The average Nusselt number with the use of nanofluid is higher than

The average Nusselt number with the use of nanofluid is higher than the use of water under the
same Rayleigh number. However, the heat transfer rate of the nanofluid takes on a lower value
than water at a fixed temperature difference across the enclosure mainly due to the
significant enhancement of dynamic viscosity. Furthermore, great deviations of computed
Nusselt numbers using different models associated with the physical properties of a nanofluid are
A thermal lattice BGK model with doubled populations, together with a new boundary condition
for temperature and heat flux, is proposed to simulate the two-dimensional natural convection
flow in a cavity.
In this framework, main aim of the present paper is to propose, discuss and validate a general
purpose thermal boundary condition (GPTBC). The GPTBC proposed here, successfully
demonstrated for the Dirichlet-type constraint in the case of thermal Couette and Poiseuille
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on
the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the
double-distribution-function (DDF) approach in which the viscous heat dissipation and
compression work are considered.
The discrete equilibrium density and total energy distribution functions are obtained from the
Hermite expansions of the corresponding continuous equilibrium distribution functions. The
pressure given by the equation of state of perfect gases is recovered in the macroscopic
momentum and energy equations. The coupling between the momentum and energy transports
makes the model applicable for general thermal flows such as non-Boussinesq flows, while the
existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which
the temperature variation is small.
Extensive parametric studies on mixed convection in a driven cavity filled with porous medium
are carried out for various values of Reynolds number, Richardson number and Darcy number. It
is found that the flow and temperature patterns change greatly with variations of these
The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics
are investigated and discussed. It is found that the effects of solid volume fraction for Cu are
stronger than Al2O3.
This study presents a numerical investigation of laminar natural convection heat transfer in an
inclined enclosure, differentially heated, with inclined partitions attached to its hot wall.
Effects of partition length, partition inclination angle, partitions number and aspect ratio cavity
are studied for Prandtl number 0.71 and cavity inclination angles of 45 and 90. Rayleigh
numbers considered are 5 105 for a square cavity and 10 4 for a cavity with an aspect ratio equal
to 6.
The investigation is performed for various inclination angles and gap widths W. At lower Ra (Ra
6 10 5),the average hot wall Nusselt number Num is higher in inclined cavities than in vertical
ones; while at larger Ra (Ra = 10 6
), the opposite occurs. In vertical cavities, Num decreases with decreasing W. However in
inclined ones, this trend is found only at lower Ra whereas at higher Ra, Num shows a maximum
at about W = 0.5. Num also decreases when the number of partitions (Np) attached to the cold
wall of the enclosure increases; however beyond a certain value of (Np), which depends of Ra,
Num becomes almost constant.
. The numerical approach adopted uses a hybrid thermal lattice Boltzmann method (HTLBM)
in which the mass and momentum conservation equations are solved by using multiple
relaxation time (MRT) model and the energy equation is solved separately by using the finite
difference method (FDM). In addition, the radiative transfer equation (RTE) is treated by the
discrete ordinates method (DOM) using the S8 quadrature to evaluate the source term of the
energy equation.
The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that
in the absence of the radiation, the temperature and the flow fields are centro-symmetrics and the
cavity core is thermally stratified. However, radiation causes an overall increase in temperature
and velocity gradients along both thermally active walls.
We adopted the double-distribution model to simulate heat transfer process. To simplify the
calculation, a simpler model D2Q5 is applied to simulate temperature while D2Q9 is for velocity
simulation. Brownian motion and the interaction potential between nanoparticles are considered
in the simulation.
This paper reports a numerical study on natural convection from a protruding heater located at
the bottom of a square cavity filled with a copper-water nanofluid. The vertical walls of the
cavity are cooled isothermally; the horizontal ones are adiabatic, and the heater is attached to the
bottom wall. The heat source is assumed either to be isothermal or to have a constant heat flux.
The effective viscosity and thermal conductivity of the nanofluid are modeled according to
Brinkman and Patel, respectively.
This work focuses on the study of natural convection heat transfer characteristics in a
differentially-heated enclosure filled with a CuOeEGeWater nanofluid for different
published variable thermal conductivity and variable viscosity models. The problem is
given in terms of the vorticityestream function formulation and the resulting governing
equations are solved numerically using an efficient finite-volume method.
Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number
as the volume fraction of nanoparticles increases depending on the combination of
CuOeEGeWater variable thermal conductivity and viscosity models employed. In general, the
effects the viscosity models are predicted to be more predominant on the behavior of the average
Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio
is predicted to have significant effects on the behavior of the average Nusselt number which
decreases as the enclosure aspect ratio increases.
Transient natural convection in a low-Prandtl-number ¯uid was computed for a shallow
rectangular enclosure of 5 5 1 heated from below and cooled from above with four dragless,
adiabatic, vertical walls. The model consists of three-directional mass, momentum and energy
balances. These equations were approximated by a HSMAC ®nite-difference method with a
hybrid scheme for the inertial terms.
The transient response after a step increase of the lower-wall temperature was at ®rst a regular
oscillation, which then evolved to a series of long rolls with their axes in one direction.
The present study aims to identify effects due to uncertainties in effective dynamic viscosity and
thermal conductivity of nanofluid on laminar natural convection heat transfer in a square
enclosure. Numerical simulations have been undertaken incorporating a homogeneous solid–
liquid mixture formulation for the two-dimensional buoyancy-driven convection in the enclosure
filled with alumina–water nanofluid.
Significant difference in the effective dynamic viscosity enhancement of the nanofluid calculated
from the two adopted formulas, other than that in the thermal conductivity enhancement, was
found to play as a major factor, thereby leading to contradictory results concerning the heat
transfer efficacy of using nanofluid in the enclosure.
A thermal lattice BGK model with doubled populations is proposed to simulate the twodimensional natural convection flow in porous media (porous metals). The accuracy of this
method is validated by the benchmark solutions. The detailed flow and heat transfer at the pore
level are revealed. The effects of pore density (cell size) and porosity on the natural convection
are examined. Also the effect of porous media configuration (shape) on natural convection is
investigated. The results showed that the overall heat transfer will be enhanced by lowering the
porosity and cell size. The square porous medium canhave a higher heat transfer performance
than spheres due to the strong flow mixing and more surface area.
The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM)
was used in this paper to extend the current thermal model to an arbitrary geometry so that it can
be used to solve practical thermo-hydrodynamics in the incompressible limit. The new explicit
method is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and
the least squares approach. The final formulation is an algebraic form and essentially has no
limitation on the mesh structure and lattice model. Numerical simulations of natural convection
in a square cavity on both uniform and nonuniform grids have been carried out. Favorable results
were obtained and compared well with the benchmark data. It was found that, to get the same
order of accuracy, the number of mesh points used on the nonuniform grid is much less than that
used on the uniform grid.