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Modeling and optimization of dynamic viscosity of oil-based nanofluids containing alumina particles and carbon nanotubes by response surface methodology (RSM)

  • Materials (Organic, Inorganic, Electronic, Thin Films)
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Abstract

The dynamic viscosity of MWCNT−Al2O3 (40:60)/SAE50 nanofluid (NF) is investigated. NF viscosity modeling is also performed using the response surface methodology (RSM). Several different models are proposed, including modified and unmodified cubic, quartic and fifth models, and the best modeling is selected using the parameters R2, Adjusted R2, Predicted R2 and Square root of the residual mean square (Std. Dev.). The results show that the fifth-order model has values of 0.9997, 0.9997, 0.9996 and 2.39 for R2, Adjusted R2, Predicted R2 and Std. Dev. parameters, respectively, which indicates high accuracy of modeling. Using the perturbation diagram, it was found that among the parameters of temperature, solid volume fraction (φ) and shear rate (γ), the temperature parameter has the greatest effect on the dynamic viscosity of NF. The trend of changes in viscosity also shows that φ and γ have little effect on viscosity. Due to the importance of low viscosity in fluid flow and pumping, the optimal values of NF viscosity are presented, including dynamic viscosity equal to 108.092 cP in φ=0.063 and T=49.998 °C and γ=7,866.7786 s−1.

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Abbreviations

MSs:

mean squares

R2 :

regression coefficient

R 2 adj :

adjusted regression coefficient

R 2pre :

predicted regression coefficient

SSmod :

sum of the squares of the model

SStot :

sum of squares

SSres :

the total squares of the remaining model

T:

temperature

X:

independent parameter

w:

weight coefficient

Y:

response

yi :

acctual value

ŷi :

predicted value

ANN:

artificial neural network

ANOVA:

analysis of variance

DOE:

design of experiment

EG:

ethylene glycol

MWCNT:

multi walled carbon nanotube

NF:

nanofluid

RSM:

response surface methodology

Std. Dev.:

square root of the residual mean square

ε :

experimental error

ξ :

controllable input variable

γ :

shear rate

φ :

solid volume fraction

μ :

viscosity

References

  1. N. Zhang, B. Jiao, Y. Ye, Y. Kong, X. Du, R. Liu, B. Cong, L. Yu, S. Jia and K. Jia, Energy Convers. Manag., 253, 115124 (2022).

    Article  Google Scholar 

  2. Y. Ye, B. Jiao, Y. Kong, R. Liu, X. Du, K. Jia, S. Yan and D. Chen, Appl. Therm. Eng., 202, 117849 (2022).

    Article  CAS  Google Scholar 

  3. K. Huang, B. Su, T. Li, H. Ke, M. Lin and Q. Wang, Appl. Therm. Eng., 204, 117942 (2022).

    Article  Google Scholar 

  4. L. Sun, G. Wang, C. Zhang, Q. Jin and Y. Song, Nanotechnol. Rev., 10(1), 1339 (2021).

    Article  CAS  Google Scholar 

  5. Y.-M. Chu, U. Nazir, M. Sohail, M. M. Selim and J.-R. Lee, Fractal and Fractional, 5(3), 119 (2021).

    Article  Google Scholar 

  6. H. Li, P. Xu, D. Liu, J. He, H. Zu, J. Song, J. Zhang, F. Tian, M. Yun and F. Wang, Nanotechnology, 32(37), 375202 (2021).

    Article  CAS  Google Scholar 

  7. M. Cao, Z. Chang, J. Tan, X. Wang, P. Zhang, S. Lin, J. Liu and A. Li, ACS Appl. Mater. Interfaces, 14(11), 13025 (2022).

    Article  CAS  PubMed  Google Scholar 

  8. H. Wu, F. Zhang, Z. Zhang and L. Hou, Int. J. Multiph. Flow, 15, 104043 (2022).

    Article  Google Scholar 

  9. Y.-M. Chu, B. M. Shankaralingappa, B. J. Gireesha, F. Alzahrani, M. Ijaz Khan and S. U. Khan, Appl. Math. Comput., 419, 126883 (2021).

