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Time-Dependent Nonlinear Convective Flow and Radiative Heat Transfer of Cu-Al2O3-H2O Hybrid Nanoliquid with Polar Particles Suspension: a Statistical and Exact Analysis

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Abstract

The statistical and exact analysis of heat transfer rate and skin friction coefficient of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is performed. The heat transport phenomenon includes radiative heat effect. A micropolar fluid model is accounted. Exact solutions to the governing problem are found via Laplace transform method (LTM). The heat transfer rate and skin friction are analysed critically via statistical methods like probable error and regression models. The slope of linear regression of data points for skin friction and Nusselt number is estimated to quantify the increase/decrease. The Nusselt number and thermophysical properties for twenty-four different hybrid nanofluids are presented. A novel idea of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is investigated for the first time. Opposite behaviour of velocity and microrotation profile are established when the physical parameters are varied.

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Abbreviations

\( \overrightarrow{V} \) :

Fluid velocity vector (m/s)

T :

Temperature (K)

\( \overrightarrow{N} \) :

Microrotation vector

c p :

Effective specific heat coefficient of fluid (J/kg K)

g :

Acceleration due to gravity (m/s2)

p :

Pressure (kg/m s2)

K :

Thermal conductivity (W/m K)

k ∗ :

Rosseland mean absorption coefficient

b :

Body force

t :

Time (s)

j :

Micro-inertia density

I :

Body couple per unit mass

U :

Characteristic velocity

Gr:

Thermal Grashof number

R :

Thermal radiation parameter

Pr:

Prandtl number

a 1 − a 13, b 1, b 2 :

Symbols denoting the expressions involving constants.

β T :

Thermal expansion coefficient

α, λ :

Spin-gradient viscosity coefficient

ν :

Kinematic viscosity (m2/s)

μ :

Dynamic viscosity (kg/m s)

ɸ :

Nanoparticle volume fraction

ρ :

Density (kg/m3)

σ ∗ :

Stefan-Boltzmann constant

κ 1 :

Vortex viscosity

η :

Spin-gradient viscosity

κ :

Microrotation parameter

γ :

Nonlinear convection parameter

f :

Base fluid

hnf:

Hybrid nanofluid

Cu, Al2O3 :

Nanoparticles

Z 1 − Z 6 :

Symbols denoting the definition of functions

References

  1. Choi, S. (1995). Enhancing thermal conductivity of fluids with nanoparticles. In D. A. Siginer & H. P. Wang (Eds.), Developments and applications of non-Newtonian flows (Vol. 66, pp. 99–105). New York: ASME.

    Google Scholar 

  2. Yacob, N. A., Dasman, A., Ahmad, S., & Dzulkifli, N. F. (2018). Numerical solutions of forced convection boundary layer flow towards a horizontal permeable stretching sheet in ZnO–water, ZnO–kerosene, MgO–water and MgO–kerosene nanofluids. In Regional Conference on Science, Technology and Social Sciences (RCSTSS 2016) (pp. 917–927). Springer, Singapore.

  3. Rahimi-Gorji, M., Pourmehran, O., Hatami, M., & Ganji, D. D. (2015). Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis. The European Physical Journal Plus, 130(2), 22.

    Article  Google Scholar 

  4. Mahanthesh, B., Gireesha, B. J., Shehzad, S. A., Rauf, A., & Kumar, P. S. (2018). Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition. Physica B: Condensed Matter, 537, 98–104.

    Article  Google Scholar 

  5. Sheikholeslami, M., & Rokni, H. B. (2018). Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation. International Journal of Heat and Mass Transfer, 118, 823–831.

    Article  Google Scholar 

  6. Pourmehran, O., Rahimi-Gorji, M., & Ganji, D. D. (2016). Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field. Journal of the Taiwan Institute of Chemical Engineers, 65, 162–171.

    Article  Google Scholar 

  7. Rahimi-Gorji, M., Pourmehran, O., Gorji-Bandpy, M., & Ganji, D. D. (2016). Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field. Journal of the Taiwan Institute of Chemical Engineers, 67, 467–475.

