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This article addresses the abilities and limitations of the Lattice Boltzmann (LB) method in solving advection-dominated mass transport problems. Several schemes of the LB method, including D2Q4, D2Q5, and D2Q9, were assessed in the simulation of two-dimensional advection-dispersion equations. The concepts of Single Relaxation Time (SRT), Multiple Relaxation Time (MRT), and linear and quadratic Equilibrium Distribution Functions (EDF) were taken into account. The results of LB models were compared to the well-known Finite Difference (FD) solutions, including Explicit Finite Difference (EFD) and Crank-Nicolson (CN) methods. All LB models are more accurate than the aforementioned FD schemes. The results also indicate the high potency of D2Q5 SRT and D2Q9 SRT in describing advection-controlled mass transfer problems. The numerical artificial oscillations are observed when the Grid Peclet Number (GPN) is greater than 10, 25, 20, 25, and 10 regarding D2Q4 SRT, D2Q5 SRT, D2Q5 MRT, D2Q9 SRT, and D2Q9 MRT, respectively, while the corresponding GPN values obtained for the EFD and CN methods were 2 and 5, respectively. Finally, several LB models were used to satisfactorily solve a coupled system of groundwater and solute transport equations. In terms of computational time, all LB models are much faster than CN method.

The numerical modeling of transverse laminar flow past a new type of hollow-fiber membranes with external profiling has been performed. A model system of parallel fibers with symmetrical parallel protrusion obstacles or grooves is considered. The absorption of point particles (solute or gas molecules) from a laminar transverse flow of a viscous incompressible liquid (gas) is calculated for a row of fibers, and the dependences of the efficiency of retention of particles by fibers on the Peclet (Pe), Reynolds (Re), and Schmidt (Sc) numbers and on the distance between neighbor fibers in a row are determined. The flow velocity and concentration fields are calculated by numerical solution of the Navier–Stokes equations and the convective diffusion equation in a wide range of Peclet numbers Pe = 0.1 − 105 for Sc = 1, 10, 1000 and Re ≤ 100.

Purpose – The purpose of this paper is to present a simple meshless solution method for challenging engineering problems such as those with high wave numbers or convection-diffusion ones with high Peclet number. The method uses a set of residual-free bases in a local form. Design/methodology/approach – The residual-free bases, called here as exponential basis functions, are found so that they satisfy the governing equations within each subdomain. The compatibility between the subdomains is weakly satisfied by enforcing the local approximation of the main state variables pass through the data at nodes surrounding the central node of the subdomain. The central state variable is first recovered from the approximation and then re-assigned to the central node to construct the associated equation. This leads to the least compatibility required in the solution, e.g. C0 continuity in Laplace problems. Findings – The authors shall show that one can solve a variety of problems with regular and irregular point distribution with high convergence rate. The authors demonstrate that this is impossible to achieve using finite element method. Problems with Laplace and Helmholtz operators as well as elasto-static problems are solved to demonstrate the effectiveness of the method. A convection-diffusion problem with high Peclet number and problems with high wave numbers are among the examples. In all cases, results with high rate of convergence are obtained with moderate number of nodes per cloud. Originality/value – The paper presents a simple meshless method which not only is capable of solving a variety of challenging engineering problems but also yields results with high convergence rate.

