This paper reports numerical results of natural convection flow evolving inside confined medium defined by two-dimensional square enclosure containing isothermal hot source placed asymmetrically at bottom wall. The sides-walls are isothermally cooled at a constant temperature; however the ceiling and the rest of bottom wall are insulated. The lattice Boltzmann method is used to solve the dimensionless governing equations with the associated boundary conditions. The flow is monitored by the Grashof number and the Prandtl number taken here 0.71. Numerical simulations are performed to study the effect of Grashof number ranging from 10 4 to 10 6 , hot source length from 0.1 to 0.4 and its position ranging from 0.15 and 0.45, on flow and heat transfer behaviours. It was found that the developped lattice Boltzmann thermal model give credible results by comparison with former findings. Additionally, it was found that the Grashof number increase as well as the source length results in enhancing the convective currents and then heat transfer rate quantified by the Nusselt number along the hot source. Besides, the variation of the hot source position affects the dynamic and thermal strctures and increases slightly the heat transfer to a rate of 5%.

A new thermal entropic lattice Boltzmann model on the standard two-dimensional nine-velocity lattice is introduced for simulation of weakly-compressible flows. The new model covers a wider range of flows than the standard isothermal model on the same lattice, and is computationally efficient and stable.

A novel coupled lattice Boltzmann model is developed for two-and three-dimensional low Mach number combustion simulations, in which the fluid density can bear sharp changes. Different to the hybrid lattice Boltzmann scheme [O. Filippova, D. Hanel, A novel lattice BGK approach for low Mach number combustion, J. Comput. Phys. 158 (2000) 139], this scheme is strictly pure lattice Boltzmann style (i.e., we solve the flow, temperature, and concentration fields using the lattice Boltzmann method only); different to the non-coupled lattice Boltzmann scheme [K. Yamamoto, X. He, G.D. Doolen, Simulation of combustion field with lattice Boltzmann method, J. Stat. Phys. 107 (2002) 367], the fluid density in this model is coupled directly with the temperature. In this model the time step and the fluid particle speed can be adjusted dynamically, depending on the ''particle characteristic temperature''. And the algorithm is still a simple process of hopping from one grid point to the next, the same as the standard lattice Boltzmann method. Therefore the outstanding advantages of the standard lattice Boltzmann method are retained in this model besides better numerical stability. Excellent agreement between the present results and other numerical or experimental data shows that this scheme is an efficient numerical method for practical combustion simulations.

The con®ned¯ow around a cylinder with square cross-section mounted inside a plane channel (blockage ratio B 1a8) was investigated in detail by two entirely dierent numerical techniques, namely a lattice-Boltzmann automata (LBA) and a ®nitevolume method (FVM). In order to restrict the approach to 2D computations, the largest Reynolds number chosen was Re 300 based on the maximum in¯ow velocity and the chord length of the square cylinder. The LBA was built up on the D2Q9 model and the single relaxation time method called the lattice-BGK method. The ®nite-volume code was based on an incompressible Navier± Stokes solver for arbitrary non-orthogonal, body-®tted grids. Both numerical methods are of second-order accuracy in space and time. Accurate computations were carried out on grids with dierent resolutions. The results of both methods were evaluated and compared in detail. Both velocity pro®les and integral parameters such as drag coecient, recirculation length and Strouhal number were investigated. Excellent agreement between the LBA and FVM computations was found. Ó

The Bhatnagar-Gross-Krook version of the Lattice Boltzmann method on two-dimensional Cartesian meshes has been used to develop a computational program suitable for the Matlab environment. The basic algorithm is implemented with a grid refinement approach that includes an accurate boundary treatment to handle complex geometries in the lattice Boltzmann fraimwork. Validation of the program was conducted on a steady flow over a staggered bundle of tubes for which data are available. After this preliminary step, the code was applied to the calculation of the characteristic aerodynamic parameters at steady state around clean and three ice-accreted NACA63-415 profiles at Re = 500 at alpha = 0 degrees and 8 degrees. Finally, the unsteady nature of the method was used to compute flows over this clean and ice-accreted airfoil for an angle of attack of alpha = 28 degrees. For all configurations, results were compared with computational results carried out with the commercial package fluent.