    Article  Google Scholar 

  8. Pourmehran, O., Rahimi-Gorji, M., Hatami, M., Sahebi, S. A. R., & Domairry, G. (2015). Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium. Journal of the Taiwan Institute of Chemical Engineers, 55, 49–68.

    Article  Google Scholar 

  9. Suresh, S., Venkitaraj, K. P., Selvakumar, P., & Chandrasekar, M. (2011). Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 388(1–3), 41–48.

    Article  Google Scholar 

  10. Usman, M., Hamid, M., Zubair, T., Haq, R. U., & Wang, W. (2018). Cu-Al2O3/water hybrid nanofluid through a permeable surface in the presence of nonlinear radiation and variable thermal conductivity via LSM. International Journal of Heat and Mass Transfer, 126, 1347–1356.

    Article  Google Scholar 

  11. Ghalambaz, M., Doostani, A., Izadpanahi, E., & Chamkha, A. J. (2017). Phase-change heat transfer in a cavity heated from below: the effect of utilizing single or hybrid nanoparticles as additives. Journal of the Taiwan Institute of Chemical Engineers, 72, 104–115.

    Article  Google Scholar 

  12. Nadeem, S., & Abbas, N. (2018). On both MHD and slip effect in Micropolar Hybrid nanofluid past a circular cylinder under stagnation point region. Canadian Journal of Physics, (ja).

  13. Streeter, V. L. (1961). Handbook of fluid dynamics (Vol. 6, pp. 32–34). New York: McGraw Hill.

    Google Scholar 

  14. Waqas, M., Khan, M. I., Hayat, T., & Alsaedi, A. (2018). Effect of nonlinear convection on stratified flow of third grade fluid with revised Fourier-Fick relations. Communications in Theoretical Physics, 70(1), 025.

    Article  MathSciNet  Google Scholar 

  15. Hayat, T., Muhammad, T., Alsaedi, A., & Alhuthali, M. S. (2015). Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials, 385, 222–229.

    Article  Google Scholar 

  16. Vajravelu, K., Cannon, J. R., Leto, J., Semmoum, R., Nathan, S., Draper, M., & Hammock, D. (2003). Nonlinear convection at a porous flat plate with application to heat transfer from a dike. Journal of Mathematical Analysis and Applications, 277(2), 609–623.

    Article  MathSciNet  Google Scholar 

  17. Hayat, T., Qayyum, S., Alsaedi, A., & Ahmad, B. (2018). Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness. Physica B: Condensed Matter, 537, 267–276.

    Article  Google Scholar 

  18. Raju, C. S. K., Saleem, S., Al-Qarni, M. M., & Upadhya, S. M. (2018). Unsteady nonlinear convection on Eyring–Powell radiated flow with suspended graphene and dust particles. Microsystem Technologies, 1-11.

  19. Mahanthesh, B., Gireesha, B. J., Thammanna, G. T., Shehzad, S. A., Abbasi, F. M., & Gorla, R. S. R. (2017). Nonlinear convection in nano Maxwell fluid with nonlinear thermal radiation: a three-dimensional study. Alexandria Engineering Journal.

  20. Mandal, I. C., & Mukhopadhyay, S. (2018). Nonlinear convection in micropolar fluid flow past an exponentially stretching sheet in an exponentially moving stream with thermal radiation. Mechanics of Advanced Materials and Structures, 1-7.

  21. Gireesha, B. J., Kumar, P. S., Mahanthesh, B., Shehzad, S. A., & Abbasi, F. M. (2018). Nonlinear gravitational and radiation aspects in nanoliquid with exponential space dependent heat source and variable viscosity. Microgravity Science and Technology, 30(3), 257–264.

    Article  Google Scholar 

  22. Hayat, T., Haider, F., Muhammad, T., & Alsaedi, A. (2018). Darcy–Forchheimer squeezed flow of carbon nanotubes with thermal radiation. Journal of Physics and Chemistry of Solids, 120, 79–86.

    Article  Google Scholar 

  23. Khan, M. I., Waqas, M., Hayat, T., Alsaedi, A., & Khan, M. I. (2017). Significance of nonlinear radiation in mixed convection flow of magneto Walter-B nanoliquid. International Journal of Hydrogen Energy, 42(42), 26408–26416.