    Google Scholar 

  10. Z. Shen, F. Wang, Z. Wang and J. Li, Renew. Sustain. Energy Rev., 141, 110783 (2021).

    Article  CAS  Google Scholar 

  11. B. C. Pak and Y. I. Cho, Exp. Heat Transf., 11(2), 151 (1998).

    Article  CAS  Google Scholar 

  12. A. Dezfulizadeh, A. Aghaei, A. H. Joshaghani and M. M. Najafizadeh, Powder Technol., 389, 215 (2021).

    Article  CAS  Google Scholar 

  13. S. M. S. Hosseini and M. S. Dehaj, Energy, 234, 121317 (2021).

    Article  Google Scholar 

  14. A. Shahsavar, M. Jamei and M. Karbasi, Powder Technol., 393, 1 (2021).

    Article  CAS  Google Scholar 

  15. T. T. Loong, H. Salleh, A. Khalid and H. Koten, Case Stud. Therm. Eng., 101288 (2021).

  16. M. H. Esfe, H. Rostamian and M. R. Sarlak, J. Mol. Liq., 254, 406 (2018).

    Article  Google Scholar 

  17. S. U. S. Chol and J. A. Estman, ASME-Publications-Fed, 231, 99 (1995).

    Google Scholar 

  18. H. D. Koca, S. Doganay, A. Turgut, I. H. Tavman, R. Saidur and I. M. Mahbubul, Renew. Sustain. Energy Rev., 82, 1664 (2018).

    Article  CAS  Google Scholar 

  19. S. H. Kim, S. R. Choi and D. Kim, J. Heat Transfer., 129(3), 298 (2007).

    Article  CAS  Google Scholar 

  20. V. Mikkola, S. Puupponen, H. Granbohm, K. Saari, T. Ala-Nissila and A. Seppälä, Int. J. Therm. Sci., 124, 187 (2018).

    Article  CAS  Google Scholar 

  21. R. V. Pinto and F. A. S. Fiorelli, Appl. Therm. Eng., 108, 720 (2016).

    Article  CAS  Google Scholar 

  22. A. Asadi, M. Asadi, A. Rezaniakolaei, L. A. Rosendahl, M. Afrand and S. Wongwises, Int. J. Heat Mass Transf., 117, 474 (2018).

    Article  CAS  Google Scholar 

  23. S. Fuxi, S. Hamedi, M. Hajian, D. Toghraie, A. A. Alizadeh, M. Hekmatifar and N. Sina, Case Stud. Therm. Eng., 101293 (2021).

  24. X. Yang, A. Boroomandpour, S. Wen, D. Toghraie and F. Soltani, Powder Technol., 388, 418 (2021).

    Article  CAS  Google Scholar 

  25. S. R. Nfawa, A. A. Basri and S. U. Masuri, Case Stud. Therm. Eng., 101279 (2021).

  26. G. Coccia, S. Tomassetti and G. Di Nicola, Renew. Sust. Energ. Rev., 151, 111573 (2021).

    Article  CAS  Google Scholar 

  27. J. Tu, C. Qi, Z. Tang, Z. Tian and L. Chen, Appl. Therm. Eng., 202, 117893 (2022).

    Article  CAS  Google Scholar 

  28. J. Tang, C. Qi, Z. Ding, M. Afrand and Y. Yan, Int. Commun. Heat Mass Transf., 127, 105492 (2021).

    Article  CAS  Google Scholar 

  29. J. Tu, C. Qi, K. Li and Z. Tang, Powder Technol., 395, 562 (2022).

    Article  CAS  Google Scholar 

  30. M. Hemmat Esfe, S. S. M. Esforjani, M. Akbari and A. Karimipour, Heat Transf. Res., 45(6), 563 (2014).

    Article  Google Scholar 

  31. Y. Wang, C. Qi, Z. Ding, J. Tu and R. Zhao, Powder Technol., 392, 570 (2021).

    Article  CAS  Google Scholar 

  32. M. Hemmat Esfe, A. A. A. Arani, M. Rezaie, W. M. Yan and A. Karimipour, Int. Commun. Heat Mass Transf., 66, 189 (2015).

    Article  CAS  Google Scholar 

  33. M. Hemmat Esfe, H. Rostamian, M. Rejvani and M. R. S. Emami, Physica E Low Dimens. Syst. Nanostruct., 102, 160 (2018).

