Nanofluids are attractive alternatives for the current heat transfer fluids due to their remarkably higher thermal conductivity which leads to the improved thermal performance. Nanofluids are applicable in porous media for improving their heat transfer. Proposing accurate models for forecasting this feature of nanofluids can facilitate and accelerate the design and modeling of nanofluids’ thermal mediums with porous structure. In the present study, three methods including MARS, artificial neural network (ANN) with Levenberg–Marquardt for training and GMDH are employed for thermal conductivity of the nanofluids containing ZnO particles. The confidence of the models is compared according to various criteria. It is observed that the most accurate model is obtained by using ANN with Levenberg–Marquardt followed by GMDH and MARS. R2 of the mentioned models are 0.9987, 0.9980 and 0.9879, respectively. Finally, sensitivity analysis is performed to find the importance of the input variables and it is concluded that the thermal conductivity of the base fluids has the highest importance followed by volume fraction of solid phase, size of particles and temperature.
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Shadloo MS, Mahian O. Recent advances in heat and mass transfer. J Therm Anal Calorim. 2019;135:1611–5. https://doi.org/10.1007/s10973-018-7718-5.
Gholamalipour P, Siavashi M, Doranehgard MH. Eccentricity effects of heat source inside a porous annulus on the natural convection heat transfer and entropy generation of Cu-water nanofluid. Int Commun Heat Mass Transf. 2019;109:104367. https://doi.org/10.1016/j.icheatmasstransfer.2019.104367.
Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2019;137:267–87. https://doi.org/10.1007/s10973-018-7945-9.
Miri Joibary SM, Siavashi M. Effect of Reynolds asymmetry and use of porous media in the counterflow double-pipe heat exchanger for passive heat transfer enhancement. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08991-2.
Rashidi MM, Nasiri M, Shadloo MS, Yang Z. Entropy generation in a circular tube heat exchanger using nanofluids: effects of different modeling approaches. Heat Transf Eng. 2017;38:853–66. https://doi.org/10.1080/01457632.2016.1211916.
Mahdi RA, Mohammed HA, Munisamy KM, Saeid NH. Review of convection heat transfer and fluid flow in porous media with nanofluid. Renew Sustain Energy Rev. 2015;41:715–34. https://doi.org/10.1016/j.rser.2014.08.040.
Bondarenko DS, Sheremet MA, Oztop HF, Abu-Hamdeh N. Mixed convection heat transfer of a nanofluid in a lid-driven enclosure with two adherent porous blocks. J Therm Anal Calorim. 2019;135:1095–105. https://doi.org/10.1007/s10973-018-7455-9.
Safaei MR, Mahian O, Garoosi F, Hooman K, Karimipour A, Kazi SN, et al. Investigation of micro- and nanosized particle erosion in a 90° pipe bend using a two-phase discrete phase model. Sci World J. 2014. https://doi.org/10.1155/2014/740578.
Siavashi M, Talesh Bahrami HR, Aminian E, Saffari H. Numerical analysis on forced convection enhancement in an annulus using porous ribs and nanoparticle addition to base fluid. J Cent South Univ. 2019;26:1089–98. https://doi.org/10.1007/s11771-019-4073-z.
Behnampour A, Akbari OA, Safaei MR, Ghavami M, Marzban A, Sheikh Shabani GA, et al. Analysis of heat transfer and nanofluid fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs. Phys E Low-Dimens Syst Nanostruct. 2017;91:15–31. https://doi.org/10.1016/j.physe.2017.04.006.
Said Z, Rahman SMA, Assad MEH, Alami AH. Heat transfer enhancement and life cycle analysis of a Shell-and-Tube Heat Exchanger using stable CuO/water nanofluid. Sustain Energy Technol Assess. 2019;31:306–17. https://doi.org/10.1016/J.SETA.2018.12.020.
Ehyaei MA, Ahmadi A, Assad MEH, Hachicha AA, Said Z. Energy, exergy and economic analyses for the selection of working fluid and metal oxide nanofluids in a parabolic trough collector. Sol Energy. 2019;187:175–84. https://doi.org/10.1016/J.SOLENER.2019.05.046.
Said Z, Assad MEH, Hachicha AA, Bellos E, Abdelkareem MA, Alazaizeh DZ, et al. Enhancing the performance of automotive radiators using nanofluids. Renew Sustain Energy Rev. 2019;112:183–94. https://doi.org/10.1016/J.RSER.2019.05.052.
Nasiri H, Abdollahzadeh Jamalabadi MY, Sadeghi R, Safaei MR, Nguyen TK, Safdari Shadloo M. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows: application to forced convection heat transfer over a horizontal cylinder. J Therm Anal Calorim. 2019;135:1733–41. https://doi.org/10.1007/s10973-018-7022-4.
