Concentration Boundary Conditions Research Articles

High temperature co-polyester thermoplastic elastomer nanocomposites for flexible self-regulating heating devices

Pyroresistive polymer composites are smart materials with great promise in numerous fields of electronic devices, including temperature and strain sensors, self-regulating heating, and over-current/over-temperature protective devices. However, the operational window of these materials is limited by the phase transition temperatures of the polymer matrix and the brittleness of the composites. Herein, a conductive polymer composite based on a co-polyester thermoplastic elastomer reinforced with graphene nanoplatelets (GNPs) was developed, which exhibits a positive temperature coefficient (PTC) switching temperature of 200 °C. This system shows a more gradual increase in resistivity with temperature and a less pronounced drop in resistivity past the critical transition temperature than other PTC composites. Moreover, Joule heating experiments revealed the ability to regulate at a predefined maximum temperature (within 150 – 200 °C), tuneable through parameters such as filler concentration, applied voltage and thermal boundary conditions, as also demonstrated by multiphysics simulations. Due to the more gradual PTC curve, this composite can produce steady state heating far below the PTC peak, unlike almost all other PTC materials: a unique advantage for self-regulating heating devices as the polymer is not in a melt state, reducing polymer degradation, filler mobility and increasing safety margin before onset of NTC behaviour.

Long time dynamics of nonequilibrium electroconvection

The Nernst-Planck-Stokes (NPS) system models electroconvection of ions in a fluid. We consider the system, for two oppositely charged ionic species, on three dimensional bounded domains with Dirichlet boundary conditions for the ionic concentrations (modelling ion selectivity), Dirichlet boundary conditions for the electrical potential (modelling an applied potential), and no-slip boundary conditions for the fluid velocity. In this paper, we obtain quantitative bounds on solutions of the NPS system in the long time limit, which we use to prove (1) the existence of a compact global attractor with finite fractal (box-counting) dimension and (2) space-time averaged electroneutrality ρ ≈ 0 \rho \approx 0 in the singular limit of Debye length going to zero, ϵ → 0 \epsilon \to 0 .

Study of Nano-Powell-Erying fluid flow past a porous stretching sheet by the effects of MHD, thermal and mass convective boundary conditions

AbstractThe object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented.

Numerical investigation on cooperative evaporation from microdroplet array on heated substrate

The evaporative heat and mass transport characteristics from an array of continuously fed microdroplet on a heated substrate are investigated numerically by a Multiphysics model, which incorporates heat conduction, buoyant flow, Marangoni flow, Stefan flow, and vapor diffusion. The effects of droplet spacing, contact angle, and droplet size on the evaporation rate, heat flux, and convection strength were analyzed in detail with a fixed thermal and vapor concentration boundary condition. The results revealed the existence of extremely strong convection current in the ambient gas domain for evaporation from droplet array. This convection effect dominates the vapor transport process, overcomes the suppression effect from neighboring droplet, and causes the total evaporation rate to exceed the prediction from traditional diffusion-based model by up to ten times. The strength of the convective vapor transport is characterized by a dimensionless parameter, which increases first from 2.3 to 7 and then decrease to 4 with increasing contact angle from 30° to 150°, but remains invariant at 6.3 for hemispherical droplet irrespective of the change in droplet dimension. Finally, the numerical results demonstrate potential for microdroplet array evaporation to resolve the thermal management challenge of ultrahigh power electronics with heat flux up to 1 kW/cm2.

Quantifying the effects of hydrogen concentration and cooling rates on porosity formation in Al–Li alloys

The addition of Li to Al alloys produces such benefits as a 6% increase of modulus and a 3% weight reduction upon adding 1 wt% Li, and yet it has led to difficulties for manufacturing due to the highly active Li and 25 times equilibrium [H] concentration in the liquid at elevated temperatures. In this study, the 3D porosity morphology was quantified using the X-ray computed tomography (X-CT) from both sand gravity and vacuum castings. A cellular automaton model has been adopted to predict porosity distribution as a function of equilibrium hydrogen concentration and thermal boundary conditions. Combining experimental and simulation results, it was found that the mechanical properties of vacuum casting Al–Li alloy have been improved significantly due to the reduction of hydrogen porosity. The prediction of porosity as a function of hydrogen levels and cooling conditions agrees well with experiments, and porosity has been found to decrease Young's modulus and initiating cracks in Al–Li alloys.

