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Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block

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Abstract

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–ε turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles (\( \phi = 2{{\% }} \)) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01.

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Abbreviations

B 0 :

Magnetic field strength

B :

Magnetic field (T)

Be:

Bejan number

C p :

Specific heat capacity (J kg−1 K−1)

E:

Dimensionless dissipation rate of turbulent kinetic energy

g :

Gravitational acceleration (m s−2)

Ha:

Hartmann number

k :

Dimensional turbulent kinetic energy (m2 s−2)

\(\tilde{k}\) :

Thermal conductivity (W m−1 K−1)

K:

Dimensionless turbulent kinetic energy

K P :

Permeability of the medium (m2)

L :

Length of the cavity (m)

m :

Shape factor of nanoparticles

N:

Entropy generation number

Nu:

Nusselt number

p :

Pressure (N m−2)

Pr:

Prandtl number (–)

Ra:

Rayleigh number

\(\dot{S}_{\text{gen}}\) :

Rate of entropy generation per unit volume (J s−1 K−1 m−3)

T :

Temperature (K)

u, v :

Dimensional x and y components of velocity (m s−1)

x, y :

Dimensional coordinates (m)

X, Y:

Dimensionless coordinates

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

ɛ :

Turbulent dissipation of kinetic energy (m2 s−3)

\({{\Theta}}\) :

Dimensionless temperature (–)

λ :

Inclination angle (°)

μ :

Dynamic viscosity (N s m−2)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Electrical conductivity (Ω m−1)

\(\sigma_{\text{k}}\) :

\({k} - {\varepsilon}\) Turbulent model parameters

φ :

Cavity inclination angle (°)

ΔT :

Temperature difference

ϕ :

Volume fraction

\({{\Phi}}\) :

Irreversibility distribution ratio

ψ :

Dimensional stream function (m2 s−1)

\({{\Psi }}\) :

Dimensionless stream function

ω :

Dimensional vorticity (s−1)

\({{\Omega }}\) :

Dimensionless vorticity

ave:

Average

FF:

Fluid friction

gen:

Generation

h:

Hot

HT:

Heat transfer

MF:

Magnetic field

nf:

Nanofluid

PM:

Porous medium

s:

Solid

t:

Turbulent

References

  1. Gholamalipour P, Siavashi M, Doranehgard MH. Eccentricity effects of heat source inside a porous annulus on the natural convection heat transfer and entropy generation of Cu–water nanofluid. Int Commun Heat Mass Transf. 2019;109:104367.

    Article  CAS  Google Scholar 

  2. Siavashi M, Yousofvand R, Rezanejad S. Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity. Adv Powder Technol. 2018;29(1):142–56.

    Article  CAS  Google Scholar 

  3. Seyyedi SM, Sahebi N, Dogonchi AS, Hashemi-Tilehnoee M. Numerical and experimental analysis of a rectangular single-phase natural circulation loop with asymmetric heater position. Int J Heat Mass Transf. 2019;130:1343–57.

    Article  Google Scholar 

  4. Dogonchi AS, Waqas M, Gulzar MM, Hashemi-Tilehnoee M, Seyyedi SM, Ganji DD. Simulation of Fe3O4–H2O nanoliquid in a triangular enclosure subjected to Cattaneo–Christov theory of heat conduction. Int J Numer Methods Heat Fluid Flow. 2019;29(11):4430–44. https://doi.org/10.1108/HFF-01-2019-0031.

    Article  Google Scholar 

  5. Maghsoudi P, Siavashi M. Application of nanofluid and optimization of pore size arrangement of heterogeneous porous media to enhance mixed convection inside a two-sided lid-driven cavity. J Therm Anal Calorim. 2019;135(2):947–61.

    Article  CAS  Google Scholar 

  6. Siavashi M, Ghasemi K, Yousofvand R, Derakhshan S. Computational analysis of SWCNH nanofluid-based direct absorption solar collector with a metal sheet. Sol Energy. 2018;170:252–62.

    Article  CAS  Google Scholar 

  7. Xiong Q, Abohamzeh E, Ali JA, Hamad SM, Tlili I, Shafee A, Habibeh H, Nguyen TK. Influences of nanoparticles with various shapes on MHD flow inside wavy porous space in appearance of radiation. J Mol Liq. 2019;292:111386.

    Article  CAS  Google Scholar 

  8. Abbassi MA, Safaei MR, Djebali R, Guedri K, Zeghmati B, Alrashed AA. LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. Int J Mech Sci. 2018;144:172–85.

    Article  Google Scholar 

  9. Seyyedi SM, Dogonchi AS, Ganji DD, Hashemi-Tilehnoee M. Entropy generation in a nanofluid-filled semi-annulus cavity by considering the shape of nanoparticles. J Therm Anal Calorim. 2019;138(2):1607–21.

    Article  CAS  Google Scholar 

  10. Seyyedi SM, Dogonchi AS, Hashemi-Tilehnoee M, Asghar Z, Waqas M, Ganji DD. A computational framework for natural convective hydromagnetic flow via inclined cavity: an analysis subjected to entropy generation. J Mol Liq. 2019;287:110863.

    Article  CAS  Google Scholar 

  11. Zeeshan A, Shehzad N, Abbas T, Ellahi R. Effects of radiative electro-magnetohydrodynamics diminishing internal energy of pressure-driven flow of titanium dioxide-water nanofluid due to entropy generation. Entropy. 2019;21(3):236.

    Article  CAS  Google Scholar 

  12. Alamri SZ, Khan AA, Azeez M, Ellahi R. Effects of mass transfer on MHD second grade fluid towards stretching cylinder: a novel perspective of Cattaneo–Christov heat flux model. Phys Lett A. 2019;383(2–3):276–81.

    Article  CAS  Google Scholar 

  13. Hassan M, Ellahi R, Bhatti MM, Zeeshan A. A comparative study on magnetic and non-magnetic particles in nanofluid propagating over a wedge. Can J Phys. 2018;97(3):277–85.

    Article  Google Scholar 

  14. Ellahi R, Sait SM, Shehzad N, Mobin N. Numerical simulation and mathematical modeling of electro-osmotic Couette–Poiseuille flow of MHD power-law nanofluid with entropy generation. Symmetry. 2019;11(8):1038.

    Article  CAS  Google Scholar 

  15. Sarafraz MM, Pourmehran O, Yang B, Arjomandi M, Ellahi R. Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. Int J Therm Sci. 2020;147:106131.

    Article  CAS  Google Scholar 

  16. Yousif MA, Ismael HF, Abbas T, Ellahi R. Numerical study of momentum and heat transfer of MHD Carreau nanofluid over an exponentially stretched plate with internal heat source/sink and radiation. Heat Transf Res. 2019;50(7):649–58.

    Article  Google Scholar 

  17. Izadi A, Siavashi M, Xiong Q. Impingement jet hydrogen, air and CuH2O nanofluid cooling of a hot surface covered by porous media with non-uniform input jet velocity. Int J Hydrog Energy. 2019;44(30):15933–48.

    Article  CAS  Google Scholar 

  18. Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2019;137(1):267–87.

    Article  CAS  Google Scholar 

  19. Siavashi M, Joibary SM. Numerical performance analysis of a counter-flow double-pipe heat exchanger with using nanofluid and both sides partly filled with porous media. J Therm Anal Calorim. 2019;135(2):1595–610.

    Article  CAS  Google Scholar 

  20. Ghasemi K, Siavashi M. Three-dimensional analysis of magnetohydrodynamic transverse mixed convection of nanofluid inside a lid-driven enclosure using MRT-LBM. Int J Mech Sci. 2020;165:105199.

    Article  Google Scholar 

  21. Bozorg MV, Siavashi M. Two-phase mixed convection heat transfer and entropy generation analysis of a non-Newtonian nanofluid inside a cavity with internal rotating heater and cooler. Int J Mech Sci. 2019;151:842–57.

    Article  Google Scholar 

  22. Miroshnichenko IV, Sheremet MA. Turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: a review. Renew Sustain Energy Rev. 2018;82:40–59.

    Article  Google Scholar 

  23. Vasiliev A, Sukhanovskii A, Frick P, Budnikov A, Fomichev V, Bolshukhin M, Romanov R. High Rayleigh number convection in a cubic cell with adiabatic sidewalls. Int J Heat Mass Transf. 2016;102:201–12.

    Article  Google Scholar 

  24. Pop I, Sheremet MA. Turbulent natural convection combined with entropy generation in a nanofluid cavity with non-uniformly heated side walls. J Phys Conf Ser. 2019;1366(1):012049.

    Article  CAS  Google Scholar 

  25. Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. Int J Numer Methods Fluids. 1994;18(7):695–719.

    Article  Google Scholar 

  26. Miroshnichenko IV, Sheremet MA. Turbulent natural convection combined with thermal surface radiation inside an inclined cavity having local heater. Int J Therm Sci. 2018;124:122–30.

    Article  Google Scholar 

  27. Miroshnichenko I, Sheremet M, Chamkha AJ. Turbulent natural convection combined with surface thermal radiation in a square cavity with local heater. Int J Numer Methods Heat Fluid Flow. 2018;28(7):1698–715.

    Article  Google Scholar 

  28. Saleh H, Roslan R, Hashim I. Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure. Int J Heat Mass Transf. 2011;54(1–3):194–201.

    Article  CAS  Google Scholar 

  29. Wang XQ, Mujumdar AS. Heat transfer characteristics of nanofluids: a review. Int J Therm Sci. 2007;46(1):1–9.

    Article  Google Scholar 

  30. Dogonchi AS, Ismael MA, Chamkha AJ, Ganji DD. Numerical analysis of natural convection of Cu–water nanofluid filling triangular cavity with semicircular bottom wall. J Therm Anal Calorim. 2019;135(6):3485–97.

    Article  CAS  Google Scholar 

  31. Abu-Nada E, Masoud Z, Hijazi A. Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. Int Commun Heat Mass Transf. 2008;35(5):657–65.

    Article  CAS  Google Scholar 

  32. Dogonchi AS, Waqas M, Seyyedi SM, Hashemi-Tilehnoee M, Ganji DD. CVFEM analysis for Fe3O4–H2O nanofluid in an annulus subject to thermal radiation. Int J Heat Mass Transf. 2019;132:473–83.

    Article  CAS  Google Scholar 

  33. Dincer I, Rosen MA. Eergy, energy, environment and sustainable development. Amsterdam: Elsevier Publishing; 2007.

    Google Scholar 

  34. Woods LC. The thermodynamics of fluid systems. Oxford: Oxford University Press; 1975.

    Google Scholar 

  35. Magherbi M, Abbassi H, Brahim AB. Entropy generation at the onset of natural convection. Int J Heat Mass Transf. 2003;46(18):3441–50.

    Article  Google Scholar 

  36. Hashemi-Tilehnoee M, Sahebi N, Dogonchi AS, Seyyedi SM, Tashakor S. Simulation of the dynamic behavior of a rectangular single-phase natural circulation vertical loop with asymmetric heater. Int J Heat Mass Transf. 2019;139:974–81.

    Article  Google Scholar 

  37. Hashemi-Tilehnoee M, Tashakor S, Seyyedi SM, Sahebi N. Forced reflood modeling in a 2 × 2 rod bundle with a 90% partially blocked region. Ann Nucl Energy. 2019;131:425–32.

    Article  CAS  Google Scholar 

  38. Karami M, Tashakor S, Afsari A, Hashemi-Tilehnoee M. Effect of the baffle on the performance of a micro pin fin heat sink. Therm Sci Eng Progr. 2019;14:100417.

    Article  Google Scholar 

  39. Paroncini M, Corvaro F. Natural convection in a square enclosure with a hot source. Int J Therm Sci. 2009;48(9):1683–95.

    Article  Google Scholar 

  40. Abbassi MA, Djebali R, Guedri K. Effects of heater dimensions on nanofluid natural convection in a heated incinerator shaped cavity containing a heated block. J Therm Eng. 2018;3:2018–36.

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by a research contract of the Islamic Azad University, Aliabad Katoul Branch, Iran.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

    M. Hashemi-Tilehnoee, A. S. Dogonchi & Seyyed Masoud Seyyedi

  2. Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, Saudi Arabia

    Ali J. Chamkha

  3. RAK Research and Innovation Center, American University of Ras Al Khaimah, Ras al-Khaimah, United Arab Emirates

    Ali J. Chamkha

  4. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    D. D. Ganji

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  1. M. Hashemi-Tilehnoee
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  2. A. S. Dogonchi
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  3. Seyyed Masoud Seyyedi
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Correspondence to M. Hashemi-Tilehnoee.

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Hashemi-Tilehnoee, M., Dogonchi, A.S., Seyyedi, S.M. et al. Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block. J Therm Anal Calorim 141, 2033–2045 (2020). https://doi.org/10.1007/s10973-019-09220-6

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