Search results for: Boltzmann statistics

Authors: Ji-Hyok Kim, Il-Gyong Paek, Yong-Jun Kim

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We propose a numerical model based on drift-diffusion theory and lattice Boltzmann method (LBM) to analyze the electro-hydrodynamic behavior in low-pressure direct current (DC) glow discharge plasmas. We apply the drift-diffusion theory for 4-species and employ the standard lattice Boltzmann model (SLBM) for the electron, the finite difference-lattice Boltzmann model (FD-LBM) for heavy particles, and the finite difference model (FDM) for the electric potential, respectively. Our results are compared with those of other methods, and emphasize the necessity of a two-dimensional analysis for glow discharge.

Keywords: glow discharge, lattice Boltzmann method, numerical analysis, plasma simulation, electro-hydrodynamic

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Authors: H. Lee, Jr., L. Bo-ot, R. Tumlos, H. Ramos

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The objective of the study is to be able to calculate excitation and vibrational temperatures of a 2.45 GHz microwave-induced atmospheric pressure plasma jet. The plasma jet utilizes Argon gas as a primary working gas, while Nitrogen is utilized as a shroud gas for protecting the quartz tube from the plasma discharge. Through Optical Emission Spectroscopy (OES), various emission spectra were acquired from the plasma discharge. Selected lines from Ar I and N2 I emissions were used for the Boltzmann plot technique. The Boltzmann plots yielded values for the excitation and vibrational temperatures. The various values for the temperatures were plotted against varying parameters such as the gas flow rates.

Keywords: plasma jet, OES, Boltzmann plots, vibrational temperatures

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Authors: Lloyd G. Allred

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The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: cosmology, EMP, plasma physics, relativity

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Authors: K. S. Agrawal

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The performance of jet ejector was studied in detail by different authors. Several authors have studied mass transfer characteristics like interfacial area, mass transfer coefficients etc. In this paper, we have made an attempt to develop PDE model by considering bubble properties and apply Lattice-Boltzmann technique for PDE model. We may present the results for the interfacial area which we have obtained from our numerical simulation. Later the results are compared with previous work.

Keywords: jet ejector, mass transfer characteristics, numerical simulation, Lattice-Boltzmann technique

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Authors: Jianjia Wang, Tong Yu, Haoran Zhu, Kun Liu, Jinwei Hao

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The underlying pattern in the modern city is agglomeration. To some degree, the distribution of urban spatial density can be used to describe the status of this assemblage. There are three intrinsic characteristics to measure urban spatial density, namely, Floor Area Ratio (FAR), Building Coverage Ratio (BCR), and Average Storeys (AS). But the underlying mechanism that contributes to these quantities is still vague in the statistical urban study. In this paper, we explore the corresponding extrinsic factors related to spatial density. These factors can further provide the potential influence on the intrinsic quantities. Here, we take Shanghai Inner Ring Area and Manhattan in New York as examples to analyse the potential impacts on urban spatial density with six selected extrinsic elements. Ebery single factor presents the correlation to the spatial distribution, but the overall global impact of all is still implicit. To handle this issue, we attempt to develop the Boltzmann statistical model to explicitly explain the mechanism behind that. We derive a corresponding novel quantity, called capacity, to measure the global effects of all other extrinsic factors to the three intrinsic characteristics. The distribution of capacity presents a similar pattern to real measurements. This reveals the nonlinear influence on the multi-factor relations to the urban spatial density in agglomeration.

Keywords: urban spatial density, Boltzmann statistics, multi-factor correlation, spatial distribution

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Authors: Johan Loeckx, Joeri Bultheel

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Recently, the application of deep learning to music has gained popularity. Its true potential, however, has been largely unexplored. In this paper, a new idea for representing the dynamic behavior of music is proposed. A ”forward” conditional RBM takes into account not only preceding but also future samples during training. Though this may sound controversial at first sight, it will be shown that it makes sense from a musical and neuro-cognitive perspective. The model is applied to reconstruct music based upon the first notes and to improvise in the musical style of a composer. Different to expectations, reconstruction accuracy with respect to a regular CRBM with the same order, was not significantly improved. More research is needed to test the performance on unseen data.

