Control volume finite element method for entropy generation minimization in mixed convection of nanofluids

References

• A. Bejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Time Systems and Finite-Time Processes. Boca Raton, FL: CRC Press, 1996.
   Google Scholar
• G. F. Naterer and J. A. Camberos, Entropy–Based Analysis and Design of Fluids Engineering Systems. Boca Raton, FL: CRC Press, 2008.
   Google Scholar
• S. U. S. Choi and J. A. Estman, “Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29),” ASME-Publications-Fed., vol. 231, pp. 99–106, 1995.
   Google Scholar
• O. Aydin and W. J. Yang, “Natural convection in enclosures with localized heating from below and symmetrical cooling from sides,” Int. J. Num. Meth. HFF, vol. 10, no. 5, pp. 518–529, 2000. DOI: 10.1108/09615530010338196.
   Web of Science ®Google Scholar
• B. Calcagni, F. Marsili, and M. Paroncini, “Natural convective heat transfer in square enclosures heated from below,” Appl. Therm. Eng., vol. 25, no. 16, pp. 2522–2531, 2005. DOI: 10.1016/j.applthermaleng.2004.11.032.
   Web of Science ®Google Scholar
• S. Abdelkader, R. Mebrouk, B. Abdellah, and B. Khadidja, “Natural convection in a horizontal wavy enclosure,” J. Appl. Sci. Res., vol. 7, pp. 334–341, 2007. DOI: 10.3923/jas.2007.334.341.
   Google Scholar
• J. Rostami, “Unsteady natural convection in an enclosure with vertical wavy walls,” Heat Mass Transfer, vol. 44, no. 9, pp. 1079–1087, 2008. DOI: 10.1007/s00231-007-0349-1.
   Web of Science ®Google Scholar
• R. Saidur, K. Y. Leong, and H. A. Mohammad, “A review on applications and challenges of nanofluids,” Renew. Sust. Energ. Rev., vol. 15, no. 3, pp. 1646–1668, 2011. DOI: 10.1016/j.rser.2010.11.035.
   Web of Science ®Google Scholar
• V. Trisaksri and S. Wongwises, “Critical review of heat transfer characteristics of nanofluids,” Renew. Sust. Energ. Rev., vol. 11, no. 3, pp. 512–523, 2007. DOI: 10.1016/j.rser.2005.01.010.
   Web of Science ®Google Scholar
• W. Daungthongsuk and S. Wongwises, “A critical review of convective heat transfer of nanofluids,” Renew. Sust. Energ. Rev., vol. 11, no. 5, pp. 797–817, 2007. DOI: 10.1016/j.rser.2005.06.005.
   Web of Science ®Google Scholar
• Y. Li, J. Zhou, S. Tung, E. Schneider, and S. Xi, “A review on development of nanofluid preparation and characterization,” Powder Technol., vol. 196, no. 2, pp. 89–101, 2009. DOI: 10.1016/j.powtec.2009.07.025.
   Web of Science ®Google Scholar
• S. Kakaç and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” Int. J. Heat Mass Transfer, vol. 52, no. 13–14, pp. 3187–3196, 2009. DOI: 10.1016/j.ijheatmasstransfer.2009.02.006.
   Web of Science ®Google Scholar
• A. Ghadimi, R. Saidur, and H. S. C. Metselaar, “A review of nanofluid stability properties and characterization in stationary conditions,” Int. J. Heat Mass Transfer, vol. 54, no. 17–18, pp. 4051–4068, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.04.014.
   Web of Science ®Google Scholar
• K. Khanafer and K. Vafai, “A critical synthesis of thermophysical characteristics of nanofluids,” Int. J. Heat Mass Transfer, vol. 54, no. 19–20, pp. 4410–4428, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.04.048.
   Web of Science ®Google Scholar
• G. Li, M. Aktas and Y. Bayazitoglu, “A review on the discrete Boltzmann model for nanofluid heat transfer in enclosures and channels,” Numer. Heat Transfer, Part B, vol. 67, no. 6, pp. 463–488, 2015. DOI: 10.1080/10407790.2014.992089.
   Web of Science ®Google Scholar
• H. E. Mghari, H. Louahlia-Gualous, and E. Lepinasse, “Numerical study of nanofluids condensation heat transfer in a square microchannel,” Heat Transfer, Part A, vol. 69, no. 9, pp. 957–976, 2016. DOI: 10.1080/10407782.2015.1109339.
   Web of Science ®Google Scholar
• K. S. Hwang, J. H. Lee, and S. P. Jang, “Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity,” Int. J. Heat Mass Transfer, vol. 50, no. 19–20, pp. 4003–4010, 2007. DOI: 10.1016/j.ijheatmasstransfer.2007.01.037.
   Web of Science ®Google Scholar
• K. Khanafer, K. Vafai, and M. Lightstone, “Buoyancy-driven heat transfer enhancement in 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
• G. A. Sheikhzadeh, A. Arefmanesh, M. H. Kheirkhah, and R. Abdollahi, “Natural convection of Cu–water nanofluid in a cavity with partially active side walls,” Eur. J. Mech. B-Fluid, vol. 30, no. 2, pp. 166–176, 2011. DOI: 10.1016/j.euromechflu.2010.10.003.
