Research Article
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A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models

Year 2021, Volume: 5 Issue: 2, 218 - 230, 15.08.2021

Neşe Keklikcioğlu Çakmak Hasan Hüseyin Durmazuçar Kerim Yapıcı

https://doi.org/10.35860/iarej.852562
Cited By: 2

Abstract

In the current study, heat transfer enhancement in an enclosure was investigated by utilizing Al2O3-EG nanofluid. In the numerical solutions, the solid-liquid mixture equations were applied for the enclosure that composed alumina-ethylene glycol nanofluid, in terms of the two-dimensional buoyancy-driven convection. Various viscosity and thermal conductivity models were utilized for the purpose of assessing heat transfer improvement. The purpose of this study was to reveal the impacts caused by uncertainties in the viscosity and thermal conductivity of the nanofluid on laminar natural convection heat transfer occurring in a square enclosure. The temperatures of the right and left vertical walls of the enclosure were kept constant as Tc and Th, respectively, whereas the thermal insulation of the other walls was performed. The discretization of the governing equations was performed by utilizing the finite volume method and the SIMPLE algorithm. Calculations were made for the Rayleigh number (103-106) and the volume fraction of alumina nanoparticles, ϕ= 0-5%. In this study, many parameters affecting heat transfer by natural convection were investigated in the enclosure containing Al2O3-EG nanofluid, and it was found that nanofluid viscosity was the most efficient factor for heat transfer rate.

Keywords

Al2O3 Finite volume method Fourth-order linear scheme Lid-driven cavity Nanofluid Natural convection Thermal conductivity Viscosity

Supporting Institution

The Scientific Research Project Fund of Sivas Cumhuriyet University

Project Number

M-489

Thanks

The Scientific Research Project Fund of Sivas Cumhuriyet University provided its support for the present research under the project number M-489.

