Simulation of copper–water nanofluid in a microchannel in slip flow regime using the lattice Boltzmann method

Kavehpour, 1997, Effects of compressibility and rarefaction on gaseous flows in microchannels, Numer. Heat Transfer A, 32, 677, 10.1080/10407789708913912

Hooman, 2008, A superposition approach to study slip-flow forced convection in straight microchannels of uniform but arbitrary cross-section, Int. J. Heat Mass Transfer, 51, 3753, 10.1016/j.ijheatmasstransfer.2007.12.014

Hooman, 2008, Effects of temperature-dependent viscosity on forced convection inside a porous medium, Transp. Porous Media, 75, 249

Goodarzi, 2014, Comparison of the finite volume and lattice boltzmann methods for solving natural convection heat transfer problems inside cavities and enclosures, Abstr. Appl. Anal., 10.1155/2014/762184

Nguyen, 2006

Hooman, 2007, Entropy generation for microscale forced convection: Effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry, Int. Commun. Heat Mass Transfer, 34, 945, 10.1016/j.icheatmasstransfer.2007.05.019

Naris, 2008, Rarefied gas flow in a triangular duct based on a boundary fitted lattice, Eur. J. Mech. Fluids, 27, 810, 10.1016/j.euromechflu.2008.01.002

Pantazis, 2013, Rarefied gas flow through a cylindrical tube due to a small pressure difference, Eur. J. Mech. Fluids, 38, 114, 10.1016/j.euromechflu.2012.10.006

Hooman, 2009, Scaling effects for flow in micro-channels: Variable property, viscous heating, velocity slip, and temperature jump, Int. Commun. Heat Mass Transfer, 36, 192, 10.1016/j.icheatmasstransfer.2008.10.003

G. Bird, Molecular gas dynamics and the direct simulation of gas flows, Oxford, 1994.

Oran, 1998, Direct simulation Mont Carlo: recent advances and applications, Annu. Rev. Fluid Mech., 30, 403, 10.1146/annurev.fluid.30.1.403

Lim, 2002, Application of lattice Boltzmann method to simulate microchannel flows, Phys. Fluids, 14, 2299, 10.1063/1.1483841

Shu, 2005, A lattice Boltzmann kinetic model for microflow and heat transfer, J. Stat. Phys., 121, 239, 10.1007/s10955-005-8413-z

Sofonea, 2005, Boundary conditions for the upwind finite difference Lattice Boltzmann model: evidence of slip velocity in micro-channel flow, J. Comput. Phys., 207, 639, 10.1016/j.jcp.2005.02.003

Zhang, 2005, Gas flow in microchannels — a lattice Boltzmann method approach, J. Stat. Phys., 121, 257, 10.1007/s10955-005-8416-9

Hung, 2006, A numerical study for slip flow heat transfer, Appl. Math. Comput., 173, 1246, 10.1016/j.amc.2005.04.068

Karimipour, 2014, Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method, Physica A, 402, 150, 10.1016/j.physa.2014.01.057

Tian, 2007, Lattice Boltzmann scheme for simulating thermal micro-flow, Physica A, 385, 59, 10.1016/j.physa.2007.01.021

Babovsky, 2009, A numerical model for the Boltzmann equation with applications to micro flows, Comput. Math. Appl., 58, 791, 10.1016/j.camwa.2009.05.003

Chen, 2009, Simulation of microchannel flow using the lattice Boltzmann method, Physica A, 388, 4803, 10.1016/j.physa.2009.08.015

Bhatnagar, 1954, A model for collision process in gases. I. Small amplitude processes in charged and neutral one-component system, Phys. Rev., 94, 511, 10.1103/PhysRev.94.511

S. Succi, The lattice Boltzmann equation for fluid dynamics and beyond, first ed., Oxford, 2001.

Chen, 2010, Lattice Boltzmann method for slip flow heat transfer in circular microtubes: extended Graetz problem, Appl. Math. Comput., 217, 3314, 10.1016/j.amc.2010.08.063

