Brownian Motion Forces Research Articles

Chemically reactive flow of non‐Newtonian nano‐liquid over different magnetized and slippery inclined surfaces

AbstractFlow behavior of nonlinear materials over magnetized and contracting and extending inclined surfaces is described specifically by Jeffery–Hamel type flow, where the flow is caused by a convergent/divergent channel with the appearance of a source or sink. The role of the conversion of more than one species to more than every other species is significant in the flow conduct of such types of nonlinear materials. However, for the desired higher thermal conductivity, the Brownian motion and thermophoretic forces are incorporated in this particular work. Moreover, the impacts of first‐order chemical reaction and slips on the velocity, thermal, and concentration distributions, respectively presented to portray the importance of the entire study. The liquid motion on such surfaces is further addressed with the involvement of viscous dissipation and solar radiation. The newly mathematically formulated work is then approximated via one of the built‐in approaches based on collocation methods. The key findings are determined through graphical illustration. The physically interesting growing velocity of the liquid motion is noticed with variation in the slippery motion parameter during the convergent channel case. The opposite trend is noted for the divergent channel case. Furthermore, the Brownian motion‐related parameter escalated the temperature of the liquid, and the reverse status of the liquid concentration is determined with variation in the same parameter. The mass fraction is determined in a declining conduct with the ascending variation in first‐order chemical reaction factor. At the end of the work, a comparison with existing results is provided with excellent agreement.

Direct numerical simulation of supersonic nanoparticles flow in free-molecule regime using the angular coefficient method

We employ molecular flow methods to numerically simulate the supersonic nanoparticles flow in free-molecule regime. To streamline the computational complexity, interaction forces between the gas and solid particles are disregarded. We first develop a discrete phase model (DPM) method that integrates the non-rigid body collision model, enabling an accurate simulation of nanoparticle diffusion under the influence of the drag force and Brownian motion force. The nanoparticles considered in this study have sizes below 10 nm, and the accuracy of the DPM method is verified by comparing its results with experimental data. Subsequently, we theoretically and numerically investigate the transmission probability and number density of N2 molecules flowing through two-dimensional (2D) channels and three-dimensional (3D) tubes by using the angular coefficient (AC) method and the direct simulation Monte Carlo (DSMC) method. The findings indicate that as the diameter of the nanoparticle (dp) decreases to 1 nm, the diffusion coefficient (D) and the root mean square displacement (x) of nanoparticles approach the N2 molecules. The microscopic velocity of most N2 molecules falls within the range of 62–1400 m/s, and the macroscopic velocity of N2 flow falls within the range of Ma = 1.28–1.35. In contrast to the DSMC method, the AC method exhibits enhanced accuracy even with a reduced number of grids and obviates the process for large-scale sampling. Additionally, the solution time required by the AC method is approximately 1/10 and 1/13–1/32 of the DSMC method in 3D cylindrical tubes and 2D channels, respectively. Moreover, the AC method demonstrates superior adaptability when dealing with complex geometries.

Comprehensive Computational Study on the Influences of Particle Size and Relative Humidity on Aerosol/Droplet Transmission in a Ventilated Room Under Stationary and Dynamic Conditions

Given the concerns surrounding the possibility of crosscontamination caused by the airborne transmission of respiratory aerosols (> 5 μm in diameter) and droplets (> 5 μm in diameter) containing infectious viruses, there is a great need for simulations that reliably characterize the behaviour of these particles in real‐world scenarios. This study performs a comprehensive transient CFD analysis to investigate the transmission of virus‐carrying aerosols and droplets released through coughing by a mobile patient within a typical room equipped with a ventilation system. This computational study elaborately examines how particle size and relative humidity impact the dispersion of aerosols and droplets carrying virus in both mobile and stationary conditions of patients. To enhance the accuracy of this study, effective factors such as evaporation of liquid content within aerosols and droplets and random distribution of the particles, along with considerations for buoyancy, drag, lift, Brownian motion, and gravitational forces, are taken into account. To investigate the influence of aerosol and droplet size, this study considers uniform size distributions of 1, 10, and 100 μm in diameter, comprising 98.2% liquid water and 1.8% solid content. Additionally, different relative humidity levels, 0%, 50%, and 90%, are incorporated to indicate their impact on the dispersion pattern and residence time of the particles in both stationary and dynamic scenarios. According to the results, high levels of relative humidity and individuals’ movement significantly affect the turbulence intensity, airflow pattern, travelling distance, residence time and trajectory of particles, air pressure, and density distributions in such environments.