Safaei MR, Safdari Shadloo M, Goodarzi MS, Hadjadj A, Goshayeshi HR, Afrand M, et al. A survey on experimental and numerical studies of convection heat transfer of nanofluids inside closed conduits. Adv Mech Eng. 2016;8:168781401667356. https://doi.org/10.1177/1687814016673569.
Ramezanizadeh M, Alhuyi Nazari M, Hossein Ahmadi M, Chen L. A review on the approaches applied for cooling fuel cells. Int J Heat Mass Transf. 2019;139:517–25. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2019.05.032.
Alhuyi Nazari M, Ahmadi MH, Ghasempour R, Shafii MB. How to improve the thermal performance of pulsating heat pipes: a review on working fluid. Renew Sustain Energy Rev. 2018. https://doi.org/10.1016/j.rser.2018.04.042.
Ramezanizadeh M, Alhuyi Nazari M, Ahmadi MH, Chau K. Experimental and numerical analysis of a nanofluidic thermosyphon heat exchanger. Eng Appl Comput Fluid Mech. 2019;13:40–7. https://doi.org/10.1080/19942060.2018.1518272.
Nazari MA, Ghasempour R, Ahmadi MH, Heydarian G, Shafii MB. Experimental investigation of graphene oxide nanofluid on heat transfer enhancement of pulsating heat pipe. Int Commun Heat Mass Transf. 2018;91:90–4. https://doi.org/10.1016/j.icheatmasstransfer.2017.12.006.
Gandomkar A, Saidi MH, Shafii MB, Vandadi M, Kalan K. Visualization and comparative investigations of pulsating ferro-fluid heat pipe. Appl Therm Eng. 2017;116:56–65. https://doi.org/10.1016/j.applthermaleng.2017.01.068.
Ghalandari M, Mirzadeh Koohshahi E, Mohamadian F, Shamshirband S, Chau KW. Numerical simulation of nanofluid flow inside a root canal. Eng Appl Comput Fluid Mech. 2019;13:254–64. https://doi.org/10.1080/19942060.2019.1578696.
Siavashi M, Miri Joibary SM. Numerical performance analysis of a counter-flow double-pipe heat exchanger with using nanofluid and both sides partly filled with porous media. J Therm Anal Calorim. 2019;135:1595–610. https://doi.org/10.1007/s10973-018-7829-z.
Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids. Numer Heat Transf Part A Appl. 2014;66:1321–40. https://doi.org/10.1080/10407782.2014.916101.
Qin Y, Zhang M, Hiller JE. Theoretical and experimental studies on the daily accumulative heat gain from cool roofs. Energy. 2017;129:138–47. https://doi.org/10.1016/J.ENERGY.2017.04.077.
Qin Y, Hiller JE. Water availability near the surface dominates the evaporation of pervious concrete. Constr Build Mater. 2016;111:77–84. https://doi.org/10.1016/J.CONBUILDMAT.2016.02.063.
Hemmat Esfe M, Hajmohammad MH, Sina N, Afrand M. Optimization of thermophysical properties of Al2O3/water-EG (80:20) nanofluids by NSGA-II. Phys E Low-Dimens Syst Nanostruct. 2018;103:264–72. https://doi.org/10.1016/J.PHYSE.2018.05.031.
Hemmat Esfe M, Firouzi M, Afrand M. Experimental and theoretical investigation of thermal conductivity of ethylene glycol containing functionalized single walled carbon nanotubes. Phys E Low-Dimens Syst Nanostruct. 2018;95:71–7. https://doi.org/10.1016/J.PHYSE.2017.08.017.
Aberoumand S, Jafarimoghaddam A. Experimental study on synthesis, stability, thermal conductivity and viscosity of Cu–engine oil nanofluid. J Taiwan Inst Chem Eng. 2017;71:315–22. https://doi.org/10.1016/J.JTICE.2016.12.035.
Bagheri H, Ahmadi Nadooshan A. The effects of hybrid nano-powder of zinc oxide and multi walled carbon nanotubes on the thermal conductivity of an antifreeze. Phys E Low-Dimens Syst Nanostruct. 2018;103:361–6. https://doi.org/10.1016/j.physe.2018.06.017.
Hemmat Esfe M, Naderi A, Akbari M, Afrand M, Karimipour A. Evaluation of thermal conductivity of COOH-functionalized MWCNTs/water via temperature and solid volume fraction by using experimental data and ANN methods. J Therm Anal Calorim. 2015;121:1273–8. https://doi.org/10.1007/s10973-015-4565-5.
Hemmat Esfe M, Wongwises S, Naderi A, Asadi A, Safaei MR, Rostamian H, et al. Thermal conductivity of Cu/TiO2–water/EG hybrid nanofluid: experimental data and modeling using artificial neural network and correlation. Int Commun Heat Mass Transf. 2015;66:100–4. https://doi.org/10.1016/J.ICHEATMASSTRANSFER.2015.05.014.
Taherialekouhi R, Rasouli S, Khosravi A. An experimental study on stability and thermal conductivity of water-graphene oxide/aluminum oxide nanoparticles as a cooling hybrid nanofluid. Int J Heat Mass Transf. 2019;145:118751. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2019.118751.
de Oliveira LR, Ribeiro SRFL, Reis MHM, Cardoso VL, Bandarra Filho EP. Experimental study on the thermal conductivity and viscosity of ethylene glycol-based nanofluid containing diamond-silver hybrid material. Diam Relat Mater. 2019;96:216–30. https://doi.org/10.1016/j.diamond.2019.05.004.
Mirbagheri MH, Akbari M, Mehmandoust B. Proposing a new experimental correlation for thermal conductivity of nanofluids containing of functionalized multiwalled carbon nanotubes suspended in a binary base fluid. Int Commun Heat Mass Transf. 2018;98:216–22. https://doi.org/10.1016/J.ICHEATMASSTRANSFER.2018.09.007.
Ahmadi M-A, Ahmadi MH, Fahim Alavi M, Nazemzadegan MR, Ghasempour R, Shamshirband S. Determination of thermal conductivity ratio of CuO/ethylene glycol nanofluid by connectionist approach. J Taiwan Inst Chem Eng. 2018. https://doi.org/10.1016/J.JTICE.2018.06.003.
Vafaei M, Afrand M, Sina N, Kalbasi R, Sourani F, Teimouri H. Evaluation of thermal conductivity of MgO-MWCNTs/EG hybrid nanofluids based on experimental data by selecting optimal artificial neural networks. Phys E Low-Dimens Syst Nanostruct. 2017;85:90–6. https://doi.org/10.1016/j.physe.2016.08.020.
Ahmadi MH, Mirlohi A, Alhuyi Nazari M, Ghasempour R. A review of thermal conductivity of various nanofluids. J Mol Liq. 2018;265:181–8. https://doi.org/10.1016/J.MOLLIQ.2018.05.124.
Karimipour A, Bagherzadeh SA, Goodarzi M, Alnaqi AA, Bahiraei M, Safaei MR, et al. Synthesized CuFe2O4/SiO2 nanocomposites added to water/EG: evaluation of the thermophysical properties beside sensitivity analysis and EANN. Int J Heat Mass Transf. 2018;127:1169–79. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.112.
Ramezanizadeh M, Alhuyi Nazari M, Ahmadi MH, Lorenzini G, Pop I. A review on the applications of intelligence methods in predicting thermal conductivity of nanofluids. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08154-3.
Ramezanizadeh M, Alhuyi Nazari M. Modeling thermal conductivity of Ag/water nanofluid by applying a mathematical correlation and artificial neural network. Int J Low-Carbon Technol. 2019. https://doi.org/10.1093/ijlct/ctz030.
Komeilibirjandi A, Raffiee AH, Maleki A, Alhuyi Nazari M, Safdari Shadloo M. Thermal conductivity prediction of nanofluids containing CuO nanoparticles by using correlation and artificial neural network. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08838-w.
Ahmadi MH, Hajizadeh F, Rahimzadeh M, Shafii MB, Chamkha AJ. Application GMDH artificial neural network for modeling of Al2O3/water and Al2O3/ethylene glycol thermal conductivity. Int J Heat Technol. 2018;36:773–82.
Radkar RN, Bhanvase BA, Barai DP, Sonawane SH. Intensified convective heat transfer using ZnO nanofluids in heat exchanger with helical coiled geometry at constant wall temperature. Mater Sci Energy Technol. 2019;2:161–70. https://doi.org/10.1016/j.mset.2019.01.007.
Ali HM, Ali H, Liaquat H, Bin Maqsood HT, Nadir MA. Experimental investigation of convective heat transfer augmentation for car radiator using ZnO-water nanofluids. Energy. 2015;84:317–24. https://doi.org/10.1016/j.energy.2015.02.103.
Kole M, Dey TK. Investigations on the pool boiling heat transfer and critical heat flux of ZnO-ethylene glycol nanofluids. Appl Therm Eng. 2012;37:112–9. https://doi.org/10.1016/j.applthermaleng.2011.10.066.
Zhang W, Maleki A, Rosen MA. A heuristic-based approach for optimizing a small independent solar and wind hybrid power scheme incorporating load forecasting. J Clean Prod. 2019. https://doi.org/10.1016/J.JCLEPRO.2019.117920.
Li DHW, Chen W, Li S, Lou S. Estimation of hourly global solar radiation using Multivariate Adaptive Regression Spline (MARS): a case study of Hong Kong. Energy. 2019;186:115857. https://doi.org/10.1016/j.energy.2019.115857.
Fridedman JH. Multivariate adaptive regression splines (with discussion). Ann Stat. 1991;19:79–141.
Zhang W, Goh ATC. Multivariate adaptive regression splines and neural network models for prediction of pile drivability. Geosci Front. 2016;7:45–52. https://doi.org/10.1016/j.gsf.2014.10.003.
Ivakhnenko AG. The group method of data of handling; a rival of the method of stochastic approximation. Sov Autom Control. 1968;13:43–55.
Rezaei MH, Sadeghzadeh M, Alhuyi Nazari M, Ahmadi MH, Astaraei FR. Applying GMDH artificial neural network in modeling CO2 emissions in four nordic countries. Int J Low-Carbon Technol. 2018;13:266–71. https://doi.org/10.1093/ijlct/cty026.
Mohamadian F, Eftekhar L, Haghighi Bardineh Y. Applying GMDH artificial neural network to predict dynamic viscosity of an antimicrobial nanofluid. Nanomed J. 2018;5:217–21. https://doi.org/10.22038/NMJ.2018.05.00005.
Gholipour Khajeh M, Maleki A, Rosen MA, Ahmadi MH. Electricity price forecasting using neural networks with an improved iterative training algorithm. Int J Ambient Energy. 2018;39:147–58. https://doi.org/10.1080/01430750.2016.1269674.
Hemmat Esfe M, Abbasian Arani AA, Firouzi M. Empirical study and model development of thermal conductivity improvement and assessment of cost and sensitivity of EG-water based SWCNT-ZnO (30%:70%) hybrid nanofluid. J Mol Liq. 2017;244:252–61. https://doi.org/10.1016/J.MOLLIQ.2017.08.087.
Hemmat Esfe M, Saedodin S. Experimental investigation and proposed correlations for temperaturedependent thermal conductivity enhancement of ethylene glycol based nanofluid containing ZnO nanoparticles. J Heat Mass Transf Res. 2014;1:47–54. https://doi.org/10.22075/JHMTR.2014.153.
Satti JR, Das DK, Ray D. Investigation of the thermal conductivity of propylene glycol nanofluids and comparison with correlations. Int J Heat Mass Transf. 2017;107:871–81. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.121.
Qin Y. Pavement surface maximum temperature increases linearly with solar absorption and reciprocal thermal inertial. Int J Heat Mass Transf. 2016;97:391–9. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2016.02.032.
Qin Y, Liang J, Tan K, Li F. The amplitude and maximum of daily pavement surface temperature increase linearly with solar absorption. Road Mater Pavement Des. 2017;18:440–52. https://doi.org/10.1080/14680629.2016.1162732.
Afrand M, Hemmat Esfe M, Abedini E, Teimouri H. Predicting the effects of magnesium oxide nanoparticles and temperature on the thermal conductivity of water using artificial neural network and experimental data. Phys E Low-Dimens Syst Nanostruct. 2017;87:242–7. https://doi.org/10.1016/j.physe.2016.10.020.
Hemmat Esfe M, Rostamian H, Afrand M, Karimipour A, Hassani M. Modeling and estimation of thermal conductivity of MgO-water/EG (60:40) by artificial neural network and correlation. Int Commun Heat Mass Transf. 2015;68:98–103. https://doi.org/10.1016/j.icheatmasstransfer.2015.08.015.
Kannaiyan S, Boobalan C, Nagarajan FC, Sivaraman S. Modeling of thermal conductivity and density of alumina/silica in water hybrid nanocolloid by the application of artificial neural networks. Chin J Chem Eng. 2018. https://doi.org/10.1016/J.CJCHE.2018.07.018.
Hemmat Esfe M, Esfandeh S, Rejvani M. Modeling of thermal conductivity of MWCNT-SiO2 (30:70%)/EG hybrid nanofluid, sensitivity analyzing and cost performance for industrial applications. J Therm Anal Calorim. 2018;131:1437–47. https://doi.org/10.1007/s10973-017-6680-y.
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Maleki, A., Elahi, M., Assad, M.E.H. et al. Thermal conductivity modeling of nanofluids with ZnO particles by using approaches based on artificial neural network and MARS. J Therm Anal Calorim (2020). https://doi.org/10.1007/s10973-020-09373-9
- ZnO particles
- Artificial neural network
- Thermal conductivity