Mixed convection of copper-water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method

The goal of this work is to study the laminar mixed convection of water–Cu nanofluid in an inclined shallow driven cavity using the lattice Boltzmann method. The upper lid of the cavity moves with constant velocity, U0, and its temperature is higher than that of the lower wall. The side walls are assumed to be adiabatic. The effects of different values of the cavity inclination angle and nanoparticles volume fraction at three states of free, force and mixed convection domination are investigated while the Reynolds number is kept fixed as Re=100 and Re=10. Validation of present results with those of other available ones shows a suitable agreement. Streamlines, isotherms, Nusselt numbers, and velocity and temperature profiles are presented. More Nusselt numbers can be achieved at larger values of the inclination angle and nanoparticles volume fraction at free convection domination. Results imply the appropriate ability of LBM to simulate the mixed convection of nanofluid in a shallow inclined cavity.

[1]  Chuguang Zheng,et al.  Lattice Boltzmann scheme for simulating thermal micro-flow , 2007 .

[2]  Jae Min Hyun,et al.  Mixed convection in a driven cavity with a stable vertical temperature gradient , 1993 .

[3]  M. Farhadi,et al.  Lattice Boltzmann simulation of nanofluid in lid-driven cavity , 2010 .

[4]  C. Shu,et al.  A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows , 2007 .

[5]  A. Norouzi,et al.  Two relaxation time lattice Boltzmann model for rarefied gas flows , 2014 .

[6]  H. Oztop,et al.  Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids , 2008 .

[7]  Y. Xuan,et al.  Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach , 2007 .

[9]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[10]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[11]  Zhiwei Tian,et al.  Simulation of microchannel flow using the lattice Boltzmann method , 2009 .

[12]  R. Bennacer,et al.  Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method , 2012 .

[13]  Amin Behzadmehr,et al.  Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model , 2008 .

[14]  Shiyi Chen,et al.  A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , 1998 .

[15]  Y. Xuan,et al.  Investigation on Convective Heat Transfer and Flow Features of Nanofluids , 2003 .

[16]  Goodarz Ahmadi,et al.  Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model , 2014 .

[17]  Gian Piero Celata,et al.  Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition , 2004 .

[18]  Zhiwei Tian,et al.  Entropy generation analysis of thermal micro-Couette flows in slip regime , 2010 .

[19]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[20]  Stéphane Colin,et al.  Heat Transfer and Fluid Flow in Minichannels and Microchannels , 2005 .

[21]  Mostafa Mahmoodi,et al.  Numerical study of natural convection of a nanofluid in C-shaped enclosures , 2012 .

[22]  M. Afrand,et al.  Simulation of Fluid Flow and Heat Transfer in the Inclined Enclosure , 2012 .

[23]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[24]  C. Chon,et al.  Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement , 2005 .

[25]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[26]  David R. Emerson,et al.  Gas Flow in Microchannels – A Lattice Boltzmann Method Approach , 2005 .

[27]  Shiyi Chen,et al.  Lattice-Boltzmann Simulations of Fluid Flows in MEMS , 1998, comp-gas/9806001.

[28]  A. D'Orazio,et al.  The effects of inclination angle and Prandtl number on the mixed convection in the inclined lid driven cavity using lattice Boltzmann method , 2013 .

[29]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[30]  Woo Tae Kim,et al.  Simulation of micro- and nano-scale flows via the lattice Boltzmann method , 2006 .

[31]  Mohammad Reza Safaei,et al.  Numerical investigation of laminar and turbulent mixed convection in a shallow water-filled enclosure by various turbulence methods , 2011 .

[32]  R. Tiwari,et al.  HEAT TRANSFER AUGMENTATION IN A TWO-SIDED LID-DRIVEN DIFFERENTIALLY HEATED SQUARE CAVITY UTILIZING NANOFLUIDS , 2007 .

[33]  Goodarz Ahmadi,et al.  Numerical Study of Entropy Generation in a Flowing Nanofluid Used in Micro- and Minichannels , 2013, Entropy.

[34]  M. Sharif,et al.  Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom , 2007 .

[35]  Mohamed Gad-el-Hak,et al.  Flow physics in MEMS , 2001 .

[36]  M. Mahmoodi,et al.  Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid , 2012 .

[37]  Ioan Pop,et al.  A heatline analysis of natural convection in a square inclined enclosure filled with a CuO nanofluid under non-uniform wall heating condition , 2012 .

[38]  P. Lallemand,et al.  Lattice-Boltzmann computation of natural convection in a partitioned enclosure with inclined partitions attached to its hot wall , 2006 .

[39]  B. Z. Cybyk,et al.  Direct Simulation Monte Carlo: Recent Advances and Applications , 1998 .

[40]  Chang Shu,et al.  Application of lattice Boltzmann method to simulate microchannel flows , 2002 .

[41]  C. Shu,et al.  A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer , 2005 .

[42]  A. D'Orazio,et al.  Investigation of the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method , 2012 .

[43]  M. Farhadi,et al.  Lattice Boltzmann simulation of natural convection heat transfer in nanofluids , 2012 .

[44]  H. Brinkman.  The Viscosity of Concentrated Suspensions and Solutions , 1952 .

[45]  Yue-Tzu Yang,et al.  Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure , 2011 .

[46]  Hans Babovsky,et al.  A numerical model for the Boltzmann equation with applications to micro flows , 2009, Comput. Math. Appl..

[47]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[48]  Jacek Pozorski,et al.  Lattice Boltzmann simulation of fluid flow in porous media of temperature-affected geometry , 2012 .

[49]  M. Rahimian,et al.  Investigation of heat transfer enhancement in an enclosure filled with nanofluids using multiple relaxation time lattice Boltzmann modeling , 2011 .

[50]  Niladri Chakraborty,et al.  Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates , 2009 .

[51]  Saiied M. Aminossadati,et al.  Effects of magnetic field on nanofluid forced convection in a partially heated microchannel , 2011 .

[52]  Sheng Chen.  Lattice Boltzmann method for slip flow heat transfer in circular microtubes: Extended Graetz problem , 2010, Appl. Math. Comput..

[53]  G. Bird.  Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[54]  H. Sajjadi,et al.  Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid , 2011 .

[55]  C. T. Nguyen,et al.  Heat transfer performance and hydrodynamic behavior of turbulent nanofluid radial flows , 2012 .

[56]  Numerical investigation of natural convection heat transfer of nanofluids in a C shaped cavity , 2012 .

[57]  Goodarz Ahmadi,et al.  Computer simulations of natural convection of single phase nanofluids in simple enclosures: A critical review , 2012 .

[58]  C. Shu,et al.  Simplified thermal lattice Boltzmann model for incompressible thermal flows. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Ru Yang,et al.  A numerical study for slip flow heat transfer , 2006, Appl. Math. Comput..

[60]  R. Dehnavi,et al.  Numerical investigation of natural convection heat transfer of nanofluids in a C shaped cavity , 2012 .

[61]  Ihsan Dagtekin,et al.  Mixed convection in two-sided lid-driven differentially heated square cavity , 2004 .

[62]  Victor Sofonea,et al.  Boundary conditions for the upwind finite difference Lattice Boltzmann model: Evidence of slip velocity in micro-channel flow , 2005 .

[63]  B. Ghasemi,et al.  Cooling enhancement of two fins in a horizontal channel by nanofluid mixed convection , 2012 .