Thermal enhancement, thermophoretic diffusion, and Brownian motion impacts on MHD micropolar nanofluid over an inclined surface: Numerical simulation

The majority of liquids are undesirable for engineering due to their low heat conductivity. Scientists and researchers are developing nanofluids, which are made of nanoparticles (NPs) scattered in a base fluid, to boost the capacity for heat transfer in a variety of industries, including molten metals, pharmaceuticals, and computers. In this study, the magneto-hydrodynamics (MHD) flow of a micropolar nanofluid model with particle microstructure and inertial properties is investigated. A micropolar nanofluid’s flow is examined concerning the effects of a magnetic field. Aspects of heat and mass transfer are investigated using thermal radiation, thermophoresis, Brownian motion, and double diffusion theory toward an inclined surface. With the right level of similarity, the process converts partial differential equations emerging in nanofluidic systems into nonlinear differential equation systems. The FDM finite difference approach (FDM) (Lobatto IIIA) is used for the nonlinear nanofluid issue with the precision of order 4–5 and is implemented using a variety of collocation locations. The strength of Lobatto IIIA is its effectiveness in handling coupled differential equations that are extremely nonlinear. The higher-order differential equations are converted into a first-order method utilizing the boundary value dilemma (bvp4c) solver, which is part of the MATLAB software package, to computationally analyze the simplified mathematical model. The data obtained demonstrated a high degree of accuracy and symmetry when measured against previously published studies. Numerous variables’ effects on fluid flow are examined and graphically displayed with obtained numerical data. The results show that the temperature profile behaves in a way that is consistent with increasing thermophoresis and Brownian motion forces. This work provides insights into practical applications such as nanofluidic, energy conservation, friction reduction, and power generation. However, the work makes a significant point that the flow of a micropolar nanofluid including NPs can be regulated by appropriately modifying the thermophoresis parameter and Brownian motion parameter.

Instability analysis of vibrated thermo-convection in Casson nanofluid suspension

This work is motivated by the importance of vertical vibration in nanofluids suspension, because of its wide applications in heat exchangers from one fluid to another, controlling the mixing in microvolumes, pharmaceutical industry, and engineering. The current study analyzes the effects of high-frequency vertical vibration on a horizontal Casson nanofluid layer heated from below saturated between rigid-rigid, rigid-free, and free-free boundary conditions. Field equations are derived by using time-average method, which describes the vibrational thermo-convection. These field equations are solved by utilizing linear stability analysis and Galerkin technique to obtain the thermal stability curve. By using this curve, the impacts of vertical vibration and physical governing factors on temperature profile are discussed. High-frequency vertical vibration is observed to have a stabilizing effect on Casson nanofluid suspension, thereby reducing thermo-convective heat transfer from one fluid to another. Stability threshold of vibrated suspension is increased approximately as [Formula: see text] and [Formula: see text] when [Formula: see text] and [Formula: see text], respectively. The significance of Brownian motion and thermophoretic force on convective heat transfer with vertical vibration is discussed. The resisting nature of Casson nanofluid on vibrational convective heat transfer is also tabulated.