References

  • 1. Baïri, A., E. Zarco-Pernia, and J.-M.G. De María, A review on natural convection in enclosures for engineering applications. The particular case of the parallelogrammic diode cavity. Applied Thermal Engineering, 2014. 63(1): p. 304-322.
  • 2. Tyagi, H., P. Phelan, and R. Prasher, Predicted efficiency of a low-temperature nanofluid-based direct absorption solar collector. Journal of solar energy engineering, 2009. 131(4).
  • 3. Mahian, O., et al., A review of the applications of nanofluids in solar energy. International Journal of Heat and Mass Transfer, 2013. 57(2): p. 582-594.
  • 4. Tyagi, H., Radiative and combustion properties of nanoparticle-laden liquids. 2008: Arizona State University.
  • 5. Çakmak, N.K., Experımental study of thermal conductıvıty of borıc acıd-water solutıons. 2019. 50(17): p. 1675-1684.
  • 6. Hussein, A.K., et al., The effect of the baffle length on the natural convection in an enclosure filled with different nanofluids. Journal of Thermal Analysis and Calorimetry, 2020.
  • 7. Said, Z., et al., Recent advances on nanofluids for low to medium temperature solar collectors: energy, exergy, economic analysis and environmental impact. Progress in Energy and Combustion Science, 2021. 84: p. 100898.
  • 8. Maxwell, J.C., A treatise on electricity and magnetism, Clarendon. Oxford, 1881. 314: p. 1873.
  • 9. Choi, S.U. and J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. 1995, Argonne National Lab., IL (United States).
  • 10. Bazdar, H., et al., Numerical investigation of turbulent flow and heat transfer of nanofluid inside a wavy microchannel with different wavelengths. Journal of Thermal Analysis and Calorimetry, 2020. 139(3): p. 2365-2380.
  • 11. Keklikcioglu, O., T. Dagdevir, and V. Ozceyhan, Heat transfer and pressure drop investigation of graphene nanoplatelet-water and titanium dioxide-water nanofluids in a horizontal tube. Applied Thermal Engineering, 2019. 162: p. 114256.
  • 12. Khanafer, K., K. Vafai, and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer, 2003. 46(19): p. 3639-3653.
  • 13. Hwang, K.S., J.-H. Lee, and S.P. Jang, Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity. International Journal of Heat and Mass Transfer, 2007. 50(19-20): p. 4003-4010.
  • 14. Abu-Nada, E., Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection. International Journal of Heat and Fluid Flow, 2009. 30(4): p. 679-690.
  • 15. Oztop, H.F. and E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International journal of heat and fluid flow, 2008. 29(5): p. 1326-1336.
  • 16. Corcione, M., M. Cianfrini, and A. Quintino, Enhanced natural convection heat transfer of nanofluids in enclosures with two adjacent walls heated and the two opposite walls cooled. International Journal of Heat and Mass Transfer, 2015. 88: p. 902-913.
  • 17. Mahalakshmi, T., et al., Natural convective heat transfer of Ag-water nanofluid flow inside enclosure with center heater and bottom heat source. Chinese Journal of Physics, 2018. 56(4): p. 1497-1507.
  • 18. Yıldız, Ç., M. Arıcı, and H. Karabay, Comparison of a theoretical and experimental thermal conductivity model on the heat transfer performance of Al2O3-SiO2/water hybrid-nanofluid. International Journal of Heat and Mass Transfer, 2019. 140: p. 598-605.
  • 19. Wen, D. and Y. Ding, Formulation of nanofluids for natural convective heat transfer applications. International Journal of Heat and Fluid Flow, 2005. 26(6): p. 855-864.
  • 20. Ho, C., et al., Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. International Journal of Thermal Sciences, 2010. 49(8): p. 1345-1353.
  • 21. Keklikcioğlu Çakmak, N., Durmazuçar, H , Yapıcı, K . A numerical study of mixed convection heat transfer in a lid-driven cavity using Al2O3-water nanofluid . International Journal of Chemistry and Technology, 2020. 4(1): p. 22-37.
  • 22. Putra, N., W. Roetzel, and S.K. Das, Natural convection of nano-fluids. Heat and mass transfer, 2003. 39(8-9): p. 775-784.
  • 23. Abu-Nada, E., Z. Masoud, and A. Hijazi, Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. International Communications in Heat and Mass Transfer, 2008. 35(5): p. 657-665.
  • 24. Kim, C.S., K. Okuyama, and J.F. de la Mora, Performance evaluation of an improved particle size magnifier (PSM) for single nanoparticle detection. Aerosol Science & Technology, 2003. 37(10): p. 791-803.
  • 25. Yapici, K. and S. Obut, Benchmark results for natural and mixed convection heat transfer in a cavity. International Journal of Numerical Methods for Heat & Fluid Flow, 2015.
  • 26. Chandrasekar, M., S. Suresh, and A.C. Bose, Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid. Experimental Thermal and Fluid Science, 2010. 34(2): p. 210-216.
  • 27. Brinkman, H., The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 1952. 20(4): p. 571-571.
  • 28. Einstein, A., Investigations on the Theory of the Brownian Movement. 1956: Courier Corporation.
  • 29. Batchelor, G., The effect of Brownian motion on the bulk stress in a suspension of spherical particles. Journal of fluid mechanics, 1977. 83(1): p. 97-117.
  • 30. Nguyen, C., et al., Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer enhancement using nanofluids reliable? International journal of thermal sciences, 2008. 47(2): p. 103-111.
  • 31. Maı̈ga, S.E.B., et al., Heat transfer behaviours of nanofluids in a uniformly heated tube. Superlattices and Microstructures, 2004. 35(3-6): p. 543-557.
  • 32. Wang, X., X. Xu, and S.U. Choi, Thermal conductivity of nanoparticle-fluid mixture. Journal of thermophysics and heat transfer, 1999. 13(4): p. 474-480.
  • 33. Ding, Y., et al., Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). International Journal of Heat and Mass Transfer, 2006. 49(1-2): p. 240-250.
  • 34. Yapici, K., et al., Rheological characterization of polyethylene glycol based TiO 2 nanofluids. Korea-Australia Rheology Journal, 2014. 26(4): p. 355-363.
  • 35. Wang, L., H. Chen, and S. Witharana, Rheology of nanofluids: a review. Recent patents on nanotechnology, 2013. 7(3): p. 232-246. 36. Sharma, A.K., A.K. Tiwari, and A.R. Dixit, Rheological behaviour of nanofluids: a review. Renewable and Sustainable Energy Reviews, 2016. 53: p. 779-791.
  • 37. Tiwari, A.K., et al., 4S consideration (synthesis, sonication, surfactant, stability) for the thermal conductivity of CeO2 with MWCNT and water based hybrid nanofluid: An experimental assessment. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2021. 610: p. 125918.
  • 38. Tiwari, A.K., et al., 3S (Sonication, surfactant, stability) impact on the viscosity of hybrid nanofluid with different base fluids: An experimental study. Journal of Molecular Liquids, 2021. 329: p. 115455.
  • 39. Keklikcioglu Cakmak, N., The impact of surfactants on the stability and thermal conductivity of graphene oxide de-ionized water nanofluids. Journal of Thermal Analysis and Calorimetry, 2020. 139(3): p. 1895-1902.
  • 40. Keklikcioğlu Çakmak, N., Temel, Ü , Yapıcı, K, Examination of Rheological Behavior of Water-Based Graphene Oxide Nanofluids Cumhuriyet Science Journal, 2017. 38(4): p. 176-183.
  • 41. Cakmak, N.K., et al., Preparation, characterization, stability, and thermal conductivity of rGO-Fe3O4-TiO2 hybrid nanofluid: An experimental study. Powder Technology, 2020. 372: p. 235-245.
  • 42. Das, S.K., N. Putra, and W. Roetzel, Pool boiling characteristics of nano-fluids. International journal of heat and mass transfer, 2003. 46(5): p. 851-862.
  • 43. Prasher, R., et al., Measurements of nanofluid viscosity and its implications for thermal applications. Applied physics letters, 2006. 89(13): p. 133108.
  • 44. He, Y., et al., Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International journal of heat and mass transfer, 2007. 50(11-12): p. 2272-2281.
  • 45. Kwak, K. and C. Kim, Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol. Korea-Australia Rheology Journal, 2005. 17(2): p. 35-40.
  • 46. Studart, A.R., et al., Rheology of concentrated suspensions containing weakly attractive alumina nanoparticles. Journal of the American Ceramic Society, 2006. 89(8): p. 2418-2425.
  • 47. Tseng, W.J. and K.-C. Lin, Rheology and colloidal structure of aqueous TiO2 nanoparticle suspensions. Materials science and engineering: A, 2003. 355(1-2): p. 186-192.