Features of Phase Formation in the CsOH–H2SO4–H3PO4–H2O System and the Growth of the Cs6(SO4)3(H3PO4)4 Crystals

In this paper, the conditions of phase formation in the system CsOH–H2SO4–H3PO4–H2O are considered for the first time. The phase formation of Cs6(SO4)3(H3PO4)4 at t = 50 °C has been studied extensively. The main concentration boundary conditions for this compound are considered for the first time. The solubility congruence of Cs6(SO4)3(H3PO4)4 is shown. Conditions and approaches for obtaining crystals by isothermal evaporation and saturated solution temperature reduction methods are considered. The results of obtaining Cs6(SO4)3(H3PO4)4 crystals with maximum dimensions of ~20 mm are presented.

Significance of generalized Fourier and Fick’s law and stagnation point flow for magnetized viscoelastic liquids

This analysis describes the stagnation point and mixed convection flow of a viscoelastic micropolar fluid into a porous medium towards a stretchable sheet and magnetic field. Concentration and thermal stratification boundary conditions and activation energy are studied. For the flow of heat and mass transportation, Fourier and Fick’s law is also accommodated into account. Suitable similarity variables are utilized to attain the dimensionless form of the governed equations. These dimensionless equations have been resolved numerically with the help of BVP4C approach. The velocity profile is reduced with the stronger estimations of εand M. The coefficient of skin friction has an increasing effect by improving values of K,β,M, and ∊. The velocity sketch has the opposite behavior for ∊ and βt. Stronger estimations of β and δe lead to the decay of the temperature profile. The angular velocity of the fluid upsurges due to the stronger values of K.

Sutterby hybrid nanofluid flow and heat transfer over a nonlinearly expanding sheet with convective boundary condition and zero-mass flux concentration

This paper examines the impacts of a nonlinearly expanding sheet on velocity, heat and mass transport for a Suttery hybrid nanoliquid (mixture of Sutterby fluid and [Formula: see text] and [Formula: see text]. The zero-mass flux concentration and convective boundary conditions are considered. Nondimensionalization of governing equations may be achieved through similarity conversions. The governing equations are solved utilizing the Optimal Homotopy Analysis Method. Graphs and tables were used to document the effects of different variables. The numerical values for skin friction, Sherwood number and Nusselt number are provided in a table for diverse relevant factors. Comparisons were made to a previous study’s findings. The results obtained are in agreement with the findings of the prior study. The outcome is that the occurrence of hybrid nanoparticles ([Formula: see text] and [Formula: see text] in ethylene glycol liquid enhances its thermal conductivity thereby increasing the thermal boundary layer thickness. The presence of hybrid nanoparticles ([Formula: see text] and [Formula: see text] in ethylene glycol liquid also increases the momentum boundary layer thickness.

The coupled effect of bentonite colloid and radioactive ingrowth on the transport of actinide decay chains in a single fracture

An analytical model is used to illustrate the colloid-facilitated transport of decay chain radionuclides (RNs) in the granitic fractured porous media. The colloid source is assumed from the erosion of the bentonite used as buffer materials in a spent nuclear fuel repository. A conservative assumption that all colloids are mobile and have reached a sufficiently high concentration before RNs start to release is made in the present model. The latest reported distribution coefficient (Kd) values for both local granite and bentonite are used for several calculations. Investigating the simulation results shows that the second peaks of the breakthrough curves and profiles for daughter RNs are found using various initial concentration boundary conditions. The second peak is caused by the radioactive decay of the parent RN. Therefore, the contribution of the parents of a decay chain should not be ignored when performing a safety assessment. Moreover, the existence of colloids promotes a higher influence of the parents on the transport of their daughter RNs. A conservative colloid velocity that could reflect the effect of hydrodynamic chromatography phenomena is also investigated. Simulation results show that the Kd values of RNs on rock and bentonite colloids are the dominant factor that affects the colloid-facilitated-decay chain transport in the fractured rock system.

