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The parabolic trough solar collector (PTSC) is a medium-temperature solar system that operates in the temperature range of 60–400 ºC. This technology is utilized dominantly for heat and power generation. Recently, numerous theoretical and numerical investigations have been carried out to evaluate and enhance the performance of PTSCs. This review paper provides fundamentals of PTSC systems, mathematical models, discretization methods, and turbulence models utilized for the simulation of PTSCs. Challenges in the field and future directions are presented to provide a perspective for researchers to achieve more accurate numerical results with lower computational costs. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. These properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV. • A stochastic delay HIV system with humoral immunity is proposed. • Asymptotic properties,persistence in mean and extinction, are investigated. • A series of Lyapunov functions and differential inequality are constructed and used. • Numerical simulations confirmed the effects of stochastic fluctuations on HIV. • Stochastic fluctuations can effectively suppress the outbreak of HIV. [ABSTRACT FROM AUTHOR]

Purpose - In engineering applications, gas-solid two-phase reaction flow with multi-moving boundaries is a common phenomenon. The launch process of multiple projectiles is a typical example. The flow of adjacent powder chambers is coupled by projectile's motion. The purpose of this paper is to study this flow by numerical simulation. Design/methodology/approach - A one-dimensional two-phase reaction flow model and MacCormack difference scheme are implemented in a computational code, and the code is used to simulate the launch process of a system of multiple projectiles. For different launching rates and loading conditions, the simulated results of the launch process of three projectiles are obtained and discussed. Findings - At low launching rates, projectiles fired earlier in the series have little effect on the launch processes of projectiles fired later. However, at higher launching rates, the projectiles fired first have a great influence on the launch processes of projectiles fired later. As the launching rate increases, the maximum breech pressure for the later projectiles increases. Although the muzzle velocities increase initially, they reach a maximum at some launching rate, and then decrease rapidly. The muzzle velocities and maximum breech pressures of the three projectiles have an approximate linear relationship with the charge weight, propellant web size and chamber volume. Originality/value - This paper presents a prediction tool to understand the physical phenomenon of the gas-solid two-phase reaction flow with multi-moving boundaries, and can be used as a research tool for future interior ballistics studies of launch system of multiple projectiles. [ABSTRACT FROM AUTHOR]

This paper considers a fractional order Rosenzweig-MacArthur (R-M) model incorporating a prey refuge. The model is constructed and analyzed in detail. The existence, uniqueness, non-negativity and boundedness of the solutions as well as the local and global asymptotic stability of the equilibrium points are studied. Sufficient conditions for the stability and the occurrence of Hopf bifurcation for the fractional order R-M model are demonstrated. The resolution of the paradox of enrichment is investigated. The impact of fractional order and the prey refuge effects on the stability of the system are also studied both theoretically and by using numerical simulations. [ABSTRACT FROM AUTHOR]

Purpose The numerical simulation of the serial launch process of multiple projectiles is an important engineering problem. However, the projectiles’ motion law is hard to obtain completely only by interior ballistic model. The muzzle flow field affects the projectiles’ velocities when the projectiles pass through it. Also, the propellant gas from previous projectiles may decelerate the later projectiles. Therefore, the aftereffect period should be simulated together with the interior ballistic process of multiple projectiles when researching the serial launch process for accurate motion law of the projectiles.Design/methodology/approach The computational fluid dynamics (CFD) software is used to simulate the muzzle flow field. A one-dimensional two-phase reaction flow model is implemented in a computational code for the numerical simulation of gas-solid two-phase reaction flow, during the serial launch process. The computational code is coupled with CFD software by a user-defined function.Findings Compared with the first projectile, the formation process of the shock bottle of the second projectile is different. After the projectile head flies out of the muzzle, the projectile head pressure decreases rapidly, but then, it is not always equal to 0.1 MPa. After the projectiles leave the muzzle, the velocity increments of each projectile are mainly determined by muzzle pressure.Originality/value This paper presents a prediction tool to understand the projectiles’ motion law during the serial launch process of the multiple projectiles considering aftereffect period, and can be used as a research tool for future ballistic studies of a serial launch system of multiple projectiles. [ABSTRACT FROM AUTHOR]

The spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable and inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study. [ABSTRACT FROM AUTHOR]

Purpose – Nowadays, various software is available for simulating physical processes in induction heating. The software is often limited in its ability to simulate the billet movement, sometimes assuming uniform distribution of voltages on the inductor winding, uniformity of the physical properties of the billet, etc. The mathematical model of moving cylindrical ferromagnetic billets described in this paper takes into account the billet's movement, the billet phase heterogeneity and the nonuniformity of the supply voltage distribution in the inductor turns. The paper aims to discuss these issues. Design/methodology/approach – The research methodology is based on FEM analysis of the coupled problem, including the electromagnetic and thermal boundary problem with additional algebraic equations, using Comsol 3.5a software. Findings – The electromagnetic and temperature field in the billet and the voltage distribution on the winding turns have been calculated. The phase distribution in the billet has been predicted. Significant interaction of the nonuniformity of the supply voltage distribution, the billet's movement, the billet phase heterogeneity and side effect on the ends of the inductor have been shown. Practical implications – The results received can be used for designing the induction heating unit for moving cylindrical billets made from ferromagnetic material and improving their characteristics. Originality/value – Investigation of moving cylindrical ferromagnetic billets induction heating can be done by numerical solving the coupled problem including the electromagnetic and thermal boundary problem with additional algebraic equations for the supply voltage distribution. [ABSTRACT FROM AUTHOR]