Year 2021, Volume: 5 Issue: 2, 218 - 230, 15.08.2021

Neşe Keklikcioğlu Çakmak Hasan Hüseyin Durmazuçar Kerim Yapıcı

https://doi.org/10.35860/iarej.852562
Cited By: 2

Abstract

Project Number

M-489

References

  • 1. Baïri, A., E. Zarco-Pernia, and J.-M.G. De María, A review on natural convection in enclosures for engineering applications. The particular case of the parallelogrammic diode cavity. Applied Thermal Engineering, 2014. 63(1): p. 304-322.
  • 2. Tyagi, H., P. Phelan, and R. Prasher, Predicted efficiency of a low-temperature nanofluid-based direct absorption solar collector. Journal of solar energy engineering, 2009. 131(4).
  • 3. Mahian, O., et al., A review of the applications of nanofluids in solar energy. International Journal of Heat and Mass Transfer, 2013. 57(2): p. 582-594.
  • 4. Tyagi, H., Radiative and combustion properties of nanoparticle-laden liquids. 2008: Arizona State University.
  • 5. Çakmak, N.K., Experımental study of thermal conductıvıty of borıc acıd-water solutıons. 2019. 50(17): p. 1675-1684.
  • 6. Hussein, A.K., et al., The effect of the baffle length on the natural convection in an enclosure filled with different nanofluids. Journal of Thermal Analysis and Calorimetry, 2020.
  • 7. Said, Z., et al., Recent advances on nanofluids for low to medium temperature solar collectors: energy, exergy, economic analysis and environmental impact. Progress in Energy and Combustion Science, 2021. 84: p. 100898.
  • 8. Maxwell, J.C., A treatise on electricity and magnetism, Clarendon. Oxford, 1881. 314: p. 1873.
  • 9. Choi, S.U. and J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. 1995, Argonne National Lab., IL (United States).
  • 10. Bazdar, H., et al., Numerical investigation of turbulent flow and heat transfer of nanofluid inside a wavy microchannel with different wavelengths. Journal of Thermal Analysis and Calorimetry, 2020. 139(3): p. 2365-2380.
  • 11. Keklikcioglu, O., T. Dagdevir, and V. Ozceyhan, Heat transfer and pressure drop investigation of graphene nanoplatelet-water and titanium dioxide-water nanofluids in a horizontal tube. Applied Thermal Engineering, 2019. 162: p. 114256.
  • 12. Khanafer, K., K. Vafai, and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International journal of heat and mass transfer, 2003. 46(19): p. 3639-3653.
  • 13. Hwang, K.S., J.-H. Lee, and S.P. Jang, Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity. International Journal of Heat and Mass Transfer, 2007. 50(19-20): p. 4003-4010.
  • 14. Abu-Nada, E., Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection. International Journal of Heat and Fluid Flow, 2009. 30(4): p. 679-690.
  • 15. Oztop, H.F. and E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International journal of heat and fluid flow, 2008. 29(5): p. 1326-1336.
  • 16. Corcione, M., M. Cianfrini, and A. Quintino, Enhanced natural convection heat transfer of nanofluids in enclosures with two adjacent walls heated and the two opposite walls cooled. International Journal of Heat and Mass Transfer, 2015. 88: p. 902-913.
  • 17. Mahalakshmi, T., et al., Natural convective heat transfer of Ag-water nanofluid flow inside enclosure with center heater and bottom heat source. Chinese Journal of Physics, 2018. 56(4): p. 1497-1507.
  • 18. Yıldız, Ç., M. Arıcı, and H. Karabay, Comparison of a theoretical and experimental thermal conductivity model on the heat transfer performance of Al2O3-SiO2/water hybrid-nanofluid. International Journal of Heat and Mass Transfer, 2019. 140: p. 598-605.
  • 19. Wen, D. and Y. Ding, Formulation of nanofluids for natural convective heat transfer applications. International Journal of Heat and Fluid Flow, 2005. 26(6): p. 855-864.
  • 20. Ho, C., et al., Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. International Journal of Thermal Sciences, 2010. 49(8): p. 1345-1353.
  • 21. Keklikcioğlu Çakmak, N., Durmazuçar, H , Yapıcı, K . A numerical study of mixed convection heat transfer in a lid-driven cavity using Al2O3-water nanofluid . International Journal of Chemistry and Technology, 2020. 4(1): p. 22-37.
  • 22. Putra, N., W. Roetzel, and S.K. Das, Natural convection of nano-fluids. Heat and mass transfer, 2003. 39(8-9): p. 775-784.