Lifetime Prediction with Combined Hygro‐Thermo‐Mechanical Influences on Thick Layer Adhesives

AbstractSemi‐structural bonded joints of steel components are exposed to long‐term stresses in addition to water diffusion, temperature changes and varying external forces during operation. These hygro‐thermomechanical loadings lead to successive degradation of stiffness and strength due to damage resulting from chemical aging and fatigue processes, causing failure of the bonded joint when its service life is reached. In the following contribution, a methodology is presented to predict the service life of hygro‐thermo‐mechanically loaded semistructural adhesive joints with transient FE simulation. The lifetime prediction is based on a constitutive model with a viscoelastic and a damage part. The first part for viscoelasticity consists of the generalized Maxwell model, in which the effects of temperature changes and varying humidity on the viscoelastic properties of the adhesive bond are captured by the time‐temperature and time‐water concentration shifts. The second part for the material damage is based on an ordinary differential equation for the damage evolution. It consists of a creep and a moisture damage part for the void developments caused by the local water concentration due to mechanical stress and chemical aging. Both damage parts are multiplied by an Arrhenius‐type function to account for the effect of temperature change on the defect growth. The interaction of the creep and the moisture damage part is studied by applying the analytical and numerical solution of the damage differential equation. All parameters of the damage model are determined by using fracture times from creep tests under different climatic conditions and loading levels. The local water concentration in the adhesive is calculated by Fick's model and a concentration boundary condition. The diffusion parameters are determined by gravimetric measurements. A numerical example is setup to demonstrate the lifetime prediction methodology and to show the influence of viscoelasticity on the predicted lifetimes for different hygro‐thermo‐mechanical loading cases.

Global regularity for Nernst–Planck–Navier–Stokes systems with mixed boundary conditions

We consider electrodiffusion of ions in fluids, described by the Nernst–Planck–Navier–Stokes system, in three-dimensional bounded domains, with mixed blocking (no-flux) and selective (Dirichlet) boundary conditions for the ionic concentrations and Robin boundary conditions for the electric potential, representing the presence of an electrical double layer. We prove global existence of strong solutions for large initial data in the case of two oppositely charged ionic species. The result hold unconditionally in the case where fluid flow is described by the Stokes equations. In the case of Navier–Stokes coupling, the result holds conditionally on Navier–Stokes regularity. We use a simplified argument to also establish global regularity for the case of purely blocking boundary conditions for the ionic concentrations for two oppositely charged ionic species and also for more than two species if the diffusivities are equal and the magnitudes of the valences are also equal.

Effect of hydrogen traps on hydrogen permeation in X80 pipeline steel —— a joint experimental and modelling study

The permeation of hydrogen in the X80 steel was studied in this paper through thermal desorption spectroscopy, stepwise hydrogen permeation experiments and finite element modelling. Firstly, one kind of shallow trap and deep traps in X80 steel were identified through thermal desorption spectroscopy and the corresponding binding energies were obtained. According to the experiment and simulation, the deep hydrogen traps can significantly retard the first hydrogen permeation process but have almost no effect during the following charging. The X80 steel used in hydrogen compressed natural gas pipelines is exposed to hydrogen for long periods and deep traps are filled, its hydrogen permeation process is more in line with the stepwise hydrogen charging. Therefore, the stepwise hydrogen charging experiments were performed and the apparent diffusion coefficients (Dapp) and the hydrogen trap density involved in the hydrogen permeation transient (N1) were obtained using three different thickness samples. Then, a quantitative relationship in X80 steel was fitted between the N1 and the variation of hydrogen concentration. Based on the quantitative relationship and the hydrogen trap binding energies, a hydrogen permeation model in X80 steel was established. By comparing the hydrogen permeation curves obtained by our model under different boundary conditions with experiment curves, it is found that the constant concentration boundary condition model can better describe the hydrogen permeation kinetic in X80 steel under electrochemical hydrogen charging. As a result, this model can be used to predict the distribution of hydrogen in X80 steel, laying the foundation for predicting the occurrence of hydrogen embrittlement in pipeline steels.

