Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T14:24:59.193Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical investigation of nanofluid particle migration and convective heat transfer in microchannels using an Eulerian–Lagrangian approach

Published online by Cambridge University Press:  04 September 2019

Omar Z. Sharaf Open the ORCID record for Omar Z. Sharaf [Opens in a new window] ,
Ashraf N. Al-Khateeb Open the ORCID record for Ashraf N. Al-Khateeb [Opens in a new window] ,
Dimitrios C. Kyritsis Open the ORCID record for Dimitrios C. Kyritsis [Opens in a new window]  and
Eiyad Abu-Nada Open the ORCID record for Eiyad Abu-Nada [Opens in a new window]
Omar Z. Sharaf
Affiliation:
Department of Mechanical Engineering, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE
Ashraf N. Al-Khateeb
Affiliation:
Department of Aerospace Engineering, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE
Dimitrios C. Kyritsis
Affiliation:
Department of Mechanical Engineering, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE
Eiyad Abu-Nada*
Affiliation:
Department of Mechanical Engineering, Khalifa University of Science and Technology, P.O. Box 127788, Abu Dhabi, UAE
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An Eulerian–Lagrangian modelling approach was employed in order to investigate the flow field, heat transfer and particle distribution in nanofluid flow in a parallel-plate microchannel, with a focus on relatively low Reynolds numbers ($Re\leqslant 100$). Momentum and thermal interactions between fluid and particle phases were accounted for using a transient two-way coupling algorithm implemented within an in-house code that tracked the simultaneous evolution of the carrier and particulate phases while considering timescale differences between the two phases. The inaccuracy of assuming a homogeneous particle distribution in modelling nanofluid flow in microchannels was established. In particular, shear rate and thermophoresis were found to play a key role in the lateral migration of nanoparticles and in the formation of particle depletion and accumulation regions in the vicinity of the channel walls. At low Reynolds numbers, nanoparticle distribution near the walls was observed to gradually flatten in the streamwise direction. On the other hand, for relatively higher Reynolds numbers, higher particle non-uniformities were observed in the vicinity of the channel walls. Furthermore, it was established that convective heat transfer between channel walls and the bulk fluid can either improve or deteriorate with the addition of nanoparticles, depending on whether the flow exceeded a critical Reynolds number of enhancement. It was also established that Brownian motion and thermophoresis had a major role in nanoparticle deposition on the channel walls. In particular, Brownian motion was the main deposition mechanism for nano-sized particles, whereas due to thermophoresis, nanoparticles were repelled away from channel walls. The result of the competition between the two is that deposition gradually increased along the streamwise direction.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , pp. 62 - 97
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abu-Nada, E. 2011 Rayleigh–Bénard convection in nanofluids: effect of temperature dependent properties. Intl J. Therm. Sci. 50 (9), 1720–1730.Google Scholar