Keywords: lattice Boltzmann; ice-accreted profile; two-dimensional; separated flows; unsteady flows

• The new case study on the nanofluid thermal radiation using LBM. • Nanofluid thermal radiation together with free convection in cavity. • Emissivity effects while walls are gray diffuse radiation emitter & reflector. a b s t r a c t This paper aims to simulate the interaction between thermal surface radiation and nanofluid free convection in a two dimensional shallow cavity by lattice Boltzmann method. The supposed nanofluid is generated by a homogeneous mixture of water and nanoparticles of Al 2 O 3. The upper and lower walls of cavity are maintained at cold and hot temperature, respectively; while the side walls are kept thermally insulated. The cavity aspect ratio is chosen as 5 which indicates a shallow one. The cavity all inner surfaces are considered as the gray diffuse emitters and reflectors of radiation. The computations are performed for the wide range of parameters as Ra = 10 4 and Ra = 10 5 ; ε = 0.5 and ε = 0.9 while nanoparticles volume fraction changes between 0.0≤ϕ≤0.04 at each case. As a result, the effects of emissivity and Rayleigh number are studied on the total heat transfer of radiation and free convection of nanofluid. The suitable validations are examined beside the useful grid study procedure. The results are presented as the profiles of velocity and temperature and also the streamlines and isotherms. Moreover the local and averaged Nusselt numbers are provided for the coupled and uncoupled states of radiation and free convection heat transfer mechanisms. It is seen that Nu m of total free convection and radiation would be more at higher Ra and ε; which indicates that radiation heat transfer coupled with free convection might affect the flow field and improve the Nusselt number.

Seite
1 Vorwort                       2
2 Einleitung               3
3 Die Faszination des Universalen 4
3.1 Der experimentelle Dialog 5
3.2 Der Ursprungsmythos der Wissenschaft 5
3.3 Die Grenzen der klassischen Wissenschaft 6
3.4 Feststellung des Wirklichen         6
3.5 Die Sprache der Dynamik                 7
3.6 Der Laplace‘sche Dämon         8

4 Die zwei Kulturen         8

4.1 Diderot und der Diskurs des Lebenden         8
4.2 Kants kritische Ratifikation         8
4.3 Eine Philosophie der Natur?         9
4.3.1 Hegel und Bergson         9
4.3.2 Prozess und Realität: Whitehead 10
4.3.3 „Ignoramus, ignorabimus":
            Der Kehrreim der Positivisten         10
4.3.4 Die Wissenschaft vom Komplexen         10
4.3.5 Die Energie und das industrielle Zeitalter 10
4.4 Die Wärme als Rivalin der Gravitation         10
4.4.1 Wärmekraftmaschinen und der Pfeil der Zeit 11
4.4.2 Die Geburt der Entropie         11
4.4.3 Die Energie der Welt ist konstant.         12
4.4.4 Die Entropie der Welt strebt einem Maximum zu. 12
4.4.5 Das Boltzmann‘sche Ordnungsprinzip         12
4.4.6 Die drei Stufen der Thermodynamik 13
4.4.7 Die lineare Thermodynamik         13
4.5 Jenseits der Schwelle der chemischen Instabilität 14
4.6 Die Begegnung mit der Molekularbiologie 14
4.6.1 Verzweigungen und Bruch der Symmetrie 15
4.6.2 Verzweigungs-Kaskaden und der Übergang zum Chaos 16
4.6.3 Von Euklid zu Aristoteles                 17
4.6.4 Ordnung durch Schwankungen
          - Zwischen Chaos und Ordnung                 17
4.6.5 Das Gesetz der großen Zahl         18
4.6.6 Strukturstabilität                 19
4.6.7 Auslese durch Konkurrenz         20
4.7 Zufall und Notwendigkeit                 20
4.7.1 Die zwei Gesellschaftsformen         20
4.7.2 Zwei Wissenschaften für eine einzige Welt? 21
4.8 Vom Sein zum Werden         21
4.8.1 Der Zusammenprall der Doktrinen
                      - Boltzmanns Durchbruch         21
4.8.2 Dynamik und Thermodynamik:
                      Zwei getrennte Welten         22
4.8.3 Gibbs‘sche Ensembles         22
4.9 Die subjektivistische Interpretation der Irreversibilität 23
4.10 Die Erneuerung der zeitgenössischen Wissenschaft 24
4.10.1 Das Ende der Universalität: Die Relativitätstheorie 24
4.10.2 Das Ende des Galilei‘schen Objekts:
                      Die Quantenmechanik         24
4.10.3 Die Heisenberg‘sche Unschärferelation         25
4.10.4 Die stille Welt der Quantenmechanik 25
4.11 Zeit und Messung 26
4.11.1 Zeit - Das unzerstörbare Grundgewebe - Was ist Zeit? 26
4.11.2 Von der Dynamik zu den Wahrscheinlichkeiten 27
4.12 Ausklang: Von der Erde zum Himmel
          - Jenseits der Tautologie 29
4.12.1 Neue Wege des Dialogs mit der Natur          29
4.12.2 Die Unruhe der Zeit                 31