Chen, 2010, Entropy generation analysis of thermal micro-Couette flows in slip regime, Int. J. Therm. Sci., 49, 2211, 10.1016/j.ijthermalsci.2010.06.019

He, 1998, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146, 282, 10.1006/jcph.1998.6057

D’Orazio, 2003, Lattice Boltzmann simulation of open flows with heat transfer, Phys. Fluids, 15, 2778, 10.1063/1.1597681

D’Orazio, 2004, Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition, Int. J. Therm. Sci., 43, 575, 10.1016/j.ijthermalsci.2003.11.002

Karimipour, 2013, The effects of inclination angle and Prandtl number on the mixed convection in the inclined lid driven cavity using lattice Boltzmann method, J. Theoret. Appl. Mech., 51, 447

Szalmas, 2007, Multiple-relaxation time lattice Boltzmann method for the finite Knudsen number region, Physica A, 379, 401, 10.1016/j.physa.2007.01.013

Goodarzi, 2014, Numerical study of entropy generation due to coupled laminar and turbulent mixed convection and thermal radiation in an enclosure filled with a semitransparent medium, Sci. World J., 8

Verhaeghe, 2009, Lattice Boltzmann modeling of microchannel flow in slip flow regime, J. Comput. Phys., 228, 147, 10.1016/j.jcp.2008.09.004

Chen, 2010, Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model, Int. J. Heat Fluid Flow, 31, 227, 10.1016/j.ijheatfluidflow.2009.12.006

Tian, 2010, Lattice Boltzmann simulation of gaseous finite-Kundsen microflows, Internat. J. Modern Phys. C, 21, 769, 10.1142/S0129183110015464

Karimipour, 2012, Investigation of the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method, Int. J. Therm. Sci., 54, 142, 10.1016/j.ijthermalsci.2011.11.015

Khorasanizadeh, 2013, Entropy generation of Cu–water nanofluid mixed convection in a cavity, Eur. J. Mech. B Fluids, 37, 143, 10.1016/j.euromechflu.2012.09.002

Santra, 2009, Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates, Int. J. Therm. Sci., 48, 391, 10.1016/j.ijthermalsci.2008.10.004

Goodarzi, 2014, An investigation of laminar and turbulent nanofluid mixed convection in a shallow rectangular enclosure using a two-phase mixture model, Int. J. Therm. Sci., 75, 204, 10.1016/j.ijthermalsci.2013.08.003

Togun, 2014, Heat transfer to turbulent and laminar Cu/water flow over a backward-facing step, Appl. Math. Comput., 239, 153, 10.1016/j.amc.2014.04.051

Sheikhzadeh, 2011, Natural convection of Cu–water nanofluid in a cavity with partially active side walls, Eur. J. Mech. B Fluids, 30, 166, 10.1016/j.euromechflu.2010.10.003

Safaei, 2011, Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method, Int. J. Multiphys., 5, 307, 10.1260/1750-9548.5.4.307

Karimipour, 2011, Periodic mixed convection of a nanofluid in a cavity with top lid sinusoidal motion, Proc. IMechE Part C: J. Mech. Eng. Sci., 225, 2149, 10.1177/0954406211404634

Esfe, 2014, Effect of nanofluid variable properties on mixed convection flow and heat transfer in an inclined two-sided lid-driven cavity with sinusoidal heating on sidewalls, Heat Transfer Res., 45, 409, 10.1615/HeatTransRes.2013007127

Esfe, 2014, Numerical simulation of natural convection around an obstacle placed in an enclosure filled with different types of nanofluids, Heat Transfer Res., 45, 279

Aminossadati, 2011, Effects of magnetic field on nanofluid forced convection in a partially heated microchannel, Int. J. Non-Linear Mech., 46, 1373, 10.1016/j.ijnonlinmec.2011.07.013

Kalteh, 2011, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow, 32, 107, 10.1016/j.ijheatfluidflow.2010.08.001

Mital, 2013, Semi-analytical investigation of electronics cooling using developing nanofluid flow in rectangular microchannels, Appl. Therm. Eng., 52, 321, 10.1016/j.applthermaleng.2012.12.020