Abuzeid, S., Busnaina, A. A. & Ahmadi, G. 1991 Wall deposition of aerosol particles in a turbulent channel flow. J. Aerosol Sci. 22 (1), 43–62.Google Scholar
Ackler, H. D., French, R. H. & Chiang, Y.-M. 1996 Comparisons of Hamaker constants for ceramic systems with intervening vacuum or water: from force laws and physical properties. J. Colloid Interface Sci. 179 (2), 460–469.Google Scholar
Akinsete, V. A. & Coleman, T. A. 1982 Heat transfer by steady laminar free convection in triangular enclosures. Intl J. Heat Mass Transfer 25 (7), 991–998.Google Scholar
Al-Amri, F. G. & El-Shaarawi, M. A. I. 2010 Combined forced convection and surface radiation between two parallel plates. Intl J. Numer. Meth. Heat Fluid Flow 20 (2), 218–239.Google Scholar
Alawi, O. A., Sidik, N. A. C., Xian, H. W., Kean, T. H. & Kazi, S. N. 2018 Thermal conductivity and viscosity models of metallic oxides nanofluids. Intl J. Heat Mass Transfer 116, 1314–1325.Google Scholar
Asan, H. & Namli, L. 2000 Laminar natural convection in a pitched roof of triangular cross-section: summer day boundary conditions. Energy Build. 33 (1), 69–73.Google Scholar
Atashafrooz, M. & Nassab, S. A. G. 2012 Combined heat transfer of radiation and forced convection flow of participating gases in a three-dimensional recess. J. Mech. Sci. Technol. 26 (10), 3357–3368.Google Scholar
Baghdar Hosseini, S., Haghighi Khoshkhoo, R. & Javadi Malabad, S. M. 2017 Numerical study on polydisperse particle deposition in a compact heat exchanger. Appl. Therm. Engng 127, 330–346.Google Scholar
Bahiraei, M. 2014 A comprehensive review on different numerical approaches for simulation in nanofluids: traditional and novel techniques. J. Dispersion Sci. Technol. 35 (7), 984–996.Google Scholar
Bahiraei, M. 2016 Particle migration in nanofluids: a critical review. Intl J. Therm. Sci. 109, 90–113.Google Scholar
Baïri, A. 2018a Natural convection between concentric and inclined hemispherical cavities filled with Cu-water nanofluid. J. Mol. Liq. 249, 1263–1270.Google Scholar
Baïri, A. 2018b Effects of ZnO-H2O nanofluid saturated porous medium on the thermal behavior of cubical electronics contained in a tilted hemispherical cavity. An experimental and numerical study. Appl. Therm. Engng 138, 924–933.Google Scholar
Baïri, A., Alilat, N., Baïri, I., Hocine, A. & Hamouda, A. 2017 Numerical and experimental study of free convection on wire-bonded QFN64b electronic package. Intl J. Numer. Meth. Heat Fluid Flow 27 (6), 1323–1331.Google Scholar
Baïri, A., Laraqi, N. & Adeyeye, K. 2018 Thermal behavior of an active electronic dome contained in a tilted hemispherical enclosure and subjected to nanofluidic Cu-water free convection. Eur. Phys. J. Plus 133, 93.Google Scholar
Basu, S. & Miglani, A. 2016 Combustion and heat transfer characteristics of nanofluid fuel droplets: a short review. Intl J. Heat Mass Transfer 96, 482–503.Google Scholar
Bhattad, A., Sarkar, J. & Ghosh, P. 2018a Discrete phase numerical model and experimental study of hybrid nanofluid heat transfer and pressure drop in plate heat exchanger. Intl Commun. Heat Mass Transfer 91, 262–273.Google Scholar
Bhattad, A., Sarkar, J. & Ghosh, P. 2018b Energy-economic analysis of plate evaporator using brine-based hybrid nanofluids as secondary refrigerant. Intl J. Air-Cond. Refrig. 26 (01), 1850003.Google Scholar
Bhattad, A., Sarkar, J. & Ghosh, P. 2018c Energetic and exergetic performances of plate heat exchanger using brine-based hybrid nanofluid for milk chilling application. Heat Transfer Engng 1–14; doi:10.1080/01457632.2018.1546770.Google Scholar