A chemical engineering application on hyperbolic tangent flow examination about sphere with Brownian motion and thermo phoresis effects using BVP5C

Brownian motion and thermophoresis impacts are discussed in relation to a tangent hyperbolic fluid encircling a sphere subject to a convective boundary condition and a Biot number. Concentration boundary conditions involving a wall normal flow of zero nanoparticles are an unexplored area of research. The governing non-linear BVP is transformed into a higher-order non-linear ODE using similarity transformations. Following equations were numerically solved for various values of emerging parameters using the matlab function bvp5c. Calculated values for velocity, concentration, temperature, the skin friction coefficient, Sherwood and Nusselt numbers are all shown, tabulated for analysis. Laminar boundary layer flow and heat transfer from a sphere in two-dimensional nano fluid is the novelty of the current work. The Weissenberg number decreases the velocity boundary layer thickness. The Biot number parameter lowers the field's temperature and speed.

Electro-osmotic optimized flow of Prandtl nanofluid in vertical wavy channel with nonlinear thermal radiation and slip effects

The simulations have been performed for the nonlinear radiative flow of Prandtl nanofluid following the peristaltic pumping in a wavy channel. The applications of entropy generation for the electrokinetic pumping phenomenon are also focused as a novelty. The complex wavy channel induced the flow of Prandtl nanofluid. Moreover, the formulated problem is solved by using the convective thermal and concentration boundary conditions. The Keller Box numerical procedure is adopted as a tool for the simulation task. The results are also verified by implementing the built-in numerical technique bvp4c. The comparison tasked against obtained numerical measurement has been done with already reported results with excellent manner. The physical characteristics based on the flow parameters for velocity, heat transfer phenomenon, concentration field, and entropy generation pattern is visualized graphically. It has been observed that the presence of thermal slip and concentration enhanced the heat transfer rate and concentration profile, respectively. The skin friction coefficient declines with electro-osmotic force and slip parameter. The increasing variation in Nusselt number is observed for electro-osmotic parameter for both linear and non-linear radiative phenomenon.

A two-dimensional semi-analytical model for tracer gas injection and transport in a landfill system

Identifying the location of a leakage is the very first basic step for preventing the escape of landfill gas and leachate from defects. A two-dimensional semi-analytical model is presented for the transport of tracer gas injection in landfills. Tracer gas transport in the landfill cover, liner and waste body is considered. Constant concentration and flux boundary conditions for the injection well are adopted. The proposed approach can be used for leakage detection of the barrier systems in landfills. It is shown that the air-filled porosities of the waste body and the upper cover have a great influence on the tracer gas emission flux on the cover system while the effect of air-filled porosity of the bottom liner can be neglected. The transport mechanism of the tracer gas in the waste body can have a significant impact on the behaviour of the tracer gas in the upper cover and the bottom liner. SF6 emission flux increases with decreasing of the thickness of the upper cover and increasing thickness of the waste body. It is proposed that a constant flux injection boundary should be adopted in the field for leakage detection. The analytical model presented here is a relatively simplified model, which can be used for the validation and guidance of field tracer test.

The Novelty of Thermo-Diffusion and Diffusion-Thermo, Slip, Temperature and Concentration Boundary Conditions on Magneto–Chemically Reactive Fluid Flow Past a Vertical Plate with Radiation

The significance of radiation, Soret and Dufour’s effects on MHD flow in a porous media near a stagnation point past a vertical plate with slip, temperature, and concentration boundary conditions were investigated. Local similarity variables are used in the solution, which reduces the PDEs into analogous boundary value problem for ODEs. Symmetry analysis can be used to detect these variations in local similarity. To numerically explain the problem, a shooting approach and the MATLAB bvp4c solver are utilized. As the magnetic field and porous medium parameters are raised, the skin friction increases, and the temperature increases as the radiation pointer is increased. As the Soret number grows, the concentration profile rises.

Heat transport and the aspects of retardation time phenomenon in the flow of highly viscoelastic nanofluid with a Newtonian heating agent

This study investigates the convective thermal and solutal characteristics in the stagnation point flow of Burgers nanofluid accelerated due to stretching cylinder. The thermal features of the flow are examined by employing Fourier's law in addition to the effects of heat source/sink and Joule heating. The essential feature of this research is to utilize the activation energy and binary chemical reaction effects to investigate the convective mass transform phenomenon. Moreover, the process of heat as well as mass convection from the surface to the fluid is also observed by employing convective thermal and concentration boundary conditions. The dimensionless similarity transformations are invoked to attain the ordinary differential equations (ODE's) from governed partial differential equations (PDE's). The numerical solutions are carried out by utilizing bvp midrich numerical procedure. The section on physical analysis is proposed to elaborate on the outcomes of this study physically. The graphical illustration of physical parameters is also depicted and physically analyzed. The rate of mass transfer is depreciated for the augmenting scales of reaction rate and temperature difference constraints. Moreover, the escalating magnitudes of thermal Biot number drive up the thermal energy transport in the flow.