Magneto-Convection in Casson Nanofluids with Three Different Boundaries

This paper is centered on the numerical and analytical solution of a non-Newtonian Casson nanofluid flow problem in the presence of vertical magnetic field. Brownian motion and thermophoretic forces are introduced due to the addition of nanoparticles and; the magnetic field adds an extra Lorentz’s force term along with Maxwell’s equations. Using Normal mode technique, the system of PDEs with the corresponding boundary conditions is reduced to a system of ODEs. The Galerkin-type weighted residual method is used to get a numerical solution for the formulated differential system. Numerical simulation is carried out to make the investigation helpful for practical applications like nano-drug delivery systems as in clinical and medical research, magnets are extremely important to create three-dimensional images of anatomical and diagnostic importance from nuclear magnetic resonance signals. Comparisons of the numerical results with previously published results are made and fine agreements are noted for the considered values of the parameters. The impact of magnetic field, Casson parameter and nanoparticle parameters are discussed for different types of boundary conditions (free–free, rigid-free and rigid–rigid). The system is found to be the most stable for more realistic rigid–rigid boundaries out of three different boundaries. For the purpose of numerical computations, blood has been considered as the Casson nanofluid. The novelty of the work lies in the fact that the strong stabilizing influence of Lorentz force on blood-based Casson nanofluid enables the red blood cells to pass through the blood in a more streamlined fashion which may play a significant role in human health, more specifically in the cardiovascular system. Further, although the Casson parameter hastens the onset of convection yet Casson fluids are more stable as compared to regular fluids.

Homotopy analysis of mixed convection flow of a magnetized viscoelastic nanofluid from a stretching surface in non-Darcy porous media with revised Fourier and Fickian approaches

This article addresses theoretically the mixed convection hydromagnetic flow of electrically conducting viscoelastic nanofluid from a vertical permeable stretching sheet in a non-Darcy porous medium with Cattaneo–Christov double-diffusion model to evaluate the heat transfer phenomena in steady boundary layer flow on a stretchable surface. In this regard, thermal and solutal hyperbolic wave relaxation effects are included for non-Fourier and non-Fickian models. Heat absorption is also included in the analysis. The Buongiorno two-component nanoscale model is adopted for simulating Brownian motion and thermophoretic body force effects. A non-Darcy drag force model is employed for the porous medium and the Reiner–Rivlin second-grade model for non-Newtonian characteristics. Via appropriate dimensionless similarity variables, the nonlinear dimensional partial differential conservation equations for momentum, energy and concentration with associated boundary conditions are rendered into a nonlinear dimensionless ordinary differential boundary value problem. The homotopy analysis method (HAM) is utilized to solve the boundary value problem and the impact of emerging parameters including thermal relaxation parameters, non-Newtonian material parameter, Darcy permeability parameter, porous inertial parameter and Hartmann magnetic number on the momentum, heat and mass transfer characteristics are visualized graphically and in tables. A 30th-order approximation for HAM is shown to produce sufficient accuracy for the velocity and temperature fields and a 40th-order estimates is adequate for the concentration field. It is observed that increasing the magnitude of thermal and solutal relaxation parameters has the opposite effect on the thermal and concentration distributions. The novelty of the work is the simultaneous inclusion of multiple effects (non-Fourier and non-Fickian thermal relaxation hyperbolic wave models, non-Darcy drag effects and heat generation/absorption) which are relevant to rheological nanomaterials processing and also the deployment of homotopy analysis as an alternative to conventional numerical methods such as finite differences, finite elements and MATLAB solvers. The study is relevant to the manufacture of electro-conductive polymers (ECPs) and smart (functional) magnetic nano-liquids.

Pore-scale analysis of two-phase nanofluid flow and heat transfer in open-cell metal foams considering Brownian motion