Bianco, V., Chiacchio, F., Manca, O. & Nardini, S. 2009 Numerical investigation of nanofluids forced convection in circular tubes. Appl. Therm. Engng 29 (17–18), 3632–3642.Google Scholar
Breuer, M. & Almohammed, N. 2015 Modeling and simulation of particle agglomeration in turbulent flows using a hard-sphere model with deterministic collision detection and enhanced structure models. Intl J. Multiphase Flow 73, 171–206.Google Scholar
Brock, J. R. 1962 On the theory of thermal forces acting on aerosol particles. J. Colloid Sci. 17 (8), 768–780.Google Scholar
Buongiorno, J. 2006 Convective transport in nanofluids. J. Heat Transfer 128 (3), 240–250.Google Scholar
Chamkha, A. J., Molana, M., Rahnama, A. & Ghadami, F. 2018 On the nanofluids applications in microchannels: a comprehensive review. Powder Technol. 332, 287–322.Google Scholar
Choi, S. U. S. & Eastman, J. A. 1995 Enhancing thermal conductivity of fluids with nanoparticles. In Proceedings of ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, pp. 99–105.Google Scholar
Crank, J. 1975 The Mathematics of Diffusion, 2nd edn. Clarendon Press.Google Scholar
Crowe, C. T., Sharma, M. P. & Stock, D. E. 1977 The particle-source-in cell (PSI-CELL) model for gas-droplet flows. J. Fluids Engng 99 (2), 325–332.Google Scholar
Dahneke, B. 1971 The capture of aerosol particles by surfaces. J. Colloid Interface Sci. 37 (2), 342–353.Google Scholar
Davies, C. N. 1945 Definitive equations for the fluid resistance of spheres. Proc. Phys. Soc. 57 (4), 259–270.Google Scholar
Deepak Selvakumar, R. & Dhinakaran, S. 2017 Heat transfer and particle migration in nanofluid flow around a circular bluff body using a two-way coupled Eulerian–Lagrangian approach. Intl J. Heat Mass Transfer 115, 282–293.Google Scholar
Dixit, T. & Ghosh, I. 2015 Review of micro- and mini-channel heat sinks and heat exchangers for single phase fluids. Renew. Sustain. Energy Rev. 41, 1298–1311.Google Scholar
Dong, S., Zheng, L., Zhang, X., Wu, S. & Shen, B. 2014 A new model for Brownian force and the application to simulating nanofluid flow. Microfluid. Nanofluid. 16 (1–2), 131–139.Google Scholar
Durst, F., Miloievic, D. & Schönung, B. 1984 Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study. Appl. Math. Model. 8 (2), 101–115.Google Scholar
El-Askary, W. A., Eldesoky, I. M., Saleh, O., El-Behery, S. M. & Dawood, A. S. 2016 Behavior of downward turbulent gas–solid flow through sudden expansion pipe. Powder Technol. 291, 351–365.Google Scholar
Erturk, E. & Gokcol, O. 2007 Fine grid numerical solutions of triangular cavity flow. Eur. Phys. J. Appl. Phys. 38 (1), 97–105.Google Scholar
Fernández, Á., Laguna, G., Rosell, J., Vilarrubí, M., Ibañez, M., Sisó, G., Illa, J. & Barrau, J. 2018 Assessment of the impact of non-uniform illumination and temperature profiles on a dense array CPV receiver performance. Solar Energy 171, 863–870.Google Scholar
Friedlander, S. K. 1977 Smoke, Dust, and Haze: Fundamentals of Aerosol Behavior. John Wiley.Google Scholar
Ghaderian, J. & Sidik, N. A. C. 2017 An experimental investigation on the effect of Al2O3/distilled water nanofluid on the energy efficiency of evacuated tube solar collector. Intl J. Heat Mass Transfer 108, 972–987.Google Scholar
Gorman, J. & Sparrow, E. 2018 Fluid flow and heat transfer for a particle-laden gas modeled as a two-phase turbulent flow. Intl J. Numer. Meth. Heat Fluid Flow 28 (8), 1866–1891.Google Scholar
Gregory, J. 1981 Approximate expressions for retarded Van der Waals interaction. J. Colloid Interface Sci. 83 (1), 138–145.Google Scholar
Haddad, O., Baïri, A., Alilat, N., Bauzin, J. G. & Laraqi, N. 2017 Free convection in ZnO-water nanofluid-filled and tilted hemispherical enclosures containing a cubic electronic device. Intl Commun. Heat Mass Transfer 87, 204–211.Google Scholar
He, Y., Men, Y., Zhao, Y., Lu, H. & Ding, Y. 2009 Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions. Appl. Therm. Engng 29 (10), 1965–1972.Google Scholar
Hosseinzadeh, M., Salari, A., Sardarabadi, M. & Passandideh-Fard, M. 2018 Optimization and parametric analysis of a nanofluid based photovoltaic thermal system: 3D numerical model with experimental validation. Energy Convers. Manage. 160, 93–108.Google Scholar
Hu, C., Luo, K., Wang, S., Junjie, L. & Fan, J. 2019 The effects of collisional parameters on the hydrodynamics and heat transfer in spouted bed: A CFD-DEM study. Powder Technol. 353, 132–144.Google Scholar
Inthavong, K., Tian, L. & Tu, J. 2016 Lagrangian particle modelling of spherical nanoparticle dispersion and deposition in confined flows. J. Aerosol Sci. 96, 56–68.Google Scholar
Jing, D., Song, S., Pan, Y. & Wang, X. 2018 Size dependences of hydraulic resistance and heat transfer of fluid flow in elliptical microchannel heat sinks with boundary slip. Intl J. Heat Mass Transfer 119, 647–653.Google Scholar
Jyotsna, R. & Vanka, S. P. 1995 Multigrid calculation of steady, viscous flow in a triangular cavity. J. Comput. Phys. 122 (1), 107–117.Google Scholar
Kalteh, M., Abbassi, A., Saffar-Avval, M., Frijns, A., Darhuber, A. & Harting, J. 2012 Experimental and numerical investigation of nanofluid forced convection inside a wide microchannel heat sink. Appl. Therm. Engng 36, 260–268.Google Scholar
Kandlikar, S. G., Garimella, S., Li, D., Colin, S. & King, M. R. 2006 Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier.Google Scholar
Kewalramani, G. V., Agrawal, A. & Saha, S. K. 2017 Modeling of microchannel heat sinks for electronic cooling applications using volume averaging approach. Intl J. Heat Mass Transfer 115, 395–409.Google Scholar
Khodabandeh, E. & Abbassi, A. 2018 Performance optimization of water-Al2O3 nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian–Lagrangian approach. Powder Technol. 323, 103–114.Google Scholar
Kim, S., Kim, C., Lee, W.-H. & Park, S.-R. 2011 Rheological properties of alumina nanofluids and their implication to the heat transfer enhancement mechanism. J. Appl. Phys. 110 (3), 034316.Google Scholar
Kondaraju, S., Jin, E. K. & Lee, J. S. 2010 Direct numerical simulation of thermal conductivity of nanofluids: the effect of temperature two-way coupling and coagulation of particles. Intl J. Heat Mass Transfer 53 (5–6), 862–869.Google Scholar
Kondaraju, S., Jin, E. K. & Lee, J. S. 2011 Effect of the multi-sized nanoparticle distribution on the thermal conductivity of nanofluids. Microfluid. Nanofluid. 10 (1), 133–144.Google Scholar
Kumar, V. & Sarkar, J. 2018 Two-phase numerical simulation of hybrid nanofluid heat transfer in minichannel heat sink and experimental validation. Intl Commun. Heat Mass Transfer 91, 239–247.Google Scholar
Li, A. & Ahmadi, G. 1992 Dispersion and deposition of spherical particles from point sources in a turbulent channel flow. Aerosol Sci. Technol. 16 (4), 209–226.Google Scholar