    Article  CAS  Google Scholar 

  34. S. H. Rostamian, S. Saedodin, S. A. Asgari and A. H. Salarian, J. Therm. Anal. Calorim., 147, 155 (2020).

    Article  Google Scholar 

  35. O. A. Alawi, N. A. C. Sidik, H. W. Xian, T. H. Kean and S. N. Kazi, Int. J. Heat Mass Transf., 116, 1314 (2018).

    Article  CAS  Google Scholar 

  36. S. Aberoumand and A. Jafarimoghaddam, J. Taiwan Inst. Chem. Eng., 71, 315 (2017).

    Article  CAS  Google Scholar 

  37. M. Hemmat Esfe, M. Bahiraei and O. Mahian, Powder Technol., 338, 383 (2018).

    Article  CAS  Google Scholar 

  38. H. W. Chiam, W. H. Azmi, N. A. Usri, R. Mamat and N. M. Adam, Exp. Therm. Fluid Sci., 81, 420 (2017).

    Article  CAS  Google Scholar 

  39. A. S. Dalkılıç, Ö. Açıkgöz, B. O. Küçükyıldırım, A. A. Eker, B. Lüleci, C. Jumpholkul and S. Wongwises, Int. Commun. Heat Mass Transf., 97, 30 (2018).

    Article  Google Scholar 

  40. M. Hemmat Esfe, Appl. Therm. Eng., 126, 559 (2017).

    Article  CAS  Google Scholar 

  41. A. Abdulrahman, Mater. Today: Proc., 42, 771 (2021).

    CAS  Google Scholar 

  42. Y. M. Chu, M. Ibrahim, T. Saeed, A. S. Berrouk, E. A. Algehyne and R. Kalbasi, J. Mol. Liq., 333, 115969 (2021).

    Article  CAS  Google Scholar 

  43. Y. Cao, A. Khan, A. Abdi and M. Ghadiri, Arab. J. Chem., 14(7), 103204 (2021).

    Article  CAS  Google Scholar 

  44. W. Ji, L. Yang, Z. Chen, M. Mao and J. N. Huang, Powder Technol., 388, 212 (2021).

    Article  CAS  Google Scholar 

  45. M. Hemmat Esfe and M. R. Sarlak, J. Mol. Liq., 242, 326 (2017).

    Article  CAS  Google Scholar 

  46. M. Hemmat Esfe, S. Esfandeh and S. Niazi, J. Mol. Liq., 288, 111020 (2019).

    Article  CAS  Google Scholar 

  47. L. Eriksson, E. Johansson, N. Kettaneh-Wold, C. Wikström and S. Wold, Design of experiments, Principles and applications, Learn ways AB, Stockholm (2000).

    Google Scholar 

  48. R. H. Myers, D. C. Montgomery and C. M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments, John Wiley & Sons (2016).

  49. M. Ghafarzadeh, R. Abedini and R. Rajabi, J. Clean. Prod., 150, 361 (2017).

    Article  Google Scholar 

  50. M. Mäkelä, Energy Convers. Manag., 151, 630 (2017).

    Article  Google Scholar 

  51. T.-H. Zhao, M. I. Khan and Y.-M. Chu, Math. Methods Appl. Sci., In press (2021), https://doi.org/10.1002/mma.7310.

  52. T.-H. Zhao, O. Castillo, H. Jahanshahi, A. Yusuf, M. O. Alassafi, F. E. Alsaadi and Y.-M. Chu, Appl. Comput. Math., 20(1), 160 (2021).

    Google Scholar 

  53. F.-Z. Wang, M. N. Khan, I. Ahmad, H. Ahmad, H. Abu-Zinadah and Y. M. Chu, Fractals, 30(2), 224005 (2022).

    Google Scholar 

  54. M. Nazeer, F. Hussain, M. Ijaz Khan, Asad-ur-Rehman, E. R. El-Zahar, Y.-M. Chu and M. Y. Malik, Appl. Math. Comput., 420, 126868 (2021).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran

    Mohammad Hemmat Esfe

  2. Department of Chemical Engineering, Imam Hossein University, Tehran, Iran

    Sayyid Majid Motallebi

  3. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Davood Toghraie

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  1. Mohammad Hemmat Esfe
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  2. Sayyid Majid Motallebi
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  3. Davood Toghraie
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Correspondence to Davood Toghraie.

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Esfe, M.H., Motallebi, S.M. & Toghraie, D. Modeling and optimization of dynamic viscosity of oil-based nanofluids containing alumina particles and carbon nanotubes by response surface methodology (RSM). Korean J. Chem. Eng. 39, 2800–2809 (2022). https://doi.org/10.1007/s11814-022-1156-6

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  • DOI: https://doi.org/10.1007/s11814-022-1156-6

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