  • 23. Abu-Nada, E., Z. Masoud, and A. Hijazi, Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. International Communications in Heat and Mass Transfer, 2008. 35(5): p. 657-665.
  • 24. Kim, C.S., K. Okuyama, and J.F. de la Mora, Performance evaluation of an improved particle size magnifier (PSM) for single nanoparticle detection. Aerosol Science & Technology, 2003. 37(10): p. 791-803.
  • 25. Yapici, K. and S. Obut, Benchmark results for natural and mixed convection heat transfer in a cavity. International Journal of Numerical Methods for Heat & Fluid Flow, 2015.
  • 26. Chandrasekar, M., S. Suresh, and A.C. Bose, Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid. Experimental Thermal and Fluid Science, 2010. 34(2): p. 210-216.
  • 27. Brinkman, H., The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 1952. 20(4): p. 571-571.
  • 28. Einstein, A., Investigations on the Theory of the Brownian Movement. 1956: Courier Corporation.
  • 29. Batchelor, G., The effect of Brownian motion on the bulk stress in a suspension of spherical particles. Journal of fluid mechanics, 1977. 83(1): p. 97-117.
  • 30. Nguyen, C., et al., Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer enhancement using nanofluids reliable? International journal of thermal sciences, 2008. 47(2): p. 103-111.
  • 31. Maı̈ga, S.E.B., et al., Heat transfer behaviours of nanofluids in a uniformly heated tube. Superlattices and Microstructures, 2004. 35(3-6): p. 543-557.
  • 32. Wang, X., X. Xu, and S.U. Choi, Thermal conductivity of nanoparticle-fluid mixture. Journal of thermophysics and heat transfer, 1999. 13(4): p. 474-480.
  • 33. Ding, Y., et al., Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). International Journal of Heat and Mass Transfer, 2006. 49(1-2): p. 240-250.
  • 34. Yapici, K., et al., Rheological characterization of polyethylene glycol based TiO 2 nanofluids. Korea-Australia Rheology Journal, 2014. 26(4): p. 355-363.
  • 35. Wang, L., H. Chen, and S. Witharana, Rheology of nanofluids: a review. Recent patents on nanotechnology, 2013. 7(3): p. 232-246. 36. Sharma, A.K., A.K. Tiwari, and A.R. Dixit, Rheological behaviour of nanofluids: a review. Renewable and Sustainable Energy Reviews, 2016. 53: p. 779-791.
  • 37. Tiwari, A.K., et al., 4S consideration (synthesis, sonication, surfactant, stability) for the thermal conductivity of CeO2 with MWCNT and water based hybrid nanofluid: An experimental assessment. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2021. 610: p. 125918.
  • 38. Tiwari, A.K., et al., 3S (Sonication, surfactant, stability) impact on the viscosity of hybrid nanofluid with different base fluids: An experimental study. Journal of Molecular Liquids, 2021. 329: p. 115455.
  • 39. Keklikcioglu Cakmak, N., The impact of surfactants on the stability and thermal conductivity of graphene oxide de-ionized water nanofluids. Journal of Thermal Analysis and Calorimetry, 2020. 139(3): p. 1895-1902.
  • 40. Keklikcioğlu Çakmak, N., Temel, Ü , Yapıcı, K, Examination of Rheological Behavior of Water-Based Graphene Oxide Nanofluids Cumhuriyet Science Journal, 2017. 38(4): p. 176-183.
  • 41. Cakmak, N.K., et al., Preparation, characterization, stability, and thermal conductivity of rGO-Fe3O4-TiO2 hybrid nanofluid: An experimental study. Powder Technology, 2020. 372: p. 235-245.
  • 42. Das, S.K., N. Putra, and W. Roetzel, Pool boiling characteristics of nano-fluids. International journal of heat and mass transfer, 2003. 46(5): p. 851-862.
  • 43. Prasher, R., et al., Measurements of nanofluid viscosity and its implications for thermal applications. Applied physics letters, 2006. 89(13): p. 133108.
  • 44. He, Y., et al., Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe. International journal of heat and mass transfer, 2007. 50(11-12): p. 2272-2281.
  • 45. Kwak, K. and C. Kim, Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol. Korea-Australia Rheology Journal, 2005. 17(2): p. 35-40.
  • 46. Studart, A.R., et al., Rheology of concentrated suspensions containing weakly attractive alumina nanoparticles. Journal of the American Ceramic Society, 2006. 89(8): p. 2418-2425.
  • 47. Tseng, W.J. and K.-C. Lin, Rheology and colloidal structure of aqueous TiO2 nanoparticle suspensions. Materials science and engineering: A, 2003. 355(1-2): p. 186-192.
There are 46 citations in total.