Keywords: deep learning, restricted boltzmann machine, music generation, conditional restricted boltzmann machine (CRBM)

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Authors: K. Noah, F.-S. Lien

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In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

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Authors: Abir Yahya, Hacen Dhahri, Khalifa Slimi

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The present paper deals with a numerical simulation of temperature field inside a solid oxide fuel cell (SOFC) components. The temperature distribution is investigated using a co-flow planar SOFC comprising the air and fuel channel and two-ceramic electrodes, anode and cathode, separated by a dense ceramic electrolyte. The Lattice Boltzmann method (LBM) is used for the numerical simulation of the physical problem. The effects of inlet temperature, anode thermal conductivity and current density on temperature distribution are discussed. It was found that temperature distribution is very sensitive to the inlet temperature and the current density.

Keywords: heat sources, Lattice Boltzmann method, solid oxide fuel cell, temperature

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Authors: H. Hruschka

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This paper presents the first comparison of the performance of the restricted Boltzmann machine and the deep belief net on binary market basket data relative to binary factor analysis and the two best-known topic models, namely Dirichlet allocation and the correlated topic model. This comparison shows that the restricted Boltzmann machine and the deep belief net are superior to both binary factor analysis and topic models. Managerial implications that differ between the investigated models are treated as well. The restricted Boltzmann machine is defined as joint Boltzmann distribution of hidden variables and observed variables (purchases). It comprises one layer of observed variables and one layer of hidden variables. Note that variables of the same layer are not connected. The comparison also includes deep belief nets with three layers. The first layer is a restricted Boltzmann machine based on category purchases. Hidden variables of the first layer are used as input variables by the second-layer restricted Boltzmann machine which then generates second-layer hidden variables. Finally, in the third layer hidden variables are related to purchases. A public data set is analyzed which contains one month of real-world point-of-sale transactions in a typical local grocery outlet. It consists of 9,835 market baskets referring to 169 product categories. This data set is randomly split into two halves. One half is used for estimation, the other serves as holdout data. Each model is evaluated by the log likelihood for the holdout data. Performance of the topic models is disappointing as the holdout log likelihood of the correlated topic model – which is better than Dirichlet allocation - is lower by more than 25,000 compared to the best binary factor analysis model. On the other hand, binary factor analysis on its own is clearly surpassed by both the restricted Boltzmann machine and the deep belief net whose holdout log likelihoods are higher by more than 23,000. Overall, the deep belief net performs best. We also interpret hidden variables discovered by binary factor analysis, the restricted Boltzmann machine and the deep belief net. Hidden variables characterized by the product categories to which they are related differ strongly between these three models. To derive managerial implications we assess the effect of promoting each category on total basket size, i.e., the number of purchased product categories, due to each category's interdependence with all the other categories. The investigated models lead to very different implications as they disagree about which categories are associated with higher basket size increases due to a promotion. Of course, recommendations based on better performing models should be preferred. The impressive performance advantages of the restricted Boltzmann machine and the deep belief net suggest continuing research by appropriate extensions. To include predictors, especially marketing variables such as price, seems to be an obvious next step. It might also be feasible to take a more detailed perspective by considering purchases of brands instead of purchases of product categories.

Keywords: binary factor analysis, deep belief net, market basket analysis, restricted Boltzmann machine, topic models

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Authors: W. Hasan, H. Farhat, A. Alhilo, L. Tamimi

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Oil in water (O/W) emulsions are utilized extensively for cooling and lubricating cutting tools during parts machining. A robust Lattice Boltzmann (LBM) thermal-surfactants model, which provides a useful platform for exploring complex emulsions’ characteristics under variety of flow conditions, is used here for the study of the fluid behavior during conventional tools cooling. The transient thermal capabilities of the model are employed for simulating the effects of the flow conditions of O/W emulsions on the cooling of cutting tools. The model results show that the temperature outcome is slightly affected by reversing the direction of upper plate (workpiece). On the other hand, an important increase in effective viscosity is seen which supports better lubrication during the work.

Keywords: hybrid lattice Boltzmann method, Gunstensen model, thermal, surfactant-covered droplet, Marangoni stress

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Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud

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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.

Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch

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Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: W. Hasan, H. Farhat

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A hybrid quasi-steady thermal lattice Boltzmann model was used to study the combined effects of temperature and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain’s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably.