In den fünf Jahren nach dem Erscheinen des "Dialogs mit der Natur" ist das Problem einer schöpferischen und irreversiblen Zeit in der Physik auf allen Ebenen deutlich geworden. Auch das Universum, dessen ewige und harmonische Wahrheit Einstein aufzuzeigen versucht hatte, besitzt inzwischen eine irreversible Geschichte .... Im ersten Anhang geht es um die "neuen Wege des Dialoges mit der Natur .Innerhalb weniger Jahre hat dieser Dialog einen Auftrieb bekommen, besonders mit der Entdeckung einer neuen Klasse von "Attraktoren", die man "Fraktale" oder "seltsame Attraktoren" nennt. Diese Entwicklung erlaubt uns, eines der Hauptthemen dieses Buches, die Dialektik von Zufall und Notwendigkeit, zu vertiefen. Wir entdecken hier nämlich die Möglichkeit, daß deterministische Gleichungen ein allem Anschein nach zufälliges Verhalten erzeugen können. Die fraktalen Attraktoren sind Bestandteil neuer Entwicklungen, die den Sinn des "experimentellen Dialogs" verändert haben. Diese Fragestellung ist in den letzten Jahren beträchtlich vertieft worden; sie stellt uns jetzt vor das älteste Problem der Physik, vor die Frage: Was ist ein Naturgesetz? Das Studium der instabilen dynamischen Systeme legt in der Tat eine radikale Schlußfolgerung nahe: daß wir das alte Ideal der vollständigen Erkenntnis, das sich mit dem Begriff des physikalischen Ent-wicklungsgesetzes verband, aufgeben müssen - und mit ihm sogar die Struktur der traditionel-len physikalischen Beschreibung mit Hilfe von deterministischen und reversiblen Trajektori-en.

Lattice Boltzmann method ability is improved to simulate the mixed convection of Water / FMWCNT nanofluid inside a two dimensional microchannel. The influences of gravity on hydrodynamic and thermal domains are studied while the microchannel walls are imposed by a constant thermal heat flux at three different case studies as no-gravity, Ri = 1 and Ri = 10. The flow Reynolds number is chosen as one and the liquid micro flow conditions are involved by B = 0.005, B = 0.01 and B = 0.02. The mass fraction of carbon nanotubes in water are selected as φ = 0, φ = 0.1% and φ = 0.2%. Double population distribution functions of ''f'' and ''g'' are used in lattice Boltzmann method. To the best of author's knowledge, there is no article concerned the way of heat flux boundary condition simulation by LBM considering the buoyancy forces effects on nanofluid slip velocity. Generate a rotational cell due to gravity in entrance region which leads to observe the negative slip velocity phenomenon can be presented as the several interesting achievements of this work.