This paper aims to understand the hydrothermal sites near the Yonaguni Knoll IV in the Okinawa Trough, and to develop new techniques to study fluid flow patterns for hydrothermal systems and their impact on ore deposits on the seafloor. Hydraulic parameters are important for hydrothermal system studies, but in-situ measurements of fluid migration rates are difficult. Hydrothermal fluids can reach several hundred degrees Celsius, temperatures high enough to perturb hydrothermal fields and pore water migration patterns. Using in-situ temperature data as constraints, we model and synthesize 1-D and 3-D cylindrical hydrothermal models to fit the spatial variations of observed temperature fields. The 1-D modeling uses Péclet number analysis along the conduit. We also construct a 3-D cylindrical model to estimate the temperature and fluid velocity fields using a finite element software. All domains are set to be porous to allow the fluid to flow. The simulation is run until it reaches a semi steadystate solution, allowing both the temperature and velocity fields to stabilize. Results show the dimension of the thermal anomaly zone is likely controlled by advective heat transfer along the vent due to upward fluid flow. We estimate a Péclet number of -1.6, and the vertical fluid flow velocities at these sites are high, approximately 10^(-6) m s^(-1), that is, about 100 m yr^(-1). This is a spatially averaged estimate over tens to hundreds of meters and does not take into account finer-scale venting, which may be very heterogeneous. The results of this work may help estimate the quantity of metal elements transported through pore fluid migration at modern hydrothermal sites.

Nanodroplets on a solid surface (i.e., surface nanodroplets) have practical implications for high-throughput chemical and biological analysis, lubrications, laboratory-on-chip devices, and near-field imaging techniques. Oil nanodroplets can be produced on a solid–liquid interface in a simple step of solvent exchange in which a good solvent of oil is displaced by a poor solvent. In this work, we experimentally and theoretically investigate the formation of nanodroplets by the solvent exchange process under well-controlled flow conditions. We find significant effects from the flow rate and the flow geometry on the droplet size. We develop a theoretical framework to account for these effects. The main idea is that the droplet nuclei are exposed to an oil oversaturation pulse during the exchange process. The analysis shows that the volume of the nanodroplets increases with the Peclet numberPeof the flow as ∝Pe 3/4, which is in good agreement with our experimental results. In addition, at fixed flow rate and thus fixed Peclet number, larger and less homogeneously distributed droplets formed at less-narrow channels, due to convection effects originating from the density difference between the two solutions of the solvent exchange. The understanding from this work provides valuable guidelines for producing surface nanodroplets with desired sizes by controlling the flow conditions.

Modeling of multimedia environmental issues is extremely complex due to the intricacy of the systems with the consideration of many factors. In this study, an improved environmental multimedia modeling is developed and a number of testing problems related to it are examined and compared with each other with standard numerical and analytical methodologies. The results indicate the flux output of new model is lesser in the unsaturated zone and groundwater zone compared with the traditional environmental multimedia model. Furthermore, about 90% of the total benzene flux was distributed to the air zone from the landfill sources and only 10% of the total flux emitted into the unsaturated, groundwater zones in non-uniform conditions. This paper also includes functions of model sensitivity analysis to optimize model parameters such as Peclet number (Pe). The analyses results show that the Pe can be considered as deterministic input variables for transport output. The oscillatory behavior is eliminated with the Pe decreased. In addition, the numerical methods are more accurate than analytical methods with the Pe increased. In conclusion, the improved environmental multimedia model system and its sensitivity analysis can be used to address the complex fate and transport of the pollutants in multimedia environments and then help to manage the environmental impacts.

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature.

The intention of this study is to carry out a numerical investigation of time-dependent magneto-hydro-dynamics (MHD) Eyring–Powell liquid by taking a moving/static wedge with Darcy-Forchheimer relation. Thermal radiation was taken into account for upcoming solar radiation, and the idea of bioconvection is also considered for regulating the unsystematic exertion of floating nanoparticles. The novel idea of this work was to stabilized nanoparticles through the bioconvection phenomena. Brownian motion and thermophoresis effects are combined in the most current revision of the nanofluid model. Fluid viscosity and thermal conductivity that depend on temperature are predominant. The extremely nonlinear system of equations comprising partial differential equations (PDEs) with the boundary conditions are converted into ordinary differential equations (ODEs) through an appropriate suitable approach. The reformed equations are then operated numerically with the use of the well-known Lobatto IIIa formula. The variations of different variables on velocity, concentration, temperature and motile microorganism graphs are discussed as well as force friction, the Nusselt, Sherwood, and the motile density organism numbers. It is observed that Forchheimer number Fr decline the velocity field in the case of static and moving wedge. Furthermore, the motile density profiles are deprecated by higher values of the bio convective Lewis number and Peclet number. Current results have been related to the literature indicated aforementioned and are found to be great achievement.

