Thermal driven flows inside a square enclosure saturated with nanofluids: Convection heat functions and transfer rate revisions from a homogenous model

References

• A. Baïri, E. Zarco-Pernia, and J. M. García de María, “A review on natural convection in enclosures for engineering applications: The particular case of the parallelogrammic diode cavity,” Appl. Therm. Eng., vol. 63, no. 1, pp. 304–322, 2014. DOI:10.1016/j.applthermaleng.2013.10.065.
   Web of Science ®Google Scholar
• A. Raisi, B. Gasemi, and S. M. Aminossadati, “A numerical study on the force convection of laminar nanofluid in a microchannel with both slip and no-slip condition,” Numer. Heat Transfer A, vol. 59, no. 2, pp. 114–129, 2011. DOI:10.1080/10407782.2011.540964.
   Web of Science ®Google Scholar
• R. Roslan, H. Saleh, and I. Hashim, “Buoyancy-driven heat transfer in nanofluid-filled trapezoidal enclosure with variable thermal conductivity and viscosity,” Numer. Heat Transfer A, vol. 60, no. 10, pp. 867–882, 2011. DOI:10.1080/10407782.2011.616778.
   Web of Science ®Google Scholar
• A. H. Mahmoudi, M. Shahi, and F. Talebi, “Entropy generation due to natural convection in a partially open cavity with a thin heat source subjected to a nanofluid,” Numer. Heat Transfer A, vol. 61, no. 4, pp. 283–305, 2012. DOI:10.1080/10407782.2012.647990.
   Web of Science ®Google Scholar
• A. K. Beydokhti, H. A. Namaghi, and S. Z. Heris, “Identification of the key variables on thermal conductivity of Cuo and nanofluid by a fractional factorial design approach,” Numer. Heat Transfer B, vol. 63, pp. 480–495, 2013. DOI:10.1080/10407790.2013.831674.
   Google Scholar
• G. Li, M. Aktas, and Y. Bayazitoglu, “A review on the discerete Boltzmann model for nanofluid heat transfer in enclosures and channles,” Numer. Heat Transfer B, vol. 67, no. 6, pp. 463–488, 2015. DOI:10.1080/10407790.2014.992089.
   Web of Science ®Google Scholar
• T. K. Tullius, and Y. Bayazitoglu, “Analysis of a hybrid nanofluid exposed to radiation,” Numer. Heat Transfer B, vol. 69, no. 4, pp. 271–286, 2016. DOI:10.1080/10407790.2015.1104210.
   Web of Science ®Google Scholar
• H. H. Mahmoudi, and E. Abu-Nada, “Combined effect of magnetic field and nanofluid variable properties on heat transfer enhancement in natural convection,” Numer. Heat Transfer A, vol. 63, no. 6, pp. 452–472, 2013. DOI:10.1080/10407782.2013.733182.
   Web of Science ®Google Scholar
• S. K. Chio, S. O. Kim, T. H. Lee, and D. Hahn, “Computation of the natural convection of nanofluid in a square cavity with homogenous and nonhomogenous models,” Numer. Heat Transfer A, vol. 65, pp. 287–301, 2014. DOI:10.1080/10407782.2013.831695.
   Web of Science ®Google Scholar
• C. L. Zhang, L. C. Zheng, Y. Y. Jiang, and X. X. Zhang, “Unsteady natural convection heat transfer of nanofluid in an annulus with a sinusoidally heated source,” Numer. Heat Transfer A, vol. 69, no. 1, pp. 97–108, 2016. DOI:10.1080/10407782.2015.1052313.
   Web of Science ®Google Scholar
• X. W. Zhu, Y. H. Fu, J. Q. Zhao, and L. Zhu, “Three-dimensional numerical study of the laminar flow and heat transfer in a wavy-finned heat sink filled with Al2O3/ethylene glycol-water nanofluid,” Numer. Heat Transfer A, vol. 69, no. 2, pp. 195–208, 2016. DOI:10.1080/10407782.2015.1052323.
