Assessment of Boron Diffusivities in Nickel Borides by Two Mathematical Approaches

In the work of this contribution, two kinetics models have been employed to assess the boron diffusivities in nickel borides in case of Inconel 718 alloy. The first approach, named the alternative diffusion model (ADM), used the modified version of mass conservation equations for a three-phase system whilst the second one employed the mean diffusion coefficient (MDC) method. The boron diffusivities in nickel borides were firstly evaluated in the interval of 1123 to 1223 K for an upper boron concentration of 11.654 wt% in Ni4B3. The boron activation energies in the three phases (Ni4B3, Ni2B and Ni3B) were secondly deduced by fitting the values of boron diffusivities with Arrhenius relations. Finally, these values of energy were compared with the results from the literature for their experimental validation.

Energy quadratization Runge-Kutta method for the modified phase field crystal equation

In this paper, we propose high order and unconditionally energy stable methods for a modified phase field crystal equation by applying the strategy of the energy quadratization Runge–Kutta methods. We transform the original model into an equivalent system with auxiliary variables and quadratic free energy. The modified system preserves the laws of mass conservation and energy dissipation with the associated energy functional. We present rigorous proofs of the mass conservation and energy dissipation properties of the proposed numerical methods and present numerical experiments conducted to demonstrate their accuracy and energy stability. Finally, we compare long-term simulations using an indicator function to characterize the pattern formation.

Modelling Thermal Conduction in Polydispersed and Sintered Nanoparticle Aggregates

Nanoparticle aggregation has been found to be crucial for the thermal properties of nanofluids and their performance as heating or cooling agents. Most relevant studies in the literature consider particles of uniform size with point contact only. A number of forces and mechanisms are expected to lead to deviation from this ideal description. In fact, size uniformity is difficult to achieve in practice; also, overlapping of particles within aggregates may occur. In the present study, the effects of polydispersity and sintering on the effective thermal conductivity of particle aggregates are investigated. A simulation method has been developed that is capable of producing aggregates made up of polydispersed particles with tailored morphological properties. Modelling of the sintering process is implemented in a fashion that is dictated by mass conservation and the desired degree of overlapping. A noticeable decrease in the thermal conductivity is observed for elevated polydispersity levels compared to that of aggregates of monodisperse particles with the same morphological properties. Sintered nanoaggregates offer wider conduction paths through the coalescence of neighbouring particles. It was found that there exists a certain sintering degree of monomers that offers the largest improvement in heat performance.

Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal

The chemotaxis-Stokes system [Formula: see text] is considered subject to the boundary condition [Formula: see text] with [Formula: see text] and a given nonnegative function [Formula: see text]. In contrast to the well-studied case when the second requirement herein is replaced by a homogeneous Neumann boundary condition for [Formula: see text], the Dirichlet condition imposed here seems to destroy a natural energy-like property that has formed a core ingredient in the literature by providing comprehensive regularity features of the latter problem. This paper attempts to suitably cope with accordingly poor regularity information in order to nevertheless derive a statement on global existence within a generalized framework of solvability which involves appropriately mild requirements on regularity, but which maintains mass conservation in the first component as a key solution property.

Gauge Symmetries in Physical Fields (Review)

Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum Electro Dynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physicalfields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.

Humidification-Dehumidification Desalination System Powered by Simultaneous Air-Water Solar Heater

A humidification–dehumidification (HDH) desalination system requires thermal energy to desalt seawater. An environmentally friendly approach to obtain thermal energy is to utilize solar energy using solar collectors. Either seawater or air (or both) are typically preheated by HDH desalination systems before these fluids are conveyed to the humidifier column. Compared with preheating only air or water, preheating both is preferred because improved performance and higher productivity are achieved. Many researchers have proposed dual preheated HDH systems utilizing two separate solar heaters/collectors for simultaneous air–seawater preheating. In this study, dual-fluid preheating is achieved using a single solar collector. The proposed simultaneous air–water solar heater (SAWSH) is a modified flat-plate collector designed for simultaneously preheating air and seawater before the fluids reach the humidifier. A thermodynamic study was conducted using formulated mathematical models based on energy and mass conservation principles. Then, the dual-fluid heating HDH system is compared with HDH systems in which only air or only water is heated. This work found that the former outperformed the latter. The daily and monthly performance levels of the system in terms of the outlet temperatures of air and water, distillate rate, and gain output ratio were calculated using the weather data of the hot and humid climate of Jeddah City, Saudi Arabia.