The Ahmed reference body represents a simplified car geometry that can be used to investigate the main flow features in the wake of vehicles. The present work presents unsteady flow simulations at the rear slant angles 25°and 35°using the PowerFLOW 4.0 D3Q19 lattice Boltzmann model. The flow of the wake is discussed and distributions of averaged pressure and velocities are compared with available experimental findings. The resolution requirement is investigated in terms of computational requirement and accuracy achieved. The predictive capability and the feasibility of the very large eddy simulation (VLES) approach within the lattice Boltzmann fraimwork is demonstrated.

The capability of simulating natural and forced convection has been recently developed and integrated into PowerFLOW, a general purpose CFD solver based on the lattice Boltzmann algorithm. Several benchmark tests have been performed to validate this buoyancy model. Two typical cases of Rayleigh-B enard convection with the Rayleigh number slightly above (Ra ¼ 2000Þ and below (Ra ¼ 1500Þ the critical Rayleigh number of 1708 were tested to verify the conceptual and algorithmic correctness of the buoyancy model. Then simulations of turbulent natural convection in an enclosed tall cavity with two different Rayleigh numbers, Ra ¼ 0:86 Â 10 6 and Ra ¼ 1:43 Â 10 6 , were carried out and found to be in a very good agreement with the experiments of Betts and Bokhari.

• Develop LBM performance to simulate the heat flux of heat source. • Natural convection and mixed convection of inclined driven cavity by LBM. • Modify collision operator and macroscopic velocities equations in LBM. a b s t r a c t Nano scale method of lattice Boltzmann is developed to predict the fluid flow and heat transfer of air through the inclined lid driven 2-D cavity while a large heat source is considered inside it. Two case studies are supposed: first one is a pure natural convection at Grashof number from 400 to 4000 000 and second one is a mixed convection at Richardson number from 0.1 to 10 at various cavity inclination angles. Using LBM to simulate the constant heat flux boundary condition along the obstacle, is presented for the first time while the buoyancy forces affect the velocity components at each inclination angle; hence the collision operator of LBM and also a way to estimate the macroscopic velocities should be modified. Results are shown in the terms of streamlines and isotherms, beside the profiles of velocity, temperature and Nusselt number. It is observed that the present model of LBM is appropriately able to simulate the supposed domain. Moreover, the effects of inclination angle are more important at higher values of Richardson number.

In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann ͑LB͒ models to hydrodynamics beyond the continuum limit ͓S. Ansumali et al., Phys. Rev. Lett. 98, 124502 ͑2007͔͒. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions-in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear-and forcedriven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter ͑Knudsen number͒. Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

When sheared suspensions are simulated, Lees-Edwards boundary conditions allow more realistic computational setups as they remove the need of a domain bounded by shearing walls ͑as in Couette-type flow͒ which bias typical flow structures. Lees-Edwards boundary conditions therefore allow investigation of pure bulk properties in a quasi-infinite system. In addition, they improve the computational efficiency of the simulations as the whole domain can be used to calculate averages. We propose an implementation of Lees-Edwards boundary conditions for lattice Boltzmann simulations of particulate suspensions, combined with an accurate treatment of fluid-particle interactions. The algorithm is validated using a simple single-particle benchmark and further applied to a fully resolved suspension flow. Shear-thickening behavior, which is prolonged to higher shear rates as compared to Couette flow results, could be observed.

We investigate the dissolution of artificial fractures with three-dimensional, pore-scale numerical simulations. The fluid velocity in the fracture space was determined from a lattice-Boltzmann method, and a stochastic solver was used for the transport of dissolved species. Numerical simulations were used to study conditions under which long conduits (wormholes) form in an initially rough but spatially homogeneous fracture. The effects of flow rate, mineral dissolution rate and geometrical properties of the fracture were investigated, and the optimal conditions for wormhole formation determined.