   Web of Science ®Google Scholar
• A. H. Saberi, and M. Kalteh, “Numerical investigation of nanofluid flow and conjugated heat transfer in a micro-heat-exchanger using the lattice Boltzmann method,” Numer. Heat Transfer A, vol. 70, no. 12, pp. 1390–1401, 2016. DOI:10.1080/10407782.2016.1244394.
   Web of Science ®Google Scholar
• S. Savithiri, A. Pattamatta, and S. K. Das, “Rayleigh-Benard convection in water-based alumina nanofluid: A numerical study,” Numer. Heat Transfer A, vol. 71, no. 2, pp. 202–214, 2017. DOI:10.1080/10407782.2016.1257302.
   Web of Science ®Google Scholar
• P. Mayeli, H. Hesami, and M. H. D. F. Moghaddam, “Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water-Al2O3 nanofluid,” Numer. Heat Transfer A, vol. 71, no. 12, pp. 1235–1250, 2017.
   Web of Science ®Google Scholar
• M. T. Nguyen, A. M. Aly, and S. W. Lee, “Effect of a wavy interface on the natural convection of a nanofluid in a cavity with a partially layered porous medium using the ISPH method,” Numer. Heat Transfer A, vol. 72, no. 1, pp. 68–88, 2017. DOI:10.1080/10407782.2017.1353385.
   Web of Science ®Google Scholar
• A. Albojamal, H. Hamzah, A. Haghighi, and K. Vafai, “Analysis of nanofluid transport through a wavy channel,” Numer. Heat Transfer A, vol. 72, no. 12, pp. 869–890, 2017. DOI:10.1080/10407782.2017.1412679.
   Web of Science ®Google Scholar
• A. Kumar, S. Nath, and D. Bhaja, “Effect of nanofluid on thermo hydraulic performance of double layer tapered microchannel heat sink used for electronic chip cooling,” Numer. Heat Transfer A, vol. 73, no. 7, pp. 429–445, 2018. DOI:10.1080/10407782.2018.1448611.
   Web of Science ®Google Scholar
• P. Mayeli, H. Hesami, H. Besharati-Foumani, and M. Niajalili, “Al2O3-water nanofluid heat transfer and entropy generation in a ribbed channel with wavy wall in the presence of magnetic field,” Numer. Heat Transfer A, vol. 73, no. 9, pp. 604–623, 2018. DOI:10.1080/10407782.2018.1461494.
   Web of Science ®Google Scholar
• Z. Haddad, H. F. Oztop, E. Abu-Nada, and A. Mataoui, “A review on natural convection heat transfer of nanofluids,” Renew Sust Energy Rev, vol. 16, no. 7, pp. 5363–5378, 2012. DOI:10.1016/j.rser.2012.04.003.
   Web of Science ®Google Scholar
• S. U. S. Chio, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME Fluids. Eng. Div., vol. 231, pp. 99–105, 1995.
   Google Scholar
• K. Khanafer, K. Vafai, and M. Lightstone, “Buoyancy-driven heat transfer enhancement on a two-dimensional enclosure utilizing nanofluids,” Int. J. Heat Mass Transfer, vol. 46, no. 19, pp. 3639–3653, 2003. DOI:10.1016/S0017-9310(03)00156-X.
   Web of Science ®Google Scholar
• E. Abu-Nada, and H. F. Oztop, “Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid,” Int. J. Heat Fluid Flow, vol. 30, no. 4, pp. 669–678, 2009. DOI:10.1016/j.ijheatfluidflow.2009.02.001.
   Web of Science ®Google Scholar
• B. Ghasemi, and S. M. Aminossadati, “Natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid,” Numer. Heat Transfer A, vol. 55, no. 8, pp. 807–823, 2009. DOI:10.1080/10407780902864623.
   Web of Science ®Google Scholar
• S. Savithiri, P. Arvind, and D. K. Sarit, “A single-component nonhomogeneous Lattice Boltzmann Method for natural convection in Al2O3/water nanofluid,” Numer. Heat Transfer A, vol. 68, pp. 1106–1124, 2015.
   Web of Science ®Google Scholar
• E. B. Ogut, “Natural convection of water-based nanofluids in an inclined enclosure with a heat source,” Int. J. Therm. Sci, vol. 48, pp. 2063–2073, 2009.