Gas flow modeling in wells

The topic of research is gas flow modeling in wells. The subject of the study is to determine the dynamic parameters of gas in a gas well, taking into account changes in the ambient temperature and gravity. Mathematical and numerical modeling of gas flow in a gas well is performed; a numerical algorithm to determine gas pressure in a gas well is built. This algorithm allows studying the state of production and injection wells with varying conditions at the wellhead and at the lower end of the well. Research methods are based on the energy equations of the transported gas; the mass conservation equation, which are the basic equations of gas flow; the methods of numerical and mathematical modeling. In the article, numerical and mathematical models of gas flow in a gas well are obtained, taking into account changes in the ambient temperature and gravity. A numerical algorithm and a program were built to determine the gas-dynamic characteristics of wells. The computational process was based on the “cycle in cycle” principle. Provisions were made to study the state of production and injection wells with varying conditions at the wellhead and at the bottom end of the well.

A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes

We consider the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, satisfying $$ \left\{ \begin{array}{l} \partial_t u - {\Delta} u - \nabla\cdot (u\nabla v)=0 \ \ \text{ in}\ {\Omega},\ t>0,\\ \partial_t v - {\Delta} v + v = u^p \ \ { in}\ {\Omega},\ t>0, \end{array} \right. $$ ∂ t u − Δ u − ∇ ⋅ ( u ∇ v ) = 0 in Ω , t > 0 , ∂ t v − Δ v + v = u p i n Ω , t > 0 , with p ∈ (1, 2), ${\Omega }\subseteq \mathbb {R}^{d}$ Ω ⊆ ℝ d a bounded domain (d = 1, 2, 3), endowed with non-flux boundary conditions. By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for d = 1, 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables (u,v) under structured meshes, and the second one by using the auxiliary variable σ = ∇v and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions.

Numerical Simulation of Dyeing Process of Cotton with Natural Dye

Cotton dyeing is a very complex process with many variables in which different phenomena occur simultaneously. This study aimed to describe the cotton dyeing process by natural dye, using a mathematical model that consists of three mass conservation equations that depict dyeing cotton in cones, taking a representative volume element at the micro, meso, and macroscales. The first equation describes the concentration changes of the dye in the solution, taking into account the diffusive, convective, adsorptive, and reactive effects. The second equation describes the changes in dye concentration in cotton fiber, considering the diffusive, adsorptive, and reactive effects within an intermediate scale. The last equation describes changes in the concentration of dye in the solution on the macroscale, based on the characteristics of the equipment and the difference in concentration before and after passing through the fiber. In addition, a fluid continuity equation was incorporated, taking into account Darcy’s law. In the simulation of the dyeing process with synthetic dye with initial concentrations of 0.408 and 2.06 kg/m3, RMSE of 0.00221 and 0.0289 kg/m3 were obtained, respectively. For the simulation of a dyeing process with natural dyeing, a behavior similar to the experimental data was obtained.

Thermodynamics of Moist Air for Vacuum Technology

The paper is focused on the developing a predictive mathematical model for describing thermodynamic processes connected with the moist air depressurization in vacuum chambers. Equations of the mathematical description are based on principles of the energy and mass conservation, which are complemented by the moist air thermodynamics, the state behavior of water and vapor, including principles of the critical flow. The described problem has been solved using the MATLAB software. In the paper, two cases are applied and discussed: the vacuum drying and the specimen chamber of an environmental scanning electron microscope. The specific requirements are especially important for environmental scanning electron microscopes, where it is possible to observe samples, which contain water, in their natural condition. If the air pressure, temperature and humidity do not have suitable values, observed sample may be dried or damaged.