Simultaneous use of porous media and nanofluids will increase the convective heat transfer multiple times compared to non-porous and pure fluid conditions. Heat transfer and flow transport of nanofluids inside porous media are usually simulated in large-scale with average properties, which are typically highly uncertain. Pore-scale simulation as an alternative approach can capture the characteristics of flow and heat transfer more accurately. Only few studies have been conducted to study nanofluid flow through porous media in pore-scale, and most of them employed single-phase approach without focus on different affective forces. This paper uses a pore-scale approach to investigate the flow characteristics and convective heat transfer of two-phase nanofluid flow in open-cell metal foams (OCMFs). Simulation of fluid flow and heat transfer is achieved by Buongiorno’s model. Therefore, a computational code through the OpenFOAM library that operates by a direct numerical simulation (DNS) approach and the finite volume method (FVM) is used. The momentum, energy, continuity, and nanoparticle distribution equations are discretized, and the SIMPLE algorithm is utilized for pressure and velocity coupling. In the present study, three OCMFs with a constant porosity (0.86) and various pore densities are investigated. Also, variations of pressure gradient, Nusselt number, and Darcy velocity are investigated as a function of pore density (as a geometric parameter), nanoparticle diameter, concentration, and Brownian motion force. The results indicate that the Brownian force enhances the heat transfer in OCMFs from 2% by up to 14% for the nanofluid flowing with 3% nanoparticle concentration. Also, increasing the diameter of nanoparticles reduces the Darcy velocity and heat transfer by up to 4%. On the other hand, increasing particle concentration from 3% to 5%, increases heat transfer by up to 10% and reduces the Darcy velocity by up to 9%. Finally, doubling the pore density demonstrates the complex behavior of the flow patterns, in which the heat transfer increases by up to 30% and permeability and velocity are reduced by up to 70%.

Significance of bio-convection, MHD, thermal radiation and activation energy across Prandtl nanofluid flow: A case of stretching cylinder

The current research investigates the effects of Brownian motion, thermophoresis, and multi buoyancy forces on MHD Prandtl fluid as it flows through a stretched cylinder with convective boundary conditions. Linear thermal conductivity is included in the energy equation's development. The nanofluid flows are important in cooling systems, modern nano-technology, electronic parts and heat exchangers. The primary objective of this research is to enhance heat transportation. The problem consists of nonlinear PDEs and these equations are transformed into ODEs by incorporating suitable similarity transformations. The shooting strategy is used to solve the problem numerically after converting the non-dimensional ordinary differential equations to a system of first-order ODEs. A comparison is made between the MATLAB-generated findings and those that have already been published. The numerical results of various parameters have been systematically organized into tabular representations. Graphs show how significant parameters affect the given velocity, temperature, concentration, and motile microorganism measurements. When the buoyancy ratio and bio-convective Rayleigh number increase, the velocity profile drops; however, the temperature profile shows increasing behavior for the thermal radiation parameter. The concentration profiles are enhanced for the higher inputs in curvature parameter, magnetic parameter, and activation parameter while the density of motile microbes' decay for enhanced inputs of bio-convective Lewis number.

Homotopic solutions of an unsteady magnetohydrodynamic flow of Casson nanofluid flow by a vertical cylinder with Brownian and viscous dissipation effects

The present study investigates the mathematical and computational framework of an unsteady magnetohydrodynamic (MHD) Casson nanofluid flow subjected to convective heat transfer enhancement in a vertically moving cylinder. The two main important aspects of nanosized particles movement in nanofluids are the Brownian motion and thermophoresis force which have substantial impacts on the thermophysical characteristics of nanofluids. The mathematical formulation regarding the assumed diversified and control parameters are modeled in constitutive partial differential equations (PDEs). The boundary layer theory is used to reduce the nonlinearity of subsequent dimensionless partial differential equations. The homotopic solution of these dimensionless PDEs is obtained via an analytical algorithm. The impact of sundry influential physical parameters comprises flow and heat transfer individualities. Computational results of the homotopic scheme toward several governing parameters of interest, such as the skin friction, heat, and mass transfer at the diverse condition and dependency of different parameters are offered by means of plotted graphs and elaborated.

Magnetization of nanofluid due to convectively heated bended surface with space-dependent heat generation

This research mainly focuses to study hydrothermal characteristics of magnetohydrodynamic nanofluid flow over a slippery permeable bended surface which is rotated in a circular cross-section with radius [Formula: see text]. In this nanofluid model, a nanoparticle concentration gradient is taken due to Brownian motion and thermophoretic force. Thermal conductivity and viscosity of nanofluid are a function of the local volume fraction of the nanoparticle. The system includes the most important parameters such as viscous dissipation and internal heat absorption (or) generation. For the supposed flow governing equations are formulated and then converted to a nonlinear system and resulted system is numerically evaluated with bvp4c in Matlab package. Multiple streamlines and three-dimensional graphics are provided to improve the results. The results obtained show that as the magnetic parameter values increase, the magnitude of the velocity field decreases and the pressure in the boundary layer decreases. Further, the parameters Brownian motion and thermophoresis increase the fluid temperature tends and the concentration should increase as the value of the slip parameter increases.