   Web of Science ®Google Scholar
• H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” Int. J. Heat Fluid Flow, vol. 29, no. 5, pp. 1326–1336, 2008. DOI: 10.1016/j.ijheatfluidflow.2008.04.009.
   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
• M. Ghalambaz, A. Doostanidezfuli, H. Zargartalebi, and A. J. Chamkha, “MHD phase change heat transfer in an inclined enclosure: effect of a magnetic field and cavity inclination,” Numer. Heat Transfer, Part A, vol. 71, no. 1, pp. 91–109, 2017. DOI: 10.1080/10407782.2016.1244397.
   Web of Science ®Google Scholar
• K. Kahveci, “Buoyancy driven heat transfer of nanofluids in a tilted enclosure,” J. Heat Transfer, vol. 132, no. 6, pp. 062501, 2010. DOI: 10.1115/1.4000744.
   Web of Science ®Google Scholar
• M. Magherbi, H. Abbassi, and A. B. Brahim, “Entropy generation at the onset of natural convection,” Int. J. Heat Mass Transfer, vol. 46, no. 18, pp. 3441–3450, 2003. DOI: 10.1016/S0017-9310(03)00133-9.
   Web of Science ®Google Scholar
• L. B. Erbay, Z. Altac, and B. Sulus, “An analysis of the entropy generation in a square enclosure,” Entropy, vol. 5, no. 5, pp. 496–505, 2003. DOI: 10.3390/e5050496.
   Google Scholar
• B. S. Yilbas, S. Z. Shuja, S. A. Gbadebo, H. I. Abu Al-Hamayle, and K. Boran, “Natural convection and entropy generation in a square cavity,” Int. J. Energy Res., vol. 22, no. 14, pp. 1275–1290, 1998. DOI: 10.1002/(SICI)1099-114X(199811)22:14<1275::AID-ER453>3.0.CO;2-B.
   Web of Science ®Google Scholar
• A. Mukhopadhyay, “Analysis of entropy generation due to natural convection in square enclosures with multiple discrete heat sources,” Int. Commun. Heat Mass, vol. 37, no. 7, pp. 867–872, 2010. DOI: 10.1016/j.icheatmasstransfer.2010.05.007.
   Web of Science ®Google Scholar
• I. Dagtekin, H. F. Oztop, and A. Bahloul, “Entropy generation for natural convection in C-shaped enclosures,” Int. Commun. Heat Mass, vol. 34, no. 4, pp. 502–510, 2007. DOI: 10.1016/j.icheatmasstransfer.2007.01.003.
   Web of Science ®Google Scholar
• S. Mahmud and A. K. M. S. Islam, “Laminar free convection and entropy generation inside an inclined wavy enclosure,” Int. J. Therm. Sci, vol. 42, no. 11, pp. 1003–1012, 2003. DOI: 10.1016/S1290-0729(03)00076-0.
   Web of Science ®Google Scholar
• M. Shahi, A. H. Mahmoudi, and A. H. Raouf, “Entropy generation due to natural convection cooling of a nanofluid,” Int. Commun. Heat Mass Transfer, vol. 38, no. 7, pp. 972–983, 2011. DOI: 10.1016/j.icheatmasstransfer.2011.04.008.
   Web of Science ®Google Scholar
• J. Li and C. Kleinstreuer, “Entropy generation analysis for nanofluid flow in microchannels,” J. Heat Transfer, vol. 132, no. 12, pp. 122401, 2010. DOI: 10.1115/1.4002395.
   Web of Science ®Google Scholar
• P. K. Singh, K. B. Anoop, T. Sundararajan, and S. K. Das, “Entropy generation due to flow and heat transfer in nanofluids,” Int. J. Heat Mass Transfer, vol. 53, no. 21–22, pp. 4757–4767, 2010. DOI: 10.1016/j.ijheatmasstransfer.2010.06.016.
   Web of Science ®Google Scholar
• M. Moghaddami, A. Mohammadzade, and S. A. Varzane Esfehani, “Second law analysis of nanofluid flow,” Energ. Convers. Manage., vol. 52, no. 2, pp. 1397–1405, 2011. DOI: 10.1016/j.enconman.2010.10.002.
   Web of Science ®Google Scholar
• Y. Feng and C. Kleinstreuer, “Nanofluid convective heat transfer in a parallel-disk system,” Int. J. Heat Mass Transfer, vol. 53, no. 21–22, pp. 4619–4628, 2010. DOI: 10.1016/j.ijheatmasstransfer.2010.06.031.
   Web of Science ®Google Scholar
• M. Mirzazadeh, A. Shafaei, and F. Rashidi, “Entropy analysis for non-linear viscoelastic fluid in concentric rotating cylinders,” Int. J. Therm. Sci., vol. 47, no. 12, pp. 1701–1711, 2008. DOI: 10.1016/j.ijthermalsci.2007.11.002.