Li, M. & Tang, T. 1996 Steady viscous flow in a triangular cavity by efficient numerical techniques. Comput. Math. Appl. 31 (10), 55–65.Google Scholar
Li, P., Luo, Y., Zhang, D. & Xie, Y. 2018 Flow and heat transfer characteristics and optimization study on the water-cooled microchannel heat sinks with dimple and pin-fin. Intl J. Heat Mass Transfer 119, 152–162.Google Scholar
Liang, G. & Mudawar, I. 2019 Review of single-phase and two-phase nanofluid heat transfer in macro-channels and micro-channels. Intl J. Heat Mass Transfer 136, 324–354.Google Scholar
Liu, D., Bu, C. & Chen, X. 2013 Development and test of CFD–DEM model for complex geometry: a coupling algorithm for Fluent and DEM. Comput. Chem. Engng 58, 260–268.Google Scholar
Liu, F., Cai, Y., Wang, L. & Zhao, J. 2018 Effects of nanoparticle shapes on laminar forced convective heat transfer in curved ducts using two-phase model. Intl J. Heat Mass Transfer 116, 292–305.Google Scholar
Loth, E. 2000 Numerical approaches for motion of dispersed particles, droplets and bubbles. Prog. Energy Combust. Sci. 26 (3), 161–223.Google Scholar
Maganti, L. S., Dhar, P., Sundararajan, T. & Das, S. K. 2016 Particle and thermohydraulic maldistribution of nanofluids in parallel microchannel systems. Microfluid. Nanofluid. 20 (7), 109.Google Scholar
Mahdavi, M., Sharifpur, M. & Meyer, J. P. 2015 CFD modelling of heat transfer and pressure drops for nanofluids through vertical tubes in laminar flow by Lagrangian and Eulerian approaches. Intl J. Heat Mass Transfer 88, 803–813.Google Scholar
Mahian, O., Kolsi, L., Amani, M., Estellé, P., Ahmadi, G., Kleinstreuer, C., Marshall, J. S., Siavashi, M., Taylor, R. A., Niazmand, H. et al. 2019 Recent advances in modeling and simulation of nanofluid flows. Part I. Fundamentals and theory. Phys. Rep. 790, 1–48.Google Scholar
Masuda, H., Ebata, A., Teramae, K. & Hishinuma, N. 1993 Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles). Netsu Bussei 7 (4), 227–233.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.Google Scholar
McNab, G. S. & Meisen, A. 1973 Thermophoresis in liquids. J. Colloid Interface Sci. 44 (2), 339–346.Google Scholar
Mehendale, S. S., Jacobi, A. M. & Shah, R. K. 2000 Fluid flow and heat transfer at micro- and meso-scales with application to heat exchanger design. Appl. Mech. Rev. 53 (7), 175–193.Google Scholar
Michaelides, E. E. 2013 Heat and Mass Transfer in Particulate Suspensions. Springer.Google Scholar
Michaelides, E. E. 2014 Nanofluidics: Thermodynamic and Transport Properties. Springer.Google Scholar
Michaelides, E. E. 2015 Brownian movement and thermophoresis of nanoparticles in liquids. Intl J. Heat Mass Transfer 81, 179–187.Google Scholar
Michaelides, E. E., Crowe, C. T. & Schwarzkopf, J. D. 2017 Multiphase Flow Handbook, 2nd edn. CRC Press.Google Scholar
Migdal, D. & Agosta, V. D. 1967 A source flow model for continuum gas-particle flow. J. Appl. Mech. 34 (4), 860–865.Google Scholar
Mirzaei, M., Saffar-Avval, M. & Naderan, H. 2014 Heat transfer investigation of laminar developing flow of nanofluids in a microchannel based on Eulerian–Lagrangian approach. Canad. J. Chem. Engng 92 (6), 1139–1149.Google Scholar
Öztop, H. F., Sakhrieh, A., Abu-Nada, E. & Al-Salem, K. 2017 Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure. Intl Commun. Heat Mass Transfer 86, 42–51.Google Scholar