Details

Primary Language English
Subjects Chemical Engineering
Journal Section Research Articles
Authors

Neşe Keklikcioğlu Çakmak 0000-0002-8634-9232

Hasan Hüseyin Durmazuçar This is me 0000-0003-2454-7003

Kerim Yapıcı 0000-0002-3902-9375

Project Number M-489
Publication Date August 15, 2021
Submission Date January 2, 2021
Acceptance Date June 9, 2021
Published in Issue Year 2021 Volume: 5 Issue: 2

Cite

APA Keklikcioğlu Çakmak, N., Durmazuçar, H. H., & Yapıcı, K. (2021). A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models. International Advanced Researches and Engineering Journal, 5(2), 218-230. https://doi.org/10.35860/iarej.852562
AMA Keklikcioğlu Çakmak N, Durmazuçar HH, Yapıcı K. A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models. Int. Adv. Res. Eng. J. August 2021;5(2):218-230. doi:10.35860/iarej.852562
Chicago Keklikcioğlu Çakmak, Neşe, Hasan Hüseyin Durmazuçar, and Kerim Yapıcı. “A Numerical Study of the Natural Convection of Al2O3-EG Nanofluid in a Square Enclosure and Impacts and a Comparison of Various Viscosity and Thermal Conductivity Models”. International Advanced Researches and Engineering Journal 5, no. 2 (August 2021): 218-30. https://doi.org/10.35860/iarej.852562.
EndNote Keklikcioğlu Çakmak N, Durmazuçar HH, Yapıcı K (August 1, 2021) A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models. International Advanced Researches and Engineering Journal 5 2 218–230.
IEEE N. Keklikcioğlu Çakmak, H. H. Durmazuçar, and K. Yapıcı, “A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models”, Int. Adv. Res. Eng. J., vol. 5, no. 2, pp. 218–230, 2021, doi: 10.35860/iarej.852562.
ISNAD Keklikcioğlu Çakmak, Neşe et al. “A Numerical Study of the Natural Convection of Al2O3-EG Nanofluid in a Square Enclosure and Impacts and a Comparison of Various Viscosity and Thermal Conductivity Models”. International Advanced Researches and Engineering Journal 5/2 (August 2021), 218-230. https://doi.org/10.35860/iarej.852562.
JAMA Keklikcioğlu Çakmak N, Durmazuçar HH, Yapıcı K. A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models. Int. Adv. Res. Eng. J. 2021;5:218–230.
MLA Keklikcioğlu Çakmak, Neşe et al. “A Numerical Study of the Natural Convection of Al2O3-EG Nanofluid in a Square Enclosure and Impacts and a Comparison of Various Viscosity and Thermal Conductivity Models”. International Advanced Researches and Engineering Journal, vol. 5, no. 2, 2021, pp. 218-30, doi:10.35860/iarej.852562.
Vancouver Keklikcioğlu Çakmak N, Durmazuçar HH, Yapıcı K. A numerical study of the natural convection of Al2O3-EG nanofluid in a square enclosure and impacts and a comparison of various viscosity and thermal conductivity models. Int. Adv. Res. Eng. J. 2021;5(2):218-30.

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