Abstract In this paper a numerical entropy generation analysis on confined slot impinging jets made up of a totally filled configuration of metal foam in mixed convection is presented. A two-dimensional domain is assumed and several Peclet numbers (equal to 350, 750, 1500) are considered. Rayleigh numbers is imposed equal to 30000. The employed working fluids are pure water or Al 2 O 3 /water based nanofluids. The nanoparticle volume concentrations are in a range from 0% to 4% and the nanoparticle diameter is varied in a range from 20 nm to 80nm. The target surface is characterized by a constant temperature, estimated starting to the value of Rayleigh number. The distance of the target surface is five times greater than the slot jet width. The thermal and fluid dynamic properties of nanofluids are evaluated by a single-phase model method. The model of local thermal non equilibrium (LTNE) is considere in order to simulate the behavior of the metal foam characterized by a number of pores per inch (PPI) equal to 5, 10, 20, 40 and a porosity around 0.90. The data in terms of total global entropy generation related to the thermal and viscous effects are given Results show increasing values of the total entropy generation for increasing values of Peclet number and nanoparticle concentration. This behaviour is more evident at higher Peclet number values. In addition, the total entropy generation increases with the increase of PPI in corresponding to the same porosity value.

Background: The improvement of the thermal conductivity of nanofluids is practical for different processes such as drug delivery, manufacturing of crystals, polymer processing, food and drink, cancer treatment, oil and gas, paper making and for many more. The bioconvection phenomenon has engrossed the attention of numerous researchers for its many applications in biotechnology, mechanical and electrical engineering. Bioconvection nanofluids are more prominent in the fields of biomedicine, pharmacy, nanodrug delivery, biomedical, automotive cooling and the military. Purpose: The major purpose of the current work was to determine the numerical and statistical analysis of a novel thermal radiation and exponential space-based heat source on the bioconvective flow of a pseudoplastic 3D nanofluid past a bidirectional stretched Riga surface. The behavior of the Arrhenius activation energy (AAE) and thermal radiation are also disclosed. Methodology: Suitable similarity transformations were used to transmute the partial differential equations of the flow-modeled phenomena into the structure of ordinary differential ones. The numerical solutions for the renewed set of ODEs were tackled by the bvp4c shooting algorithm built-in MATLAB software. Furthermore, the statistical analysis was computed by applying response surface methodology (RSM). Research implications: The numerical analysis is valid for the incompressible three-dimensional, magnetized flow of a pseudoplastic bioconvection nanofluid through a bidirectional surface with Riga plate aspects in the occurrence of activation energy. Social implications: The flow across three dimensions has quite important implementations in various fields, for example, polymer production, material production technology, the manufacturing of nano-biopolymer computer graphics, industry, powered engineering, aeroplane configurations, etc. The current analysis is more applicable in nanotechnology. Results: The consequences of flow control parameters over flow profiles were studied and explained under the graphic structures. Numerical outcomes were computed and discussed in detail. From the results, it was noted that the velocity field was increased via a larger mixed convection parameter. The temperature distribution was boosted via the thermal Biot number. The concentration of nanoparticles declined via the greater Lewis number. Furthermore, the motile microorganisms field was reduced via the Peclet number. Originality: Until now, no investigation has been recognized to examine the consequences of the bioconvection flow of three-dimensional pseudoplastic nanofluids past a Riga plate containing motile microorganisms utilizing the shooting method called bvp4c. Conclusions: From the results, it was concluded that nanofluids are more helpful for heat transfer increments. Furthermore, from the experimental design observed, the response declined via the thermophoresis parameter, which was significant from the ANOVA observed model.