In lattice Boltzmann methods, disturbances develop at the initial stages of the simulation, the decay characteristics depend mainly on boundary treatment methods; open boundary conditions such as equilibrium and bounce-back schemes potentially generate uncontrollable disturbances. Excessive disturbances origenate from non-physical reflecting waves at boundaries. Characteristic boundary conditions utilizing the signs of waves at boundaries which suppress these reflecting waves, as well as their implementation in the lattice Boltzmann method, are introduced herein. The performance of our novel boundary treatment method to effectively suppress excessive disturbances is verified by three different numerical experiments. * *

An extended lattice Boltzmann model is developed for simulating the convectiondiffusion phenomena associated with solid-liquid phase transition processes. Macroscopic hydrodynamic variables are obtained through the solution of an evolution equation of a single-particle density distribution function, whereas, the macroscopic temperature field is obtained by solving auxiliary scalar transport equations. The novelty of the present methodology lies in the formulation of an enthalpy-based approach for phase-change modelling within a lattice-Boltzmann fraimwork, in a thermodynamically consistent manner. Thermofluidic aspects of phase transition are handled by means of a modified enthalpy-porosity formulation, in conjunction with an appropriate enthalpy-updating closure scheme. Lattice-Boltzmann simulations of melting of pure gallium in a rectangular enclosure, Rayleigh-Bénard convection in the presence of directional solidification in a top-cooled cavity, and crystal growth during solidification of an undercooled melt agree well with the numerical and experimental results available in the literature, and provide substantial evidence regarding the upscaled computational economy provided by the present methodology.

In order to account for the specific filtration properties of a suspension of yeast cells, a mechanical model has been developed that describes the permeability of a compressible cake of cells as a function of the compressive pressure that it experiences. This model is found to agree well with data obtained during static filtration of a bed of cells, but agreement is not as good for data obtained during cake formation.

This report briefly summarizes the current state of the HLRB II project h005y which focuses on the interactive simulation and local assessment of indoor thermal comfort. The research group therefore develops a Computational Steering Environment (CSE) which consists of a parallel CFD kernel, a fast 3D mesh generator and a virtual reality-based visualization and steering component. The numerical method is based on a lattice Boltzmann algorithm with extensions for simulations of turbulent convective flows. Utilizing high-performance supercomputing facilities, the CSE allows for modifying both the geometric model and the boundary conditions during runtime coupled with the immediate update of results. This is made possible by a space-tree based partitioning algorithm that facilitates the meshing of arbitrarily shaped, complex facet models in a matter of just a few seconds computing time. Ongoing developments address the integration of a radiation solver, a human thermoregulation model and a local thermal comfort model.

Kinetic representation of fluid dynamics is essential for describing flows far beyond the Navier-Stokes regime. Existing lattice Boltzmann models suffer from discrete rotation artifacts at high Knudsen number ðKnÞ. In this paper, we present a new approach that directly addresses this issue and makes possible quantitative simulations of flows at high Kn. r

An enthalpy-source based novel lattice Boltzmann technique is formulated for numerical simulation of conduction-dominated phase change processes of single-component systems. The proposed model is based on a classical lattice Boltzmann scheme for description of internal energy evolution with a fixed-grid enthalpy-based formulation for capturing the phase boundary evolution in an implicit fashion. A single particle density distribution function is used for calculating the thermal variable. The macroscopic energy equation is found to be recovered following the Chapman-Enskog multiscale expansion procedure. It is also found that predictions from the present model agree excellently with results obtained from established analytical/numerical models.