Purpose – The numerical simulation of practical thermal processes is generally complicated because of multiple transport mechanisms and complex phenomena that commonly arise. In addition, the materials encountered are often not easily characterized and typically involve large property changes over the ranges of interest. The boundary conditions may not be properly defined and or may be unknown. However, it is important to obtain accurate and dependable numerical results from the simulation in order to study, design, and optimize most practical thermal processes of current and future interest. The purpose of this paper is to focus on the main challenges that are encountered in obtaining accurate numerical simulation results on practical thermal processes and systems. Design/methodology/approach – A wide range of thermal systems is considered and the challenges faced in the numerical simulation are outlined. The methods that may be used to meet these challenges are presented in terms of grid, solution strategies, multiscale modeling and combined mechanisms. The models employed must be validated and the accuracy of the simulation results established if the simulation is to form the basis for improving existing systems and developing new ones. Findings – Of particular interest are concerns like verification and validation, imposition of appropriate boundary conditions, and modelling of complex, multimode transport phenomena in multiple scales. Additional effects such as viscous dissipation, surface tension, buoyancy and rarefaction that could arise and complicate the modelling are discussed. Uncertainties that arise in material properties and in boundary conditions are also important in design and optimization. Large variations in the geometry and coupled multiple regions are also discussed. Research limitations/implications – The paper is largely focused on numerical modeling and simulation. Experimental data are considered mainly for validation and for physical insight.Practical implications – A wide variety of practical systems, ranging from materials processing to energy, cooling, and transportation is considered. Originality/value – Future needs in this interesting and challenging area are also outlined in the paper. [ABSTRACT FROM AUTHOR]

Purpose – A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and cooled, through its two vertical walls, by a linear or uniform heat flux q(y) and by a constant cold temperature, respectively. The horizontal walls are considered adiabatic. The paper aims to discuss these issues. Design/methodology/approach – The radiosity method is employed to calculate the net radiative heat exchanges between elementary surfaces, while the finite volume method is implemented to resolve the governing equations of the fluid flow. Findings – For each heat flux q(y) (ascending, descending or uniform), the effect of the emissivity ε (0ε1) on the local, average and maximum temperatures of the heated wall is determined as a function of the average Rayleigh number Ram (103Ram 6×104) and the cavity aspect ratio A (10A80). The effect of the coupling on the flow structures, convective and radiative heat transfers is also presented and analyzed. Overall, it is shown that surface radiation significantly reduces the local and average temperatures of the heated wall and therefore reduces the convective heat transfer between the active walls. Practical implications – The studied configuration is of practical interest in several areas where overheating must be avoided. For this purpose, a simple design tool is developed to estimate the mean and the maximum temperatures of the hot wall in different operating conditions (Ram, A et ε). Originality/value – The originality lies in the study of the interaction between surface radiation and natural convection in tall cavities submitted to a non-uniform heat flux and a constant cold temperature on the active walls. Also, the development of an original simplified calculation procedure for the hot wall temperatures. [ABSTRACT FROM AUTHOR]

Abstract: In this paper linear and nonlinear models of spacecraft attitude dynamics equations and gravity gradient moments are investigated. In addition, effects of gravity gradient moments on attitude dynamics of the satellite are studied. The purpose of this paper is to present a comparison between nonlinear and linear models of spacecraft attitude dynamics and gravity gradient moments in order to determine divergence of linear approximation from the nonlinear model. Simulation results indicate that designer of spacecraft attitude control subsystem should be meticulous in applying linear approximation of equations especially in low earth orbits. Consequently, finding an upper bound for small angle to keep the linear model valid and precise enough would be a vital part of using linear approximation. Results supported by numerical examples demonstrate various features of this study. [Copyright &y& Elsevier]

Abstract: We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a malaria transmission model with periodic environment. The basic reproduction number is computed for the model and it is shown that the disease-free periodic solution of the model is globally asymptotically stable when , that is, the disease goes extinct when , while the disease is uniformly persistent and there is at least one positive periodic solution when . It indicates that is the threshold value determining the extinction and the uniform persistence of the disease. Finally, some examples are given to illustrate the main theoretical results. The numerical simulations show that, when the disease is uniformly persistent, different dynamic behaviors may be found in this model, such as the global attractivity and the chaotic attractor. [Copyright &y& Elsevier]