Keywords: lattice Boltzmann method, Gunstensen model, thermal, contact angle, high viscosity ratio

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Authors: Luma Al-Tamimi, Hassan Farhat, Wessam Hasan

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A three-dimensional (3D) hybrid quasi-steady thermal lattice Boltzmann model is developed to couple the effects of surfactant, temperature, interfacial tension, and contact angle. This 3D model is an extended scheme of a previously introduced two-dimensional (2D) hybrid lattice Boltzmann model. The 3D model is used to study the combined multi-physics effects on emulsion systems flowing in rectangular microchannels with and without confinements, where the suspended phase is made of droplets, plugs, or a mixture of both. The simulation results show that emulsion systems with plugs as the suspended phase are more efficient than with droplets, whereas mixed systems that form large plugs through coalescence have even greater efficiency. The 3D contact angle model generates matching results to those of the 2D model, which were validated with experiments. Furthermore, the effects of various confinements on adhering single drop systems are investigated for delineating their influence on the power required for transporting the suspended phase through the channel. It is shown that the deeper the constriction is, the lower the system efficiency. Increasing the surfactant concentration or fluid temperature in a channel with confinement carries a substantial positive effect on oil droplet transportation.

Keywords: lattice Boltzmann method, thermal, contact angle, surfactants, high viscosity ratio, porous media

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Authors: Norjan Jumaa, David Graham

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We present a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. The motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure less Naiver-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test case. Here, we present results for some complex flow problems including two dimensional single and multiple mode Rayleigh-Taylor instability and we obtain good results when comparing with those in the literature. The main focus of our work is related to interactions between aerated or non-aerated waves and structures so we also present results for both high viscosity and low viscosity waves.

Keywords: lattice Boltzmann method, multiphase flows, Rayleigh-Taylor instability, waves

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Authors: Somruay Apichatibutarapong

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The purpose of this study was to address and comparison of the attitudes towards the statistics course for undergraduate students. Data were collected from 120 students in Faculty of Sciences and Technology, Suan Sunandha Rajabhat University who enrolled in the statistics course. The quantitative approach was used to investigate the assessment and comparison of attitudes towards statistics course. It was revealed that the overall attitudes somewhat agree both in pre-test and post-test. In addition, the comparison of students’ attitudes towards the statistic course (Form A) has no difference in the overall attitudes. However, there is statistical significance in all dimensions and overall attitudes towards the statistics course (Form B).

Keywords: statistics attitude, student’s attitude, statistics, attitude test

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Authors: Tobias Horstmann, Thomas Le Garrec, Daniel-Ciprian Mincu, Emmanuel Lévêque

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Despite the efficiency and low dissipation of the stream-collide formulation of the Lattice Boltzmann (LB) algorithm, which is nowadays implemented in many commercial LBM solvers, there are certain situations, e.g. mesh transition, in which a classical finite-volume or finite-difference formulation of the LB algorithm still bear advantages. In this paper, we present an algorithm that combines the node-based streaming of the distribution functions with a second-order finite volume discretization of the advection term of the BGK-LB equation on a uniform D2Q9 lattice. It is shown that such a coupling is possible for a multi-domain approach as long as the overlap, or buffer zone, between two domains, is achieved on at least 2Δx. This also implies that a direct coupling (without buffer zone) of a stream-collide and finite-volume LB algorithm on a single grid is not stable. The critical parameter in the coupling is the CFL number equal to 1 that is imposed by the stream-collide algorithm. Nevertheless, an explicit filtering step on the finite-volume domain can stabilize the solution. In a further investigation, we demonstrate how such a coupling can be used for mesh transition, resulting in an intrinsic conservation of mass over the interface.

Keywords: algorithm coupling, finite volume formulation, grid refinement, Lattice Boltzmann method

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Authors: Muhammad Yousaf, Shoaib Usman

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Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm basedon a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 103 to 106 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was16.66 percent at Ra number 105.

Keywords: Lattice Boltzmann method, natural convection, nusselt number, rayleigh number, roughness

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Authors: Sanjit Kumar Paul, A. A. Mamun, M. R. Amin

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The Linear propagation of the dust-acoustic wave in a dusty plasma consisting of Boltzmann distributed electrons and ions and mobile charge fluctuating positive dust grains has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and its responsible for the formation of the dust-acoustic waves in such a dusty plasma. The basic features of such dust-acoustic waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-acoustic waves predicted in this theoretical investigation.