Rabienataj Darzi, A. A., Farhadi, M. & Lavasani, A. M. 2016 Two phase mixture model of nano-enhanced mixed convection heat transfer in finned enclosure. Chem. Engng Res. Des. 111, 294–304.Google Scholar
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Part I. Chem. Engng Prog. 48, 141–146.Google Scholar
Ribbens, C. J., Watson, L. T. & Wang, C.-Y. 1994 Steady viscous flow in a triangular cavity. J. Comput. Phys. 112 (1), 173–181.Google Scholar
Rostami, J. & Abbassi, A. 2016 Conjugate heat transfer in a wavy microchannel using nanofluid by two-phase Eulerian–Lagrangian method. Adv. Powder Technol. 27 (1), 9–18.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (02), 385–400.Google Scholar
Sahoo, R. R., Ghosh, P. & Sarkar, J. 2017 Performance analysis of a louvered fin automotive radiator using hybrid nanofluid as coolant. Heat Transfer-Asian Res. 46 (7), 978–995.Google Scholar
Sarkar, J., Ghosh, P. & Adil, A. 2015 A review on hybrid nanofluids: recent research, development and applications. Renew. Sustain. Energy Rev. 43, 164–177.Google Scholar
Schiller, L. & Naumann, A. 1933 über die grundlegenden berechnungen bei der schwerkraftaufbereitung. Ver. Deut. Ing. 77, 318–320.Google Scholar
Schillings, J., Doche, O., Tano Retamales, M., Bauer, F., Deseure, J. & Tardu, S. 2017 Four-way coupled Eulerian–Lagrangian direct numerical simulations in a vertical laminar channel flow. Intl J. Multiphase Flow 89, 92–107.Google Scholar
Sharaf, O. Z., Kyritsis, D. C., Al-Khateeb, A. N. & Abu-Nada, E. 2018 Effect of bottom surface optical boundary conditions on nanofluid-based DASC: parametric study and optimization. Sol. Energy 164, 210–223.Google Scholar
Sharaf, O. Z. & Orhan, M. F. 2018 Comparative thermodynamic analysis of densely-packed concentrated photovoltaic thermal (CPVT) solar collectors in thermally in-series and in-parallel receiver configurations. Renew. Energy 126, 296–321.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2017a Magnetohydrodynamic nanofluid convection in a porous enclosure considering heat flux boundary condition. Intl J. Heat Mass Transfer 106, 1261–1269.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2017b Thermal radiation of ferrofluid in existence of Lorentz forces considering variable viscosity. Intl J. Heat Mass Transfer 109, 82–92.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2017c Magnetohydrodynamic nanofluid convective flow in a porous enclosure by means of LBM. Intl J. Heat Mass Transfer 113, 796–805.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2017d CVFEM for influence of external magnetic source on Fe3O4-H2O nanofluid behavior in a permeable cavity considering shape effect. Intl J. Heat Mass Transfer 115, 180–191.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2018a Non-Darcy free convection of Fe3O4-water nanoliquid in a complex shaped enclosure under impact of uniform Lorentz force. Chin. J. Phys. 56 (1), 270–281.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2018b Numerical analysis of Fe3O4–H2O nanofluid flow in permeable media under the effect of external magnetic source. Intl J. Heat Mass Transfer 118, 182–192.Google Scholar
Sheikholeslami, M. & Shehzad, S. A. 2018c Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model. Intl J. Heat Mass Transfer 120, 1200–1212.Google Scholar
Sidik, N. A. C., Samion, S., Ghaderian, J. & Yazid, M. N. A. W. M. 2017 Recent progress on the application of nanofluids in minimum quantity lubrication machining: a review. Intl J. Heat Mass Transfer 108, 79–89.Google Scholar
Singh, S. K. & Sarkar, J. 2018 Energy, exergy and economic assessments of shell and tube condenser using hybrid nanofluid as coolant. Intl Commun. Heat Mass Transfer 98, 41–48.Google Scholar
de Souza, F. J., de Vasconcelos Salvo, R. & de Moro Martins, D. A. 2012 Large eddy simulation of the gas–particle flow in cyclone separators. Sep. Purif. Technol. 94, 61–70.Google Scholar
Sun, M.-H. & Zhang, X.-R. 2018 Effect of inter-particle potential on the effective viscosity of nanofluids. Intl J. Heat Mass Transfer 122, 150–160.Google Scholar
Talbot, L., Cheng, R. K., Schefer, R. W. & Willis, D. R. 1980 Thermophoresis of particles in a heated boundary layer. J. Fluid Mech. 101 (04), 737–758.Google Scholar
Tijani, A. S. & bin Sudirman, A. S. 2018 Thermos-physical properties and heat transfer characteristics of water/anti-freezing and Al2O3/CuO based nanofluid as a coolant for car radiator. Intl J. Heat Mass Transfer 118, 48–57.Google Scholar
Varol, Y., Koca, A. & Oztop, H. F. 2006 Natural convection in a triangle enclosure with flush mounted heater on the wall. Intl Commun. Heat Mass Transfer 33 (8), 951–958.Google Scholar
Wang, X. & Shi, D. 2014 Numerical performance of higher-order semicompact scheme for arbitrary triangular cavity flow. Intl J. Engng Maths 2014, 1–12.Google Scholar
Wang, Y., Deng, K., Wu, J., Su, G. & Qiu, S. 2018 The characteristics and correlation of nanofluid flow boiling critical heat flux. Intl J. Heat Mass Transfer 122, 212–221.Google Scholar
Wen, D., Zhang, L. & He, Y. 2009 Flow and migration of nanoparticle in a single channel. Heat Mass Transfer 45 (8), 1061–1067.Google Scholar
Yang, Y.-T. & Lai, F.-H. 2011 Numerical study of flow and heat transfer characteristics of alumina–water nanofluids in a microchannel using the lattice Boltzmann method. Intl Commun. Heat Mass Transfer 38 (5), 607–614.Google Scholar
Yapici, M. K., Al Nabulsi, A., Rizk, N., Boularaoui, S. M., Christoforou, N. & Lee, S. 2019 Alternating magnetic field plate for enhanced magnetofection of iron oxide nanoparticle conjugated nucleic acids. J. Magn. Magn. Mater. 469, 598–605.Google Scholar
Yousefi-Lafouraki, B., Ramiar, A. & Ranjbar, A. A. 2018 Modeling of two-phase particulate flows in a confined jet with a focus on two-way coupling. Particuology 39, 78–87.Google Scholar
Yu, F., Chen, Y., Liang, X., Xu, J., Lee, C., Liang, Q., Tao, P. & Deng, T. 2017 Dispersion stability of thermal nanofluids. Prog. Nat. Sci. 27 (5), 531–542.Google Scholar
Zakaria, I., Mohamed, W. A. N. W., Azmi, W. H., Mamat, A. M. I., Mamat, R. & Daud, W. R. W. 2018 Thermo-electrical performance of PEM fuel cell using Al2O3 nanofluids. Intl J. Heat Mass Transfer 119, 460–471.Google Scholar
Zarifi, E., Jahanfarnia, G. & Veysi, F. 2013 Subchannel analysis of nanofluids application to VVER-1000 reactor. Chem. Engng Res. Des. 91 (4), 625–632.Google Scholar
Zhang, H., Zhang, Z. & Ye, H. 2012 Molecular dynamics-based prediction of boundary slip of fluids in nanochannels. Microfluid. Nanofluid. 12 (1–4), 107–115.Google Scholar
Zhang, H., Zhang, Z., Zheng, Y. & Ye, H. 2010 Corrected second-order slip boundary condition for fluid flows in nanochannels. Phys. Rev. E 81 (6), 066303.Google Scholar
Zhang, Z.-Q., Yuan, L.-S., Liu, Z., Cheng, G.-G., Ye, H.-F. & Ding, J.-N. 2018 Flow behaviors of nanofluids in parallel-plate nanochannels influenced by the dynamics of nanoparticles. Comput. Mater. Sci. 145, 184–190.Google Scholar