Mital, 2013, Analytical analysis of heat transfer and pumping power of laminar nanofluid developing flow in microchannels, Appl. Therm. Eng., 50, 429, 10.1016/j.applthermaleng.2012.07.040

Raisi, 2011, A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and no-slip conditions, Numer. Heat Transfer A, 59, 114, 10.1080/10407782.2011.540964

Tamayol, 2011, Slip-flow in microchannels of non-circular cross sections, J. Fluids Eng., 133, 091202-1, 10.1115/1.4004591

Hooman, 2010, Effects of viscous heating, fluid property variation, velocity slip, and temperature jump on convection through parallel plate and circular microchannels, Int. Commun. Heat Mass Transfer, 37, 34, 10.1016/j.icheatmasstransfer.2009.09.011

Zhou, 2010, Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method, Int. J. Multiphase Flow, 36, 364, 10.1016/j.ijmultiphaseflow.2010.01.005

Esfe, 2014, Mixed-convection flow in a liddriven square cavity filled with a nanofluid with variable properties: effect of the nanoparticle diameter and of the position of a hot obstacle, Heat Transfer Res., 45, 563, 10.1615/HeatTransRes.2014007271

Lai, 2011, Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure, Int. J. Therm. Sci., 50, 1930, 10.1016/j.ijthermalsci.2011.04.015

Guo, 2012, Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method, Int. Commun. Heat Mass Transfer, 39, 350, 10.1016/j.icheatmasstransfer.2011.12.013

Ay, 2012, Application of lattice Boltzmann method to the fluid analysis in a rectangular microchannel, Comput. Math. Appl., 64, 1065, 10.1016/j.camwa.2012.03.025

Yang, 2011, Numerical study of flow and heat transfer characteristics of alumina-water nanofluids in a microchannel using the lattice Boltzmann method, Int. Commun. Heat Mass Transfer, 38, 607, 10.1016/j.icheatmasstransfer.2011.03.010

Xuan, 2003, Investigation on convective heat transfer and flow features of nanofluids, ASME J. Heat Transfer, 125, 151, 10.1115/1.1532008

Brinkman, 1952, The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20, 571, 10.1063/1.1700493

Chon, 2005, Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Appl. Phys. Lett., 87, 153107, 10.1063/1.2093936

S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases, third ed., Cambridge, 1999.

Qian, 1992, Lattice BGK models for Navier–Stokes equation, Europhys. Lett., 17, 479, 10.1209/0295-5075/17/6/001

Niu, 2007, A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows, Comp. Fluids, 36, 273, 10.1016/j.compfluid.2005.11.007

D’Orazio, 2004, Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions, Future Gener. Comput. Syst., 20, 935, 10.1016/j.future.2003.12.005

Zou, 1997, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, 9, 1591, 10.1063/1.869307

Alamyane, 2010, Simulation of forced convection in a channel with extended surfaces by the lattice Boltzmann method, Comput. Math. Appl., 59, 2421, 10.1016/j.camwa.2009.08.070

Gad-el-Hak, 2001, Flow physics in MEMS, Rev. Mech. Ind., 2, 313

Thompson, 1997, A general boundary condition for liquid flow at solid surfaces, Phys. Rev. Lett., 63, 766, 10.1103/PhysRevLett.63.766

Ngoma, 2007, Heat flux and slip effects on liquid flow in a microchannel, Int. J. Therm. Sci., 46, 1076, 10.1016/j.ijthermalsci.2007.02.001

G. Karniadakis, A. Beskok, Micro flows: fundamentals and simulation, New York, 2002.

Succi, 2002, Mesoscopic modelling of slip motion at fluid-solid interfaces with heterogeneous catalysis, Phys. Rev. Lett., 89, 10.1103/PhysRevLett.89.064502

Akbarinia, 2011, Critical investigation of heat transfer enhancement using nanofluids in microchannels with slip and non-slip flow regimes, Appl. Therm. Eng., 31, 556, 10.1016/j.applthermaleng.2010.10.017