    Article  Google Scholar 

  24. Eringen, A. C. (1966). Theory of micropolar fluids. Journal of Mathematics and Mechanics, 1–18.

    Article  MathSciNet  Google Scholar 

  25. Ghadikolaei, S. S., Hosseinzadeh, K., Hatami, M., & Ganji, D. D. (2018). MHD boundary layer analysis for micropolar dusty fluid containing hybrid nanoparticles (Cu-Al2O3) over a porous medium. Journal of Molecular Liquids.

  26. Ebaid, A., & Al Sharif, M. A. (2015). Application of Laplace transform for the exact effect of a magnetic field on heat transfer of carbon nanotubes-suspended nanofluids. Zeitschrift für Naturforschung A, 70(6), 471–475.

    Article  Google Scholar 

  27. Hayat, T., Sajjad, R., Ellahi, R., Alsaedi, A., & Muhammad, T. (2017). Homogeneous-heterogeneous reactions in MHD flow of micropolar fluid by a curved stretching surface. Journal of Molecular Liquids, 240, 209–220.

    Article  Google Scholar 

  28. Abbas, N., Saleem, S., Nadeem, S., Alderremy, A. A., & Khan, A. U. (2018). On stagnation point flow of a micro polar nanofluid past a circular cylinder with velocity and thermal slip. Results in Physics, 9, 1224–1232.

    Article  Google Scholar 

  29. Swalmeh, M. Z., Alkasasbeh, H. T., Hussanan, A., & Mamat, M. (2018). Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method. Results in Physics, 9, 717–724.

    Article  Google Scholar 

  30. Lu, D., Ramzan, M., Ahmad, S., Chung, J. D., & Farooq, U. (2018). A numerical treatment of MHD radiative flow of micropolar nanofluid with homogeneous-heterogeneous reactions past a nonlinear stretched surface. Scientific Reports, 8(1), 12431.

    Article  Google Scholar 

  31. Khan, M. I., Qayyum, S., Hayat, T., & Alsaedi, A. (2018). Entropy generation minimization and statistical declaration with probable error for skin friction coefficient and Nusselt number. Chinese Journal of Physics, 56(4), 1525–1546.

    Article  Google Scholar 

  32. Jahan, S., Sakidin, H., Nazar, R., & Pop, I. (2018). Analysis of heat transfer in nanofluid past a convectively heated permeable stretching/shrinking sheet with regression and stability analyses. Results in Physics.

  33. Rashad, A. M., Chamkha, A. J., Ismael, M. A., & Salah, T. (2018). Magnetohydrodynamics natural convection in a triangular cavity filled with a Cu-Al2O3/water hybrid nanofluid with localized heating from below and internal heat generation. Journal of Heat Transfer, 140(7), 072502.

    Article  Google Scholar 

  34. Mahanthesh, B., Gireesha, B. J., & Gorla, R. S. R. (2016). Heat and mass transfer effects on the mixed convective flow of chemically reacting nanofluid past a moving/stationary vertical plate. Alexandria Engineering Journal, 55(1), 569–581.

    Article  Google Scholar 

  35. Hussanan, A., Salleh, M. Z., Khan, I., & Shafie, S. (2017). Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil. Journal of Molecular Liquids, 229, 482–488.

    Article  Google Scholar 

  36. Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample. Metron, 1, 3–32.

    Google Scholar 

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Acknowledgements

We express our sincere thanks to the Management, CHRIST (Deemed to be University), Banglore, India for their support to complete this work. Further, we would like to express our sincere gratitude to the Editors and anonymous Reviewers for their constructive suggestions to enhance the quality of the paper.

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  1. Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, 560029, India

    Joby Mackolil & B. Mahanthesh

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  1. Joby Mackolil
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Mackolil, J., Mahanthesh, B. Time-Dependent Nonlinear Convective Flow and Radiative Heat Transfer of Cu-Al2O3-H2O Hybrid Nanoliquid with Polar Particles Suspension: a Statistical and Exact Analysis. BioNanoSci. 9, 937–951 (2019). https://doi.org/10.1007/s12668-019-00667-3

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