Keywords: dust acoustic waves, dusty plasma, Boltzmann distributed electrons, charge fluctuation

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Authors: Ganesh Meshram, Gloria Biswal

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In this study, we present the numerical investigation of surface wettability on triangular micropillar surfaces by using a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann method with a D2Q9 model for various interaction parameters of the range varies from -1.40 to -2.50. Initially, simulation of the equilibrium state of a water droplet on a flat surface is considered for various interaction parameters to examine the accuracy of the present numerical model. We then imposed the microscale pillars on the bottom wall of the surface with different heights of the pillars to form the hydrophobic and superhydrophobic surfaces which enable the higher contact angle. The wettability of surfaces is simulated with water droplets of radius 100 lattice units in the domain of 800x800 lattice units. The present study shows that increasing the interaction parameter of the pillared hydrophobic surfaces dramatically reduces the contact area between water droplets and solid walls due to the momentum redirection phenomenon. Contact angles for different values of interaction strength have been validated qualitatively with the analytical results.

Keywords: contact angle, lattice boltzmann method, d2q9 model, pseudo-potential multiphase method, hydrophobic surfaces, wenzel state, cassie-baxter state, wettability

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Authors: Zainab A. Bu Sinnah, David I. Graham

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The Lattice Boltzmann Method has been developed and used to simulate both steady and unsteady fluid flow problems such as turbulent flows, multiphase flow and flows in the vascular system. As an example, the study of blood flow and its properties can give a greater understanding of atherosclerosis and the flow parameters which influence this phenomenon. The blood flow in the vascular system is driven by a pulsating pressure gradient which is produced by the heart. As a very simple model of this, we simulate plane channel flow under periodic forcing. This pulsatile flow is essentially the standard Poiseuille flow except that the flow is driven by the periodic forcing term. Moment boundary conditions, where various moments of the particle distribution function are specified, are applied at solid walls. We used a second-order single relaxation time model and investigated grid convergence using two distinct approaches. In the first approach, we fixed both Reynolds and Womersley numbers and varied relaxation time with grid size. In the second approach, we fixed the Womersley number and relaxation time. The expected second-order convergence was obtained for the second approach. For the first approach, however, the numerical method converged, but not necessarily to the appropriate analytical result. An explanation is given for these observations.

Keywords: Lattice Boltzmann method, single relaxation time, pulsatile flow, moment based boundary condition

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Authors: W. H. Zheng, J. Li, F. J. Hong

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Thin liquid film evaporation in ultrathin nanoporous membranes, which reduce the viscous resistance while still maintaining high capillary pressure and efficient liquid delivery, is a promising thermal management approach for high-power electronic devices cooling. Given the challenges and technical limitations of experimental studies for accurate interface temperature sensing, complex manufacturing process, and short duration of membranes, a dimensionless lattice Boltzmann method capable of restoring thermophysical properties of working fluid is particularly derived. The evaporation of R134a to its pure vapour ambient in nanoporous membranes with the pore diameter of 80nm, thickness of 472nm, and three porosities of 0.25, 0.33 and 0.5 are numerically simulated. The numerical results indicate that the highest heat transfer coefficient is about 1740kW/m²·K; the highest heat flux is about 1.49kW/cm² with only about the wall superheat of 8.59K in the case of porosity equals to 0.5. The dissipated heat flux scaled with porosity because of the increasing effective evaporative area. Additionally, the self-regulation of the shape and curvature of the meniscus under different operating conditions is also observed. This work shows a promising approach to forecast the membrane performance for different geometry and working fluids.

Keywords: high heat flux, ultrathin nanoporous membrane, thin film evaporation, lattice Boltzmann method

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Authors: Seungho Shin, Keunwoo Choi, Ali Akbar, Sukkee Um

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In this study, the nanoscale transport properties and catalyst utilization of vertically aligned carbon nanotube (VACNT) catalyst layers are computationally predicted by the three-dimensional lattice Boltzmann simulation based on the quasi-random nanostructural model in pursuance of fuel cell catalyst performance improvement. A series of catalyst layers are randomly generated with statistical significance at the 95% confidence level to reflect the heterogeneity of the catalyst layer nanostructures. The nanoscale gas transport phenomena inside the catalyst layers are simulated by the D3Q19 (i.e., three-dimensional, 19 velocities) lattice Boltzmann method, and the corresponding mass transport characteristics are mathematically modeled in terms of structural properties. Considering the nanoscale reactant transport phenomena, a transport-based effective catalyst utilization factor is defined and statistically analyzed to determine the structure-transport influence on catalyst utilization. The tortuosity of the reactant mass transport path of VACNT catalyst layers is directly calculated from the streaklines. Subsequently, the corresponding effective mass diffusion coefficient is statistically predicted by applying the pre-estimated tortuosity factors to the Knudsen diffusion coefficient in the VACNT catalyst layers. The statistical estimation results clearly indicate that the morphological structures of VACNT catalyst layers reduce the tortuosity of reactant mass transport path when compared to conventional catalyst layer and significantly improve consequential effective mass diffusion coefficient of VACNT catalyst layer. Furthermore, catalyst utilization of the VACNT catalyst layer is substantially improved by enhanced mass diffusion and electric current paths despite the relatively poor interconnections of the ion transport paths.