   Web of Science ®Google Scholar
• M. T. Nguyen, A. M. Aly, and S. W. Lee, “Natural convection in a non-Darcy porous cavity filled with Cu-water nanofluid using the characteristic-based split procedure in finite-element method,” Numer. Heat Transfer A, vol. 67, no. 2, pp. 224–247, 2015. DOI:10.1080/10407782.2014.923225.
   Web of Science ®Google Scholar
• F. H. Lai, and Y. T. Yang, “Lattice Boltzmann simulation of natural convection heat transfer of Al2O3-water nanofluids in a square enclosure,” Int. J. Therm. Sci., vol. 50, no. 10, pp. 1930–1941, 2011. DOI:10.1016/j.ijthermalsci.2011.04.015.
   Web of Science ®Google Scholar
• E. Abu-Nada, and H. F. Oztop, “Numerical analysis of Al2O3 nanofluids natural convection in wavy cavity,” Numer. Heat Transfer A, vol. 59, no. 5, pp. 403–419, 2011.
   Web of Science ®Google Scholar
• M. M. Rahman et al., “Unsteady analysis of natural convection in a carbon nanotube-water filled cavity with an inclined heater,” Numer. Heat Transfer A, vol. 69, no. 7, pp. 794–809, 2016. DOI:10.1080/10407782.2015.1090825.
   Web of Science ®Google Scholar
• L. Kolsi, K. Kalidasan, A. Alghamdi, M. N. Borjini, and P. R. Kanna, “Natural convection and entropy generation in a cubical cavity with twin adiabatic blocks filled by aluminum oxide-water nanofluid,” Numer. Heat Transfer A, vol. 70, no. 3, pp. 242–259, 2016. DOI:10.1080/10407782.2016.1173478.
   Web of Science ®Google Scholar
• A. J. Ahrar, and M. H. Djavareshkian, “Computational investigation of heat transfer and entropy generation rates of Al2O3 nanofluid with Buongiorno's model and using novel TVD hybrid LB method,” J. Mol. Liq, vol. 242, pp. 24–39, 2017. DOI:10.1016/j.molliq.2017.06.125.
   Web of Science ®Google Scholar
• M. Sheikholeslami, and A. J. Chamhka, “Flow and convection heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field,” Numer. Heat Transfer A, vol. 69, no. 10, pp. 1186–1200, 2016. DOI:10.1080/10407782.2015.1125709.
   Web of Science ®Google Scholar
• A. Rahimi, A. Amiri, A. Kasaeipoor, and E. H. Malekshah, “Heat transfer enhancement using Al2O3-EG/W(60/40 vol%) in multiple-pipe heat exchanger,” J. Mol. Liq, vol. 261, pp. 319–336, 2018. DOI:10.1016/j.molliq.2018.04.008.
   Web of Science ®Google Scholar
• D. Wen, and Y. Ding, “Formulation of nanofluids for natural convection heat transfer applications,” Int. J. Heat Fluid Flow, vol. 26, no. 6, pp. 855–864, 2005. DOI:10.1016/j.ijheatfluidflow.2005.10.005.
   Web of Science ®Google Scholar
• A. G. A. Nnanna, “Experimental model of temperature-driven nanofluid,” J. Heat Transfer, vol. 129, no. 6, pp. 697–704, 2007. DOI:10.1115/1.2717239.
   Web of Science ®Google Scholar
• K. Kouloulias, A. Sergis, and Y. Hardalups, “Sedimentation in nanofluids during a natural convection experiment,” Int. J. Heat Mass Transfer, vol. 101, pp. 1193–1203, 2016. DOI:10.1016/j.ijheatmasstransfer.2016.05.113.
   Web of Science ®Google Scholar
• W. Rashmi, A. F. Ismail, M. Kalid, and Y. Faridah, “CFD studies on natural convection heat transfer of Al2O3-water nanofluids,” Heat Mass Transf., vol. 47, no. 10, pp. 1301–1310, 2011. DOI:10.1007/s00231-011-0792-x.
   Web of Science ®Google Scholar
• N. Putra, W. Roetzel, and S. K. Das, “Natural convection of nanofluids,” Heat Mass Transf., vol. 39, no. 8-9, pp. 775–784, 2003. DOI:10.1007/s00231-002-0382-z.