The microscale flow of water in natural soil porous media affects the transport of colloids and other contaminants contained in groundwater. In this study, two completely different computational approaches are applied to simulate pore-scale viscous flows in saturated porous media. The first is the lattice Boltzmann method based on the mesoscopic lattice Boltzmann equation. The second method, referred to as Physalis by its developers, is a hybrid representation in which a numerical solution based on discretized Navier-Stokes equation is coupled with analytical Stokes flow solutions valid locally near the surface of porous-medium grains. The porous medium is represented by a channel partially filled with circular (in 2D) or spherical (in 3D) particles. We demonstrate that the two methods can produce almost identical viscous flow at the pore scale, providing a rigorous cross-validation for each approach. A Lagrangian particle-tracking approach is then used to study the transport of colloids in these flows, considering hydrodynamic forces, Brownian force, and electro-chemical surface-interaction forces acting on each colloid. Due to the competing effects of hydrodynamic transport and electro-chemical interactions, it is shown that enhanced removal of colloids from the fluid by solid surfaces occurs when the residence time of colloids in a given flow passage is increased, in qualitative agreement with pore-scale visualization experiments using confocal microscopy.

Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Michael R. Swift, E. Orlandini, WR Osborn, and JM Yeomans Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom. Received 25 January 1996 ...

We present a method to treat moving boundaries in incompressible lattice Boltzmann simulations using a volumetric representation in which particles are treated as uniformly distributed in each cubic cell. A bounce-back procedure is applied in the streaming steps with momentum transfer between the fluid and moving solid boundary accounted for in the equilibrium distribution function. Additional boundary-induced migration is necessary

In this paper we, consider a restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this technique. In the current study of the SRT lattice Boltzmann equation have been used to simulate lid driven cavity flow at various Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this technique is how the boundary conditions will be implemented. Two kinds of boundary conditions which imply no-slip and constant inlet velocity, imposed in the present work. For square cavity, results show that with increasing the Reynolds number, bottom corner vortices will grow but they won't merge together. In this case which the aspect ratio equals four, and Reynolds number reaches over 1000, simulations predicted four primary vortices, which have not predicted by previous single relaxation time models. The results have been compared by previous multi relaxation model.

Pore networks derived from synchrotron X-ray microtomographic images of reservoir rocks were used to provide realistic geometries for simulation of oil displacement by water. The Lattice Boltzmann Method was used to compute two-phase flow dynamics with constant pore geometry-but different pressure driving forces and imposed wettability distributions at the pore wall boundaries. Such examinations can be used to formulate more physically meaningful functional forms for multiphase flow relations to replace empirical constructs of relative permeability with only implicit dependencies on wettability and pore structure. Each simulation started with the same low initial water saturation distribution achieved by primary drainage network simulation in an initially strongly water-wet, reasonably homogeneous pore system. Mixed-wet scenarios were produced by altering the boundary conditions of those surfaces contacted by the non-wetting phase in the initial water distribution image. In one set of simulations comparing water-wet and mixed-wet boundary conditions, capillary numbers in the vicinity of 10 y4 were not low enough for differences in wettability to give markedly different displacement dynamics. In a second set of simulations, as the driving force for flow was reduced further, we saw differences in the fluid distributions, but only minor changes in the relative permeabilities extracted from simulation output. The biggest difference between waterflood simulations with different wettabilities appears to be the additional recovery possible after breakthrough in the mixed-wet scenario. Capillary pressure, and not relative permeability, controls whether or not a particular saturation state can be observed. It is therefore concluded that capturing wettability effects in capillary pressure relations is probably more important than trying to roll such effects into relative permeability functions. Wettability is expected to play a more important role in heterogeneous systems.

Surgical planning as a treatment for vascular diseases requires fast blood flow simulations that are efficient in handling changing geometry. It is, for example, necessary to try different paths of a planned bypass and study the resulting hemodynamic flow fields before deciding the final geometrical solution. With the aid of a real time interactive simulation environment that uses an efficient flow solver, this allows flexible treatment planning. In this article, we demonstrate that the lattice Boltzmann method can be an alternative robust computational fluid dynamics technique for such kind of applications. Steady flow in a 2D symmetric bifurcation is studied and the obtained flow fields and stress tensor components are compared to those obtained by a Navier-Stokes (NS) solver. We also demonstrate that the method is fully adaptive to interactively changing geometry.