Buoyancy driven non-Newtonian Prandtl-Eyring nanofluid flow in Darcy-Forchheimer porous medium over inclined non-linear expanding sheet with double stratification

In the existence of mixed convection and double stratification, the 2D, viscous, incompressible, steady, laminar boundary layer flow of Prandtl-Eyring nanofluid over the inclined non-linear expanding sheet in Darcy-Forchheimer porous medium is scrutinized. To analyze the impacts of Brownian motion and thermophoretic force on diffusion of nanoparticles Buongiorno model has been utilized. Flow governing equations are non-linear, higher order, coupled PDEs with no slip boundary condition, which are transforming into coupled, non-linear, higher order ODEs via suitable transformations. Obtained ODEs are solved using MATLAB bvp4c function. The impacts of flow governing parameters on flow associated distributions are acknowledged through graphs. In limiting sense, to check the credibility of numerical method, present results are compared with previously published data. The analysis reveals that fluid velocity displays an enhancement with first Prandtl-Eyring parameter α and a diminution with second Prandtl-Eyring parameter β. Whereas, due to presence of both stratifications (thermal and solutal) there is a decline in fluid velocity. Also, nanofluid temperature is augmented with Forchheimer number and inclination angle γ, whereas it declines with α and thermal stratification parameter . Nanoparticle concentration escalates with γ, whereas it drops with concentration stratification parameter . For larger thermophoresis parameter Nt, the nanoparticle concentration achieves higher level than its initial value in mid-region of boundary layer, while near surface it assumes lower value. The surface drag-force elevates with β and Nt. Whereas surface cooling rate enhances with and it weakens with .

Effect of Nonlinear Thermal Radiation on Flow of Williamson Nanofluid in a Vertical Porous Channel with Heat Source or Sink by Using Adomian Decomposition Method

The study examines the entropy generation in the Williamson nanofluid flowing in a vertical porous channel exposed to nonlinear thermal radiation and heat source or sink. Constant temperature and fixed nanoparticle concentration are maintained at the boundaries of the channel. Governing equations are derived by applying the conservation laws incorporating the brownian motion and thermophoretic force impacts of nanofluids utilizing Buongiorno’s model. These equations are non dimensionalised by choosing suitable dimensionless variables. The governing simultaneous equations are tackled by implementing adomian decomposition technique for velocity, tempearture, dimensionless shear stress heat transfer rate. The findings of the study are analysed through graphs. The major findings of the study are porous parameter reduces velocity because of resistance to the flow and enhances temperature. Thermal radiation parameter reduces both velocity and temperature fields. Williamson parameter enhances the velocity field and reduces the temperature to a very small extent. These results are also corresponds with skin friction and Nusselt number graphs. Entropy generation in the considered flow system can be minimized by increasing Williamson number.

Combined Newton–Raphson and Streamlines-Upwind Petrov–Galerkin iterations for nanoparticles transport in buoyancy-driven flow

The present study deals with the finite element discretization of nanofluid convective transport in an enclosure with variable properties. We study the Buongiorno model, which couples the Navier–Stokes equations for the base fluid, an advective-diffusion equation for the heat transfer, and an advection-dominated nanoparticle fraction concentration subject to thermophoresis and Brownian motion forces. We develop an iterative numerical scheme that combines Newton’s method (dedicated to the resolution of the momentum and energy equations) with the transport equation that governs the nanoparticles concentration in the enclosure. We show that the Stream-Upwind Petrov–Galerkin regularization approach is required to solve properly the transport equation in Buongiorno’s model, in the Finite Element framework. Indeed, we formulate this ill-posed equation as a variational problem under mean value constraint. Numerical analysis and computations are reported to show the effectiveness of our proposed numerical approach in its ability to provide reasonably good agreement with the experimental results available in the literature.