   Web of Science ®Google Scholar
• C.-C. Cho, C.-L. Chen, and C.-K. Chen, “Natural convection heat transfer and entropy generation in wavy-wall enclosure containing water-based nanofluid,” Int. J. Heat Mass Transfer, vol. 61, pp. 749–758, 2013. DOI: 10.1016/j.ijheatmasstransfer.2013.02.044.
   Web of Science ®Google Scholar
• O. Mahian, S. Mahmud, and S. Z. Heris, “Analysis of entropy generation between co-rotating cylinders using nanofluids,” Energy, vol. 44, no. 1, pp. 438–446, 2012. DOI: 10.1016/j.energy.2012.06.009.
   Web of Science ®Google Scholar
• A. Bejan, Convection Heat Transfer. Hoboken, NJ: John Wiley & Sons, 2013.
   Google Scholar
• P. Keblinski, S. R. Phillpot, S. U. S. Choi, and J. A. Eastman, “Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids),” Int. J. Heat Mass Transfer, vol. 45, no. 4, pp. 855–863, 2002. DOI: 10.1016/S0017-9310(01)00175-2.
   Web of Science ®Google Scholar
• J. Koo and C. Kleinstreuer, “Impact analysis of nanoparticle motion mechanisms on the thermal conductivity of nanofluids,” Int. Commun. Heat Mass Transfer, vol. 32, no. 9, pp. 1111–1118, 2005. DOI: 10.1016/j.icheatmasstransfer.2005.05.014.
   Web of Science ®Google Scholar
• J. Buongiorno, “Convective transport in nanofluids,” J. Heat Transfer, vol. 128, no. 3, pp. 240–250, 2006. DOI: 10.1115/1.2150834.
   Web of Science ®Google Scholar
• G. F. Naterer, Advanced Heat Transfer, 2nd ed. , Boca Raton, FL: CRC Press, 2018.
   Google Scholar
• H. C. Brinkman, “The viscosity of concentrated suspensions and solutions,” J. Chem. Phys., vol. 20, no. 4, pp. 571–571, 1952. DOI: 10.1063/1.1700493.
   Web of Science ®Google Scholar
• G. F. Naterer, “Constructing an entropy-stable upwind scheme for compressible fluid flow computations,” AIAA J, vol. 37, no. 3, pp. 303–312, 1999. DOI: 10.2514/2.731.
   Google Scholar
• S. Patankar, Numerical Heat Transfer and Fluid Flow. New York, NY: CRC Press, 1980
   Google Scholar
• G. E. Schneider and M. J. Raw, “A skewed, positive influence coefficient upwinding procedure for control-volume-based finite element convection-diffusion computation,” Numer. Heat Transfer, Part A, vol. 9, pp. 1–26, 1986. DOI: 10.1080/10407788608913462.
   Web of Science ®Google Scholar
• G. de Vahl Davis, “Natural convection of air in a square cavity: a bench mark numerical solution,” Int. J. Numer. Methods Fluids, vol. 3.3, pp. 249–264, 1983. DOI: 10.1002/fld.1650030305.
   Web of Science ®Google Scholar
• G. de Vahl Davis and I. P. Jones, “Natural convection in a square cavity: a comparison exercise,” Int. J. Numerical Methods Fluids, vol. 3.3, pp. 227–248, 1983. DOI: 10.1002/fld.1650030304.
   Web of Science ®Google Scholar
• D. C. Wan, B. S. V. Patnaik, and G. W. Wei, “A new benchmark quality solution for buoyancy-driven cavity by discrete singular convolution,” Numer. Heat Transfer, Part B, vol. 40, pp. 199–228, 2001.
   Web of Science ®Google Scholar
• B. Sarler, “A radial basis function collocation approach in computational fluid dynamics,” Comp. Model. Eng. Sci., vol. 7, pp. 185–193, 2005.
   Web of Science ®Google Scholar
• G. Kosec and B. Sarler, “Numerical solution of natural convection problems by a meshless method,” in Convection and Conduction Heat Transfer. InTech Open, 2011.
   Google Scholar
• N. C. Markatos and K. A. Pericleous, “Laminar and turbulent natural convection in an enclosed cavity,” Int. J. Heat Mass Transfer, vol. 27, no. 5, pp. 755–772, 1984. DOI: 10.1016/0017-9310(84)90145-5.
   Web of Science ®Google Scholar
• X. Tian, Z. Shui, and C. Ren, “Numerical simulation of natural convection in square cavities with power function temperature wall by lattice Boltzmann method,” 4th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering. Atlantis Press 2015.
   Google Scholar
• U. Projahn, H. Rieger, and H. Beer, “Numerical analysis of laminar natural convection between concentric and eccentric cylinders,” Numer. Heat Transfer, vol. 4, no. 2, pp. 131–146, 1981. DOI: 10.1080/01495728108961783.
   Google Scholar