Keywords: Lattice Boltzmann method, nano transport phenomena, polymer electrolyte fuel cells, vertically aligned carbon nanotube

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Authors: Jean Yves Trepanier, Sami Ammar, Sagnik Banik

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Lattice Boltzmann Method has been advantageous in simulating complex boundary conditions and solving for fluid flow parameters by streaming and collision processes. This paper includes the study of three different test cases in a confined domain using the method of the Lattice Boltzmann model. 1. An SRT (Single Relaxation Time) approach in the Lattice Boltzmann model is used to simulate Lid Driven Cavity flow for different Reynolds Number (100, 400 and 1000) with a domain aspect ratio of 1, i.e., square cavity. A moment-based boundary condition is used for more accurate results. 2. A Thermal Lattice BGK (Bhatnagar-Gross-Krook) Model is developed for the Rayleigh Benard convection for both test cases - Horizontal and Vertical Temperature difference, considered separately for a Boussinesq incompressible fluid. The Rayleigh number is varied for both the test cases (10^3 ≤ Ra ≤ 10^6) keeping the Prandtl number at 0.71. A stability criteria with a precise forcing scheme is used for a greater level of accuracy. 3. The phase change problem governed by the heat-conduction equation is studied using the enthalpy based Lattice Boltzmann Model with a single iteration for each time step, thus reducing the computational time. A double distribution function approach with D2Q9 (density) model and D2Q5 (temperature) model are used for two different test cases-the conduction dominated melting and the convection dominated melting. The solidification process is also simulated using the enthalpy based method with a single distribution function using the D2Q5 model to provide a better understanding of the heat transport phenomenon. The domain for the test cases has an aspect ratio of 2 with some exceptions for a square cavity. An approximate velocity scale is chosen to ensure that the simulations are within the incompressible regime. Different parameters like velocities, temperature, Nusselt number, etc. are calculated for a comparative study with the existing works of literature. The simulated results demonstrate excellent agreement with the existing benchmark solution within an error limit of ± 0.05 implicates the viability of this method for complex fluid flow problems.

Keywords: BGK, Nusselt, Prandtl, Rayleigh, SRT

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Authors: Oluyinka Ojedokun, S. E. Idemudia

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In Nigeria, statistics is a compulsory course required from all social sciences students as part of their academic training. However, a rising number of social sciences undergraduates usually express statistics anxiety. The prevalence of statistics anxiety among undergraduates in social sciences has created a growing concern for educators and researchers in the higher education institutions, mainly because this statistics anxiety adversely affects their performance in statistics and research methods courses. From a societal perspective it is important to reverse this trend. Although scholars and researchers have highlighted some psychosocial factors that influence statistics anxiety in students but few empirical studies exist on the association between personality traits of NEO five factors and statistics anxiety. It is in the light of this situation that this study was designed to assess the extent to which the personality traits of NEO five factors influence statistics anxiety of students in social sciences courses. The participants were 282 undergraduates in the faculty of social sciences at a state owned public university in Nigeria. The findings demonstrate that the personality traits contributing to statistics anxiety include openness to experience, conscientious, extraversion, and neuroticism. These results imply that statistics anxiety is related to individual differences in personality traits and suggest that certain aspects of statistics anxiety may be relatively stable and resistant to change. An effective and simple method to reduce statistics anxiety among social sciences students is to create awareness of the statistical and methodological requirements of the social sciences courses before commencement of their programmes.

Keywords: personality traits, statistics anxiety, social sciences, students

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Authors: M. Yousaf, S. Usman

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The present study focused on the investigation of the effects of roughness elements on heat transfer during natural convection in a rectangular cavity using a numerical technique. Roughness elements were introduced on the bottom hot wall with a normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic behavior was studied using a computational method based on Lattice Boltzmann method (LBM). Numerical studies were performed for a laminar natural convection in the range of Rayleigh number (Ra) from 103 to 106 for a rectangular cavity of aspect ratio (L/H) 2 with a fluid of Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness elements caused a minimum to the maximum decrease in the heat transfer as 7% to 17% respectively compared to the smooth enclosure. The results are presented for mean Nusselt number (Nu), isotherms, and streamlines.