Hydrodynamic resolved simulation of a char particle combustion by immersed boundary-lattice Boltzmann method

A Lattice-Boltzmann model coupled with boundary method is proposed for the hydrodynamic resolved simulation of a single char particle combustion. A pure lattice Boltzmann scheme with multi distribution functions is presented for this low Mach reactive flows. Real varying thermodynamic and transport properties are considered, and the fluid density can bear significant change depending on the varying temperature and species concentrations. The recently proposed boundary-thickening based direct forcing-immersed boundary method is extended to implement the boundary conditions of velocity, temperature, and species concentrations at the char particle surface. Two heterogeneous reactions at particle surface and one homogeneous reaction in fluid are adopted to describe the combustion. The Stefan flow near the particle surface caused by the heterogeneous reactions is also considered. A satisfactory agreement can be found between the present simulation results and the previous experimental and numerical results. Three flame modes of a char particle combustion and the transition mechanisms between them are investigated. Furthermore, the effect of hydrodynamic interaction and the oxygen concentration in O2/CO2 atmosphere on particle combustion behavior are explored in detail. The present work establishes the foundation for the efficient simulations of particle combustion with size change and motion.

Correlation between Electrostatic and Hydration Forces on Silica and Gibbsite Surfaces: An Atomic Force Microscopy Study.

The balance between hydration and Derjaguin–Landau–Verwey–Overbeek (DLVO) forces at solid–liquid interfaces controls many processes, such as colloidal stability, wetting, electrochemistry, biomolecular self-assembly, and ion adsorption. Yet, the origin of molecular scale hydration forces and their relation to the surface charge density that controls the continuum scale electrostatic forces is poorly understood. We argue that these two types of forces are largely independent of each other. To support this hypothesis, we performed atomic force microscopy experiments using intermediate-sized tips that enable the simultaneous detection of DLVO and molecular scale oscillatory hydration forces at the interface between composite gibbsite:silica–aqueous electrolyte interfaces. We extract surface charge densities from forces measured at tip–sample separations of 1.5 nm and beyond using DLVO theory in combination with charge regulation boundary conditions for various pH values and salt concentrations. We simultaneously observe both colloidal scale DLVO forces and oscillatory hydration forces for an individual crystalline gibbsite particle and the underlying amorphous silica substrate for all fluid compositions investigated. While the diffuse layer charge varies with pH as expected, the oscillatory hydration forces are found to be largely independent of pH and salt concentration, supporting our hypothesis that both forces indeed have a very different origin. Oscillatory hydration forces are found to be distinctly more pronounced on gibbsite than on silica. We rationalize this observation based on the distribution of hydroxyl groups available for H bonding on the two distinct surfaces.

Flow investigation of second grade micropolar nanofluid with porous medium over an exponentially stretching sheet.

This article mainly focuses on the influence of heat and mass transportation of micropolar second grade nanofluid toward porous medium of an exponentially stretched surface. The significance of activation energy and viscous dissipation with magnetic effect are taken into deliberated. Furthermore, to analyze the heat and mass transport scrutiny the concentration and thermal slip boundary conditions are assessed on the surface of the sheet. The convenient similarity variables are adopted to transfer the non-linear governing PDEs into the dimensionless ODEs and their corresponding boundary conditions also transformed. The nonlinear coupled ODEs are numerically solved by the usage of BVP4C MATLAB technique. The obtained numerical estimations are displayed graphically to display the significance of the various parameters against the velocity, temperature, microrotation, concentration distributions. It is noticed that larger estimations of micropolar and second grade parameter improves the fluid velocity consequently, while opposite trend is found for the higher estimation of porous medium parameter. Further, it is observed that the skin friction rate is boosted by the increment of and , whereas opposite trend is noted against the mass transfer rate and heat transfer rate.