   Web of Science ®Google Scholar
• C. H. Li, and G. P. Peterson, “Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions,” Adv. Mech. Eng., vol. 2010, pp. 1–10, 2010.
   Web of Science ®Google Scholar
• C. J. Ho, W. K. Liu, Y. S. Yang, and C. C. Lin, “Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study,” Int. J. Therm. Sci., vol. 49, no. 8, pp. 1345–1353, 2010. DOI:10.1016/j.ijthermalsci.2010.02.013.
   Web of Science ®Google Scholar
• F. Y. Zhao, D. Liu, and G. F. Tang, “Conjugate heat transfer in square enclosures,” Heat Mass Transfer, vol. 43, no. 9, pp. 907–922, 2007. DOI:10.1007/s00231-006-0136-4.
   Web of Science ®Google Scholar
• D. Liu, F. Y. Zhao, and G. F. Tang, “Conjugate heat transfer in an enclosure with a centered conducting body imposed sinusoidal temperature profiles on one side,” Numer. Heat Transfer A, vol. 53, no. 2, pp. 204–223, 2007. DOI:10.1080/10407780701454030.
   Web of Science ®Google Scholar
• F. Y. Zhao, D. Liu, and G. F. Tang, “Applications issues of the streamline, heatline and massline for conjugate heat and mass transfer,” Int. J. Heat Mass Transfer, vol. 50, no. 1-2, pp. 320–334, 2007. DOI:10.1016/j.ijheatmasstransfer.2006.06.026.
   Web of Science ®Google Scholar
• S. Kimura, and A. Bejan, “The “Heatline” visualization of convective heat transfer,” J. Heat Transfer, vol. 105, no. 4, pp. 916–919, 1983. DOI:10.1115/1.3245684.
   Web of Science ®Google Scholar
• V. A. F. Costa, “Unified streamline, heatline and massline methods for the visualization of the two-dimensional heat and mass transfer in anisotropic media,” Int. J. Heat Mass Transfer, vol. 46, no. 8, pp. 1309–1320, 2003. DOI:10.1016/S0017-9310(02)00404-0.
   Web of Science ®Google Scholar
• H. C. Brinkman, “The Viscosity of Concentrated Suspensions and Solutions,” J. Chem. Phys., vol. 20, no. 4, pp. 571–581, 1952. DOI:10.1063/1.1700493.
   Web of Science ®Google Scholar
• J. Maxwell, A Treatise or Electricity and Magnetism. Cambridge, UK: Oxford University Press, 1904.
   Google Scholar
• W. Yu, and S. U. S. Chio, “The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model,” J. Nanopart. Res., vol. 5, no. 1/2, pp. 167–171, 2003. DOI:10.1023/A:1024438603801.
   Web of Science ®Google Scholar
• F. Y. Zhao, G. F. Tang, and D. Liu, “Conjugate natural convection in enclosures with external and internal heat sources,” Int. J. Eng. Sci., vol. 44, no. 3-4, pp. 148–165, 2006. DOI:10.1016/j.ijengsci.2005.10.006.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York: McGraw-Hill, 1980.
   Google Scholar
• M. Corcione, “Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids,” Energy Convers. Manag., vol. 52, no. 1, pp. 789–793, 2011. DOI:10.1016/j.enconman.2010.06.072.
   Web of Science ®Google Scholar
• D. V. G. Davis, “Natural convection of air in a square cavity-a benchmark numerical solution,” Int. J. Numer. Meth. Fl., vol. 3, pp. 249–264, 1983.
   Web of Science ®Google Scholar
• T. Fusegi, J. M. Hyun, K. Kuwahara, and B. Farouk, “A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure,” Int. J. Heat Mass Transfer, vol. 34, no. 6, pp. 1543–1557, 1991. DOI:10.1016/0017-9310(91)90295-P.
   Web of Science ®Google Scholar
• G. Barakos, E. Mitsoulis, and D. Assimacopoulos, “Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions,” Int. J. Numer. Meth. Fl., vol. 18, no. 7, pp. 695–719, 1994. DOI:10.1002/fld.1650180705.
   Web of Science ®Google Scholar