Abstract: Striae distensae, otherwise known as stretch marks, are common skin lesions found in a variety of clinical settings. They occur frequently during adolescence or pregnancy where there is rapid tissue expansion and in clinical situations associated with corticosteroid excess. Heralding their onset is the appearance of parallel inflammatory streaks aligned perpendicular to the direction of skin tension. Despite a considerable amount of investigative research, the pathogenesis of striae remains obscure. The interpretation of histologic samples – the major investigative tool – demonstrates an association between dermal lymphocytic inflammation, elastolysis, and a scarring response. Yet the primary causal factor in their aetiology is mechanical; either skin stretching due to underlying tissue expansion or, less frequently, a compromised dermis affected by normal loads. In this paper, we investigate the pathogenesis of striae by addressing the coupling between mechanical forces and dermal pathology. We develop a mathematical model that incorporates the mechanical properties of cutaneous fibroblasts and dermal extracellular matrix. By using linear stability analysis and numerical simulations of our governing nonlinear equations, we show that this quantitative approach may provide a realistic framework that may account for the initiating events. [Copyright &y& Elsevier]

Abstract: In this paper we consider the problem of gas/liquid extraction near the bottom well in the context of geothermal energy exploitation. In particular we develop a mathematical model for the isothermal two-phase flow of a mono-component fluid in an undeformable porous media taking into account inertial effects. We use the so-called Forchheimer’s equation to model the relation between the fluid velocity and the pressure gradient in the region of co-existence of the two phases. We formulate the problem in cylindrical geometry assuming steady state and isothermal conditions. We take into account capillary pressure and we study its influence on the whole system. We derive important formulas that allow to predict the main thermodynamical quantities in the region of co-existence of the liquid and gaseous phase and we determine constraints on the physical parameters in order to predict the behavior of the fluid in the domain of the problem. Finally, we perform some numerical simulations to investigate the dependence on the physical parameters involved in the model. [Copyright &y& Elsevier]

Abstract: Natural ventilation of buildings refers to the replacement of indoor air with outdoor air due to pressure differences caused by wind and/or buoyancy. It is often expressed in terms of the air change rate per hour (ACH). The pressure differences created by the wind depend – among others – on the wind speed, the wind direction, the configuration of surrounding buildings and the surrounding topography. Computational Fluid Dynamics (CFD) has been used extensively in natural ventilation research. However, most CFD studies were performed for only a limited number of wind directions and/or without considering the urban surroundings. This paper presents isothermal CFD simulations of coupled urban wind flow and indoor natural ventilation to assess the influence of wind direction and urban surroundings on the ACH of a large semi-enclosed stadium. Simulations are performed for eight wind directions and for a computational model with and without the surrounding buildings. CFD solution verification is conducted by performing a grid-sensitivity analysis. CFD validation is performed with on-site wind velocity measurements. The simulated differences in ACH between wind directions can go up to 75% (without surrounding buildings) and 152% (with surrounding buildings). Furthermore, comparing the simulations with and without surrounding buildings showed that neglecting the surroundings can lead to overestimations of the ACH with up to 96%. [Copyright &y& Elsevier]

Abstract: We consider a relatively simple model for pool boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling fluid via a nonlinear boundary condition imposed on the fluid–heater interface. This results in a standard heat equation with a nonlinear Neumann boundary condition on part of the boundary. In this paper, we analyse the qualitative structure of steady-state solutions of this heat equation. It turns out that the model allows both multiple homogeneous and multiple heterogeneous solutions in certain regimes of the parameter space. The latter solutions originate from bifurcations on a certain branch of homogeneous solutions. We present a bifurcation analysis that reveals the multiple-solution structure in this mathematical model. In the numerical analysis a continuation algorithm is combined with the method of separation-of-variables and a Fourier collocation technique. For both the continuous and discrete problem a fundamental symmetry property is derived that implies multiplicity of heterogeneous solutions. Numerical simulations of this model problem predict phenomena that are consistent with laboratory observations for pool boiling processes. [Copyright &y& Elsevier]

This paper discusses the numerical modeling and experimental validation of a 1.2 MW DC transferred plasma torch, which is equipped with a well-type cathode (WTC). In order to investigate the complicated thermal and flow characteristics due to the interaction between the working gas and electric arc, the flow filed inside the plasma torch is modeled by the magnetic–hydrodynamic (MHD) equations. The governing equations are solved numerically using a finite volume discretization for both cold and hot flow simulations. The numerical simulations are then validated by experimental measurements at a specific operation condition. The predicted results successfully reflect some important features of the studied transferred WTC plasma torch. [Copyright &y& Elsevier]

• Mathematical model for coronavirus disease that fits well the spread in China. • New θ -SEIHRD model taking into account undetected infections. • Validation of the model with the reported data on China. • Estimation of errors when identifying parameters at early stages of the pandemic. • Different scenarios to show the impact of undetected cases on the pandemic. In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new θ -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction θ of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. [ABSTRACT FROM AUTHOR]