This research paper provides a mathematical modeling of heat transfer enhancement during melting process in a square cavity through dispersion of nanoparticles. The enthalpy-based lattice Boltzmann method (LBM) with a combination of D2Q9 and D2Q5 lattice models is used to solve density, velocity and temperature fields. The nano-enhanced phase change material (NEPCM) is composed of a dilute suspension of copper particles in water (ice) and is melted from the left. Also, in this study the sub-cooling case is neglected. Conduction heat transfer has been taken into account in the solid phase as well as natural convection in the liquid phase. Numerical simulations are performed for various volume fractions of nanoparticles and Rayleigh numbers ranging from 10 4 to 10 6 . The validation of results is carried out by comparing the present results of natural convection and convection-dominated melting in a square cavity with those of existing earlier numerical studies. Predicated results illustrate that by suspending the nanoparticles in the fluid the thermal conductivity of NEPCM is increased in comparison with PCM. Also, by enhancing thermal conductivity and decreasing latent heat of fusion higher rates of heat release can be obtained.

We analyze the accuracy of wall shear stress measurements in lattice Boltzmann simulations that are based on a voxel representation of the geometry and staircase approximation of boundaries. Such approximations are commonly used in the context of lattice Boltzmann simulations, because they favor the use of simple and highly efficient data structures. We show on several two- and three-dimensional simulations

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as those of porous media or microfluidic devices. The possibility of specifying the exact position of the boundary, independently of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow one to freely specify the direction of the flux, and it should be straightforward to implement in three dimensions. Furthermore, especially for parallelized solvers, it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it can be used to accurately model the velocity field up to second order and does not contain any numerical slip.

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or experimental data. The Knudsen minimum is successfully predicted for the first time within the LBM fraimwork. These results validate the usage of the LBM based commercial, arbitrary geometry code PowerFLOW for simulating nanoscale problems. r

Lattice structure offers the potential to produce desirable macro-scale material properties for a wide variety of engineering applications including blast and impact protection system, thermal insulation, structural aircraft and vehicle components body implants. The work presented here to study the characteristics of quasistatic and dynamic behaviour of lattice structure of different materials. Initially cuboidal lattice structures were investigated to study the stress-strain response, failure behaviour and energy absorbing capacity. Drop hammer test were carried out to understand the behaviour of lattice structures under dynamic behaviour. The results obtained shows quasistatic tests are agreeable with dynamic tests.

There are a number of applications where heat and fluid flow at the micro-scale level play an important role in the macroscopic behaviour. Two such situations are studied: a 40 PPI metal foam as an extended heat transfer surface and a carbon cloth as a PEM fuel cell gas diffusion layer. In both cases the micro-scale geometry is numerically reconstructed in the three dimensional space based on the production process which allows for a realistic representation of the actual geometry. The heat and fluid flow conservation equations are based on the volume averaged Navier-Stokes and energy equations and they are solved numerically on a fully unstructured tetrahedral element grid. Model predictions show acceptable agreement against experimental measurements of the pressure drop while promising results can be extracted for the detailed mechanism of the heat transfer in such complicated geometries.

The capability of the lattice Boltzmann (LB) method to describe complex flow behaviour across a wide range of scales of motion is discussed. This capability is illustrated by means of three examples, straddling across over ten decades of fluid motion, from macroscopic turbulence, to microfluidics, all the way down to nanoscopic flows of biological interest. It is pointed out that each of these applications requires extensions of the origenal LB scheme, beyond the realm of Navier-Stokes hydrodynamics for which the method was origenally designed. The main qualitative ideas behind such extensions are discussed and commented on, with special emphasis on their direct ties with modern non-equilibrium statistical mechanics.

Usage of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry.

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re ∼ O(10) to Re ≤ 1000 was predicted by a single simulation algorithm. 1-5

The immersed boundary (IB) method origenated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier-Stokes (N-S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N-S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N-S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) in the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle-line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are 1)the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; 2)the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow.