojamal & Kambiz Vafai

Authors
  1. Hudhaifa Hamzah
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  2. Ahmed Albojamal
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  3. Besir Sahin
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  4. Kambiz Vafai
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Hudhaifa Hamzah], [Ahmed Albojamal], [Besir Sahin], and [Kambiz Vafai].

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Correspondence to Kambiz Vafai.

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Hamzah, H., Albojamal, A., Sahin, B. et al. Thermal management of transverse magnetic source effects on nanofluid natural convection in a wavy porous enclosure. J Therm Anal Calorim 143, 2851–2865 (2021). https://doi.org/10.1007/s10973-020-10246-4

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