Irreversibility and hydrothermal analysis of the MWCNTs/GNPs-based nanofluids for electronics cooling applications of the pin-fin heat sinks: Multiphase Eulerian-Lagrangian modeling

Identifying optimal pin-fin configurations is essential to analyze the full potential of utilizing nanofluids in pin-fin heat sinks for electronics cooling applications. Therefore, the present study aimed to investigate the entropy generation and hydrothermal characteristics of water-based MWCNT (Multiwalled carbon nanotubes) and MWCNT/GNP (Multiwalled carbon nanotubes/graphene nanoplatelets) nanofluids in a heat sink equipped with fins of different configurations. The forced convection of the nanofluid was simulated through the multiphase Eulerian-Lagrangian model (discrete-phase model) by including the influence of slip mechanisms (Brownian motion, thermophoresis, Saffman lift and drag forces, pressure forces, virtual mass, and gravity) and the interphase nanolayering effect. Results showed that the performance of the MWCNT and MWCNT/GNP nanofluids was the highest in the triangular pin-fin heat sink, followed by rhombus and hydrofoil pin-fin heat sinks. The streamlined shape along with the large lateral and small stream-wise interspacing between the hydrofoil and rhombus fins hindered the effective coolant distribution across the heat sinks, thereby deteriorating their heat-dissipation capacity. However, the performance evaluation criteria results of the rhombus pin-fin heat sink outperformed the other pin-fin configurations due to the lower pressure drop.

Thermal efficiency of eco-friendly MXene based nanofluid for performance enhancement of a pin-fin heat sink: Experimental and numerical analyses

MXenes are an eco-friendly innovative type of graphene-like nanomaterials and are proven to exhibit remarkable thermal, electrical, mechanical and optical properties. This study is aimed at evaluating the thermal efficiency of novel Ti3C2Tx MXene-based nanofluid in a pin-fin heat sink was via experimental and numerical analyses. The aqueous-based 2D Ti3C2Tx MXene nanofluid was synthesised in a two-step process, followed by their characterisation and experimental testing. For the numerical analysis, the forced convection of the nanofluid was simulated through multiphase Lagrangian–Eulerian approximation by incorporating the interphase interactions of Brownian motion, thermophoresis, drag and Saffman lift forces, gravity, virtual mass and pressure gradient-induced forces. The thermal performance of the MXene nanofluids was assessed in terms of log mean temperature difference, average Nusselt number, local temperature and local Nusselt number distribution at the base of the heat sink and thermal contours. Their fluid flow characteristics were probed by analysing the coolant pumping power, flow streamlines distribution and performance evaluation criteria of the heat sink. Results demonstrated that utilising the MXene-based coolant resulted in a significant average Nusselt number enhancement at the expense of a small increase in coolant pumping power. Maximum improvements of 29.8 and 40.5% in the average Nusselt number were observed for nanoparticle concentrations of 0.013 vol% and 0.027 vol% respectively.

Numerical study on stability of diamagnetic levitation of a single-layer graphene sheet

Strong diamagnetic interactions enable carbon materials such as graphite plates and organisms to levitate stably in the atmosphere without active control. Although the repulsive force caused by diamagnetism becomes weak as the size of the object decreases, the necessary force against gravity also decreases. Thus, a nanocarbon material such as a single-layer graphene sheet may be levitated by the diamagnetic force. However, the stability worsens as the dimensions of the sheet decrease. The dominant factors affecting the stability of the diamagnetic levitation of nanomaterials are the Brownian motion and attractive surface forces such as the Casimir interactions. We calculate the potential energy of a square graphene sheet in two states, vertical and horizontal to a magnet, and considered the transition rate between these states based on Kramers’ theory for the escape problem. Furthermore, the stiction of a single-layer graphene sheet onto a substrate caused by the Casimir force, which discontinues the levitation, is examined.