Keywords: natural convection, Rayleigh number, surface roughness, Nusselt number, Lattice Boltzmann method

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Authors: Annunziata D’Orazio, Arash Karimipour, Iman Moradi

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The size and arrangement of the obstacles in the porous media has an influential effect on the fluid flow and heat transfer, even in the same porosity. Regarding to this, in the present study, several different amounts of obstacles, in both regular and stagger arrangements, in the analogous porosity have been simulated through a channel. In order to compare the effect of stagger and regular arrangements, as well as different quantity of obstacles in the same porosity, on fluid flow and heat transfer. In the present study, the Single Relaxation Time Lattice Boltzmann Method, with Bhatnagar-Gross-Ktook (BGK) approximation and D2Q9 model, is implemented for the numerical simulation. Also, the temperature field is modeled through a Double Distribution Function (DDF) approach. Results are presented in terms of velocity and temperature fields, streamlines, percentage of pressure drop and Nusselt number of the obstacles walls. Also, the correlation between tortuosity and Nusselt number of the obstacles walls, for both regular and staggered arrangements, has been proposed. On the other hand, the results illustrated that by increasing the amount of obstacles, as well as changing their arrangement from regular to staggered, in the same porosity, the rate of tortuosity and Nusselt number of the obstacles walls increased.

Keywords: lattice boltzmann method, heat transfer, porous media, pore-scale, porosity, tortuosity

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Authors: Athmane Bakhta, Sebastien Leclaire, David Vidal, Francois Bertrand, Mohamed Cheriet

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This work presents a new three-dimensional variational model proposed for the simulation of ink seepage into paper sheets at the fiber level. The model, inspired by the Hising model, takes into account a finite volume of ink and describes the system state through gravity, cohesion, and adhesion force interactions. At the mesoscopic scale, the paper substrate is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Besides, a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters, and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.

Keywords: fibrous media, lattice Boltzmann, modelling and simulation, Monte Carlo, variational model

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Authors: Wilma Coetzee

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Statistics lecturers experience that many students who are taking a service course in statistics do not like statistics. Students in these courses tend to struggle and do not perform well. This research takes a look at the student’s perspective, with the aim to determine how to change the teaching of statistics so that students will enjoy it more and perform better. Questionnaires were used to determine the perspectives of first year service statistics students at a South African university. Factors addressed included motivation to study, attitude toward statistics, statistical anxiety, mathematical abilities and tendency to procrastinate. Logistic regression was used to determine what contributes to students performing badly in statistics. The results show that the factors that contribute the most to students performing badly are: statistical anxiety, not being motivated and having had mathematical literacy instead of mathematics in secondary school. Two open ended questions were included in the questionnaire: 'I will enjoy statistics more if…' and 'I will perform better in statistics if…'. The answers to these questions were analyzed using qualitative methods. Frequent themes were identified for each of the questions. A simulation study incorporating bootstrapping was done to determine the saturation of the themes. The majority of the students indicated that they would perform better in statistics if they studied more, managed their time better, had a flare for mathematics and if the lecturer was able to explain difficult concepts better. They also want more active learning. To ensure that students enjoy statistics more, they want an active learning experience. They want fun activities, more interaction with the lecturer and with one another, more computer based problems, and more challenges. They want a better understanding of the subject, want to understand the relevance of statistics to their future career and want excellent lecturers. These findings can be used to direct the improvement of the tuition of statistics.

Keywords: active learning, performance in statistics, statistical anxiety, statistics education

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Authors: Nastaran Ahmadpour Samani, Shahram Talebi

Abstract:

Added mass is an important quantity in analysis of the motion of a submerged object ,which can be calculated by solving the equation of potential flow around the object . Here, we consider systems in which a square object is submerged in a channel of fluid and moves parallel to the wall. The corresponding added mass at a given distance from the wall d and for the object size s (which is the side of square object) is calculated via lattice Blotzmann simulation . By changing d and s separately, their effect on the added mass is studied systematically. The simulation results reveal that for the systems in which d > 4s, the distance does not influence the added mass any more. The added mass increases when the object approaches the wall and reaches its maximum value as it moves on the wall (d -- > 0). In this case, the added mass is about 73% larger than which of the case d=4s. In addition, it is observed that the added mass increases by increasing of the object size s and vice versa.

Keywords: Lattice Boltzmann simulation , added mass, square, variable size

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