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Analytical analysis of impacts of nanoparticle shapes and uncertainty in thermophysical properties on optimum operating conditions of MHD nanofluid flow in a microchannel filled with porous medium

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Abstract

The effects of different nanoparticle shapes and uncertainty in the nanofluid thermophysical properties on the optimal operating conditions of MHD flow of Al2O3/water nanofluid through a horizontal microchannel with a porous medium considering hydrodynamic slip, suction/injection and thermal radiation were investigated. The momentum and heat transfer equations were solved analytically using the methods of undetermined coefficients and variation of constants, respectively. From the exact solutions of the velocity and temperature fields, the global entropy \(\left\langle {\text{S}} \right\rangle\) and Nusselt number Nu were computed. The impacts of hydrodynamic slip \(\alpha\), Biot number \(Bi\), nanoparticle concentration \(\phi\) and Darcy number \(Da\) on entropy production and heat transport were investigated. The results revealed that optimum values of \(\mathrm{\text{Bi}}\) and \(\alpha\) with minimum global entropy and maximum heat transport were achieved for symmetric slip conditions and asymmetric heat transfer. The platelet shape of nanoparticles was the most effective to achieve the optimum conditions with the lowest minimum value of \(\left\langle {\text{S}} \right\rangle\) , while the blade shape was the most effective to reach the optimum conditions with the highest maximum value of heat transport. Thus, optimum values of both Biot number of bottom plate equal to 0.01 and slip equal to 0.045 with the smallest values of \(\left\langle {\text{S}} \right\rangle\) were achieved for the platelet shape. Also, optimum slip value of 0.15 with the largest maximum Nu at top plate of 5.13 was achieved for the blade shape. On the other hand, when \(\phi\) increased from 0 to 0.045, \(\left\langle {\text{S}} \right\rangle\) always decreased and Nu always increased. The greatest decrease of entropy from 0.133 to 0.088 (33%) occurred for the platelet shape, while the greatest increase of Nu at top plate from 4.96 to 5.57 (12.3%) occurred for the blade shape. When \(\phi\) was varied from 0 to 0.01, \(\left\langle {\text{S}} \right\rangle\) decreased 9.2% for the platelet shape compared to spherical shapes, and Nu at top plate increased 2.6% for the blade shape compared to spherical shapes. The results also indicated that the greatest variations of optimum operating conditions occurred when the experimental correlations of viscosity and thermal conductivity were used compared to theoretical correlations. This is because the estimated values of viscosity and conductivity using the different theoretical correlations differ very little from each other. Thus, the maximum value of Nu at top plate increased from 5.067 for SM1 model to 5.092 for SM6 model (0.5%), while it increased from 4.96 for EM3 model to 5.17 for EM6 model (4.2%). Finally, the effects of Al2O3, Cu and TiO2 nanoparticles in water as base fluid on the optimum conditions were investigated. Both the lowest entropy production and the highest heat transfer were reached for Cu nanoparticles. When \(\alpha\) was varied, the minimum value of \(\left\langle {\text{S}} \right\rangle\) achieved for Cu was 0.47 and 0.64% lower than the minimum value of TiO2 and Al2O3, respectively. Also, the maximum value of Nu achieved for Cu improved by approximately 0.2 and 0.4% compared to Al2O3 and TiO2, respectively.

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Abbreviations

a :

Characteristic length (m) (distance between plates)

Bi:

Biot number

Bo :

Magnetic field (T)

Br:

Brinkman number

C :

Specific heat (J kg−1 K−1)

Da:

Darcy number

Ec:

Eckert number

H :

Convective heat transfer coefficient (W m−2 K−1)

M :

Hartmann number

K :

Thermal conductivity (W m−1 K−1)

K :

Porous medium permeability (m2)

k* :

Mean Rosseland absorption coefficient (1 m−1)

Nu:

Nusselt number

P :

Pressure (N m−2)

P :

Dimensionless pressure gradient

Pe:

Peclet number

Pr:

Prandtl number

Rd:

Radiation parameter

Re:

Reynolds number

S :

Local entropy generation (W m−3·K−1)

\(\left\langle {\text{S}} \right\rangle\) :

Global entropy generation

T :

Temperature (K)

u :

Velocity (m s−1)

x :

Axial coordinate (m)

y :

Transverse coordinate (m)

ν 0 :

Uniform suction/injection velocity (m s−1)

α :

Slip length (m)

ϵ :

Surface emissivity

η :

Dynamic viscosity (kg ms−1)

θ :

Dimensionless temperature

ρ :

Density (kg m−3)

σ :

Electrical conductivity (S m−1)

σ * :

Stefan‐Boltzmann constant (W m−2 K−4)

ϕ :

Nanoparticle concentration

ψ :

Sphericity factor

1:

Bottom plate

2:

Top plate

f :

Base fluid

nf :

Nanofluid

s :

Solid nanoparticle

References

  1. Ramezanpour M, Siavashi M, Raeni AQ, Blunt MJ. Pore-scale simulation of nanoparticle transport and deposition in a microchannel using a Lagrangian approach. J Mol Liq. 2022;355: 118948. https://doi.org/10.1016/j.molliq.2022.118948.

    Article  CAS  Google Scholar 

  2. Soumya DO, Gireesha BJ, Venkatesh P. Tangent-hyperbolic nanoliquid flow in a microchannel, thermal and irreversibility rate analysis. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2108157.

    Article  Google Scholar 

  3. Izadi A, Siavashi M, Rasam H, Xiong Q. MHD enhanced nanofluid mediated heat transfer in porous metal for CPU cooling. Appl Therm Eng. 2020;168: 114843. https://doi.org/10.1016/j.applthermaleng.2019.114843.

    Article  CAS  Google Scholar 

  4. Qasemian A, Moradi F, Karamati A, Keshavarz A, Shakeri A. Hydraulic and thermal analysis of automatic transmission fluid in the presence of nano-particles and twisted tape: an experimental and numerical study. J Central South Univ. 2021;28:3404–17. https://doi.org/10.1007/s11771-021-4864-x.

    Article  CAS  Google Scholar 

  5. Khoshtarash H, Siavashi M, Ramezanpour M, Blunt MJ. Pore-scale analysis of two-phase nanofluid flow and heat transfer in open-cell metal foams considering Brownian motion. Appl Therm Eng. 2023;221: 119847. https://doi.org/10.1016/j.applthermaleng.2022.119847.

    Article  CAS  Google Scholar 

  6. Ghachem K, Kolsi L, Larguech S, Alnemer G. Heat and mass transfer enhancement in triangular pyramid solar still using CNT-water nanofluid. J Central South Univ. 2021;28:3434–48. https://doi.org/10.1007/s11771-021-4866-8.

    Article  CAS  Google Scholar 

  7. Albaqawy G, Mesloub A, Kolsi L. CFD investigation of effect of nanofluid filled Trombe wall on 3D convective heat transfer. J Central South Univ. 2021;28:3569–79. https://doi.org/10.1007/s11771-021-4876-6.

    Article  CAS  Google Scholar 

  8. Aouinet H, Dhahri M, Safaei MR, Sammouda H, Anqi AE. Turbulent boundary layers and hydrodynamic flow analysis of nanofluids over a plate. J Central South Univ. 2021;28:3340–53. https://doi.org/10.1007/s11771-021-4859-7.

    Article  CAS  Google Scholar 

  9. Afshari F, Sözen A, Khanlari A, Tuncer AD. Heat transfer enhancement of finned shell and tube heat exchanger using Fe2O3/water nanofluid. J Central South Univ. 2021;28:3297–309. https://doi.org/10.1007/s11771-021-4856-x.

    Article  CAS  Google Scholar 

  10. Jalil E, Molaeimanesh GR. Effects of turbulator shape, inclined magnetic field, and mixed convection nanofluid flow on thermal performance of micro-scale inclined forward-facing step. J Central South Univ. 2021;28:3310–26. https://doi.org/10.1007/s11771-021-4857-9.

    Article  CAS  Google Scholar 

  11. Sindhu S, Gireesha BJ. Scrutinization of unsteady non-Newtonian fluid flow considering buoyancy effect and thermal radiation: tangent hyperbolic model. Int Commun Heat Mass Transf. 2022;135:106062. https://doi.org/10.1016/j.icheatmasstransfer.2022.106062.

    Article  Google Scholar 

  12. Felicita A, Berrehal H, Venkatesh P, Gireesha BJ, Sowmya G. Slip flow of Walter’s B liquid through the channel possessing stretched walls by employing optimal homotopy asymptotic method (OHAM). J Mol Liq. 2022;353:118731. https://doi.org/10.1016/j.molliq.2022.118731.

    Article  CAS  Google Scholar 

  13. 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. https://doi.org/10.1016/j.ijheatmasstransfer.2007.12.019.

    Article  CAS  Google Scholar 

  14. Mansour RB, Galanis N, Nguyen CT. Effect of uncertainties in physical properties on forced convection heat transfer with nanofluids. Appl Therm Eng. 2007;27:240–9. https://doi.org/10.1016/j.applthermaleng.2006.04.011.

    Article  Google Scholar 

  15. Arefmanesh A, Mahmoodi M. Effects of uncertainties of viscosity models for Al2O3–water nanofluid on mixed convection numerical simulations. Int J Therm Sci. 2011;50:1706–19. https://doi.org/10.1016/j.ijthermalsci.2011.04.007.

    Article  CAS  Google Scholar 

  16. Mahdy A, ElShehabey HM. Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids. Int Commun Heat Mass Transf. 2012;39:713–9. https://doi.org/10.1016/j.icheatmasstransfer.2012.03.019.

    Article  CAS  Google Scholar 

  17. Minea AA. Uncertainties in modeling thermal conductivity of laminar forced convection heat transfer with water alumina nanofluids. Int J Heat Mass Transf. 2014;68:78–84. https://doi.org/10.1016/j.ijheatmasstransfer.2013.09.018.

    Article  CAS  Google Scholar 

  18. Selvakumar RD, Dhinakaran S. Nanofluid flow and heat transfer around a circular cylinder: a study on effects of uncertainties in effective properties. J Mol Liq. 2016;223:572–88. https://doi.org/10.1016/j.molliq.2016.08.047.

    Article  CAS  Google Scholar 

  19. Fazeli H, Pourrajabian A, Nikooei E. Simultaneous optimization of geometric and nanofluids parameters in a rectangular microchannel heat sink. Heat Transf Eng. 2022;43:1820–37. https://doi.org/10.1080/01457632.2021.2016138.

    Article  CAS  Google Scholar 

  20. López A, Ibáñez G, Pantoja J, Moreira J, Lastres O. Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions. Int J Heat Mass Transf. 2017;107:982–94. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.126.

    Article  CAS  Google Scholar 

  21. Jamshed W, Mohd Nasir NAA, Qureshi MA, Shahzad F, Banerjee R, Mohamed R. Dynamical irreversible processes analysis of Poiseuille magneto-hybrid nanofluid flow in microchannel: a novel case study. Waves Random Complex Media. 2021. https://doi.org/10.1080/17455030.2021.1985185.

    Article  Google Scholar 

  22. Ibáñez G, López A, Pantoja J, Moreira J. Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation. Int J Heat Mass Transf. 2016;100:89–97. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.089.

    Article  CAS  Google Scholar 

  23. Mondal P, Dilip KM, Shit GC, Ibañez G. Heat transfer and entropy generation in a MHD Couette-Poiseuille flow through a microchannel with slip, suction–injection and radiation. J Therm Anal Calorim. 2022;147:4253–73. https://doi.org/10.1007/s10973-021-10731-4.

    Article  CAS  Google Scholar 

  24. Gómez I, Ibáñez G, López A, Lastres O, Reyes J. Entropy generation minimization and nonlinear heat transport in MHD flow of a couple stress nanofluid through an inclined permeable channel with a porous medium, thermal radiation and slip. Heat Transf. 2020;49:4878–906. https://doi.org/10.1002/htj.21858.

    Article  Google Scholar 

  25. Ibáñez G, Cuevas S, De Haro ML. Minimization of entropy generation by asymmetric convective cooling. Int J Heat Mass Transf. 2003;46:1321–8. https://doi.org/10.1016/S0017-9310(02)00420-9.

    Article  Google Scholar 

  26. Mahian O, Mahmud S, Zeinali SH. Effect of uncertainties in physical properties on entropy generation between two rotating cylinders with nanofluids. J Heat Transf. 2012;134:101704. https://doi.org/10.1115/1.4006662.

    Article  CAS  Google Scholar 

  27. Ibáñez G, López A, López I, Pantoja J, Moreira J, Lastres O. Optimization of MHD nanofluid flow in a vertical microchannel with a porous medium, nonlinear radiation heat flux, slip flow and convective–radiative boundary conditions. J Therm Anal Calorim. 2019;135:3401–20. https://doi.org/10.1007/s10973-018-7558-3.

    Article  CAS  Google Scholar 

  28. Aaiza G, Khan I, Shafie S. Energy transfer in mixed convection MHD flow of nanofluid containing different shapes of nanoparticles in a channel filled with saturated porous medium. Nanoscale Res Lett. 2015;10:1–14. https://doi.org/10.1186/s11671-015-1144-4.

    Article  CAS  Google Scholar 

  29. Sheikholeslami M, Sajjadi H, Amiri A. Magnetic force and radiation influences on nanofluid transportation through a permeable media considering Al2O3 nanoparticles. J Therm Anal Calorim. 2019;136:2477–85. https://doi.org/10.1007/s10973-018-7901-8.

    Article  CAS  Google Scholar 

  30. Benkhedda M, Boufendi T, Tayebi T. Convective heat transfer performance of hybrid nanofluid in a horizontal pipe considering nanoparticles shapes effect. J Therm Anal Calorim. 2020;140:411–25. https://doi.org/10.1007/s10973-019-08836-y.

    Article  CAS  Google Scholar 

  31. Saleem S, Qasim M, Alderremy A, Noreen S. Heat transfer enhancement using different shapes of Cu nanoparticles in the flow of water based nanofluid. Phys Scr. 2020;95: 055209. https://doi.org/10.1088/1402-4896/ab4ffd.

    Article  CAS  Google Scholar 

  32. Ghadikolaei SS, Yassari M, Sadeghi H, Hosseinzadeh K, Ganji DD. Investigation on thermophysical properties of TiO2–Cu/H2O hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow. Powder Technol. 2017;322:428–38. https://doi.org/10.1016/j.powtec.2017.09.006.

    Article  CAS  Google Scholar 

  33. Sindhu S, Gireesha BJ, Sowmya G, Makinde OD. Hybrid nanoliquid flow through a microchannel with particle shape factor, slip and convective regime. Int J Numer Methods Heat Fluid Flow. 2022;32:3388–410. https://doi.org/10.1108/HFF-11-2021-0733.

    Article  Google Scholar 

  34. Kumar A, Ray RK. Shape effect of nanoparticles and entropy generation analysis for magnetohydrodynamic flow of (Al2O3−Cu/H2O) hybrid nanomaterial under the influence of Hall current. Indian J Phys. 2022;96:3817–30. https://doi.org/10.1007/s12648-022-02300-8.

    Article  CAS  Google Scholar 

  35. Ellahi R, Hassan M, Zeeshan A. Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation. Int J Heat Mass Transf. 2015;81:449–56. https://doi.org/10.1016/j.ijheatmasstransfer.2014.10.041.

    Article  CAS  Google Scholar 

  36. Zeeshan A, Hassan M, Ellahi R. Shape effect of nanosize particles in unsteady mixed convection flow of nanofluid over disk with entropy generation. Proc Inst Mech Eng Part E: J Process Mech Eng. 2017;231:871–9. https://doi.org/10.1177/0954408916646139.

    Article  Google Scholar 

  37. Seyyedi SM, Dogonchi AS, Ganji DD. Entropy generation in a nanofluid-filled semi-annulus cavity by considering the shape of nanoparticles. J Therm Anal Calorim. 2019;138:1607–21. https://doi.org/10.1007/s10973-019-08130-x.

    Article  CAS  Google Scholar 

  38. Zhang C, Zheng L, Zhang X, Chen G. MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl Math Model. 2015;39:165–81. https://doi.org/10.1016/j.apm.2014.05.023.

    Article  Google Scholar 

  39. Makinde OD. Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating. Entropy. 2011;13:1446–64. https://doi.org/10.3390/e13081446.

    Article  CAS  Google Scholar 

  40. Bejan A. Entropy generation minimization: the method of thermodynamic optimization of finite-size systems and finite-time processes. Boca Raton: CRC Press; 2013. https://doi.org/10.1201/9781482239171.

    Book  Google Scholar 

  41. Gupta M, Singh V, Kumar R, Said Z. A review on thermophysical properties of nanofluids and heat transfer applications. Renew Sustain Energy Rev. 2017;74:638–70. https://doi.org/10.1016/j.rser.2017.02.073.

    Article  CAS  Google Scholar 

  42. Minea AA. A review on the thermophysical properties of water-based nanofluids and their hybrids. Ann als of “Dunarea de Jos” University of Galati Fascicle IX. Ann “Dunarea de Jos” Univ Galati: Fascicle IX, Metallurgy and Materials Science. 2016;39:35–47.

    Google Scholar 

  43. Saqib M, Khan I, Shafie S. Recent advancement in thermophysical properties of nanofluids and hybrid nanofluids: an overview. Int J Comput Anal. 2019;1:16–25. https://doi.org/10.33959/cuijca.v3i2.27.

    Article  Google Scholar 

  44. Mahian O, Kianifar A, Kleinstreuer C, Al-Nimr MA, Pop I, Sahin AZ, Wongwises S. A review of entropy generation in nanofluid flow. Int J Heat Mass Transf. 2013;65:514–32. https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.010.

    Article  CAS  Google Scholar 

  45. Buongiorno J. Convective transport in nanofluids. ASME J Heat Transf. 2006;128:240–50. https://doi.org/10.1115/1.2150834.

    Article  Google Scholar 

  46. Chandrasekar M, Suresh S, Chandra A. Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid. Exp Thermal Fluid Sci. 2010;34:210–6. https://doi.org/10.1016/j.expthermflusci.2009.10.022.

    Article  CAS  Google Scholar 

  47. Huminic G, Huminic A. Entropy generation of nanofluid and hybrid nanofluid flow in thermal systems: a review. J Mol Liq. 2020;302:112533. https://doi.org/10.1016/j.molliq.2020.112533.

    Article  CAS  Google Scholar 

  48. Timofeeva EV, Gavrilov AN, McCloskey JM. Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory. Phys Rev E. 2007;76:061203. https://doi.org/10.1103/PhysRevE.76.061203.

    Article  CAS  Google Scholar 

  49. Pak BC, Cho YI. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf Int J. 1990;11:151–70. https://doi.org/10.1080/08916159808946559.

    Article  Google Scholar 

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Authors and Affiliations

  1. Universidad de Ciencias y Artes de Chiapas, Tuxtla Gutiérrez, Chiapas, México

    Rodolfo Estrada, Guillermo Ibáñez, Aracely López, Orlando Lastres, Joel Pantoja & Juan Reyes

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  1. Rodolfo Estrada
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Estrada, R., Ibáñez, G., López, A. et al. Analytical analysis of impacts of nanoparticle shapes and uncertainty in thermophysical properties on optimum operating conditions of MHD nanofluid flow in a microchannel filled with porous medium. J Therm Anal Calorim 149, 265–298 (2024). https://doi.org/10.1007/s10973-023-12678-0

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