Flow of nanofluid towards a Riga surface with heat and mass transfer under the effects of activation energy and thermal radiation

This paper numerically simulates the nanofluid flow over a thermally expanding Riga plate. Buongiorno model for nanofluid is employed to investigate the contribution of Brownian motion and thermophoretic force on the nanoflow. Magnetohydrodynamics (MHD) of viscous nanofluid through a porous medium is characterized with the help of Darcy–Forchheimer’s model. In addition, the simultaneous effects of activation energy and chemical reaction have been incorporated. Moreover, highly nonlinear coupled differential equations are formulated which highlight the influence of viscous dissipation and heat generation. A numerical solution is achieved with the help of the Range–Kutta fourth-order (RK4) method combined with the shooting technique. Finally, the role of emerging parameters is studied via performing the numerical simulation which reveals that the momentum boundary layer of nanofluid shrinks due to the porous medium. Whereas, thermal boundary layer expands for all variables, except for the Prandtl number. Finally, mass transfer rated suffers due to Schmidt number.

Brownian motion and thermophoresis significance of Casson fluid flow in an elastic-radiated surface with a suspension of transpiration and non-Fourier heat flux

ABSTRACT Passive systems that need exceptional apparent geometries, thermal packaging, or fluid additives. In passive procedures, a number of foremost efforts have been conducted. The passive methods are divided into two groups: geometry modification (e.g. nano/microchannels) and solid additives (e.g. micro/nano solid particles). In a recent development in microfabrication – the development of fabrication of minuscule buildings of micrometer measures – a variation of microstrategies including heat transfer have been industrialized. Viewing this, the heat and mass transfer characteristics of a free convective Casson fluid over an elastic stretching surface are numerically studied. Thermal radiation and non-Fourier flux are incorporated in the energy to balance the transformation. Similarity transformations are used to translate partial differential equations relating to momentum, diffusion, and energy into nonlinear ordinary differential equations. The shooting approach is used to achieve numerical solutions to these equations. The effect of various physical pertinent parameters including thermal radiation parameter, Brownian motion, thermophoresis, suction, curie parameter, thermal and diffusion buoyancy forces, thermal relaxation, stretching, or shrinking parameters on the concentration and temperature profiles is investigated. It is observed that the nonlinear case has highly mixed performance when compared to the linear case of temperature and concentration fields.

CMInject: Python framework for the numerical simulation of nanoparticle injection pipelines

CMInject simulates nanoparticle injection experiments of particles with diameters in the micrometer to nanometer-regime, e.g., for single-particle-imaging experiments. Particle-particle interactions and particle-induced changes in the surrounding fields are disregarded, due to low nanoparticle concentration in these experiments. CMInject's focus lies on the correct modeling of different forces on such particles, such as fluid-dynamics or light-induced interactions, to allow for simulations that further the scientific development of nanoparticle injection pipelines. To provide a usable basis for this framework and allow for a variety of experiments to be simulated, we implemented first specific force models: fluid drag forces, Brownian motion, and photophoretic forces. For verification, we benchmarked a drag-force-based simulation against a nanoparticle focusing experiment. We envision its use and further development by experimentalists, theorists, and software developers. Program summaryProgram Title: CMInjectCPC Library link to program files:https://doi.org/10.17632/rbpgn4fk3z.1Developer's repository link:https://github.com/cfel-cmi/cminjectCode Ocean capsule:https://codeocean.com/capsule/5146104Licensing provisions: GPLv3Programming language: Python 3Supplementary material: Code to reproduce and analyze simulation results, example input and output data, video files of trajectory moviesNature of problem: Well-defined, reproducible, and interchangeable simulation setups of experimental injection pipelines for biological and artificial nanoparticles, in particular such pipelines that aim to advance the field of single-particle imaging.Solution method: The definition and implementation of an extensible Python 3 framework to model and execute such simulation setups based on object-oriented software design, making use of parallelization facilities and modern numerical integration routines.Additional comments including restrictions and unusual features: Supplementary executable scripts for quantitative and visual analyses of result data are also part of the framework.