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In the state of the art of steel production, the temperature evolution of steel strips is typically controlled to regulate the phase contents indirectly and, with this, their material properties. This paper proposes a novel computationally efficient, real-time capable dynamic model that captures both the temperature evolution and the phase transformations in the steel strip. The steel strip is processed in a cooling section after a continuous annealing furnace. The phase transformations cover the austenite decomposition which is mainly controlled by specifically decreasing the temperature during the cooling process. For this, a phenomenological state-space model is derived, which is inspired by the Johnson-Mehl-Avrami-Kolmogorov and the Koistinen-Marburger model. Phase transformations generally change the specific latent heat of the material, which is captured in the proposed distributed-parameter model of the strip temperature by an energy balance. Lumped-parameter models are used for the temperature evolution of the wall, the rolls, and the radiant tubes. Heat transfer due to convection, radiation, and conduction couple the individual thermal submodels. A comparison of simulation results and measurements from both experimental material tests and the real plant operation demonstrate the accuracy and feasibility of the proposed model. The model is computationally inexpensive and serves as a solid basis for advanced real-time control and optimization. • A mathematical model is proposed to describe the evolution of temperature and phases in a steel strip during cooling. • The austenite decomposition is captured by a phenomenological phase transformation model. • The model is computationally efficient and real-time capable. • The accuracy and the suitability of the proposed model is demonstrated by comparing simulation results with measurements. [ABSTRACT FROM AUTHOR]

In this paper the aerothermal heating of a reusable launch vehicle is reconstructed on the basis of temperature measurements taken in the thermal protection system of this vehicle. The discussed integrated thermal protection system is composed of three layers. Mathematical model, describing the problem, takes into account the dependence on temperature of the material parameters as well as the thermal resistances occurring in the contact zones of the layers, which is a novelty in the proposed approach. For solving the direct problem, the implicit scheme of the finite difference method is applied. Next, by using the solution of the direct problem, the Tikhonov functional is created, which describes the error of the current approximate solution. Whereas for determining the solution of the inverse problem the Levenberg-Marquardt method, modified and adapted to the Tikhonov functional, is used. The paper presents the mathematical model of the problem and the method of solution together with the selected examples illustrating its exactness and stability. In order to better examination of the solution method some various values of parameters are taken in the demonstrated examples. • Reconstructing an aerothermal heating in space vehicle protection system with temperature dependent material properties. • Reconstructing an aerothermal heating taking into account the thermal resistance between layers. • Solving the problem for three layers model of the thermal protection system. • Inverse problem solved for input data taken from NASA measurements. • Heat flux measured by NASA reconstructed with good precision and stability. [ABSTRACT FROM AUTHOR]

Experimental data demonstrates that the breakthrough curves of column adsorption exhibit qualitative differences related to the size of the adsorbent particles. Standard models do not account for particle size, consequently, in this paper we develop a new formulation that incorporates the diffusion of the adsorbate into the adsorbent particles. Two kinetic models are considered, Langmuir adsorption and a linear driving force. Approximate analytical solutions are developed for these two models coupled to mass flow and intra-particle diffusion equations. The accuracy of the analytical solutions is verified through comparison with numerical solutions of the full mathematical model. Comparison with experimental data confirms that the new analytical solutions show better agreement than previous models. However, in certain cases, neither form of model predicts the behaviour suggesting a combination of different effects contribute to the breakthrough form. • Mathematical model for column adsorption including particle size effect. • Simple analytical expressions for breakthrough concentration. • Good agreement with a variety of experimental data. [ABSTRACT FROM AUTHOR]

• Analytical solution describing fluid extraction from an adsorption column. • Excellent agreement with a range of experimental data. • Proof that previous accepted models do not work. • Demonstration that to accurately characterise experiments both breakthrough and isotherm data are required. • Development of a novel analytical solution including a SIPS mass sink. In this paper we investigate the standard one-dimensional model for adsorption of a contaminant in a packed column. Initially we focus on two mass sink models: a full nonlinear Langmuir equation, including adsorption and desorption and the linearised version which neglects the local concentration. Travelling wave solutions are developed for both cases, providing exact analytical formulae for the concentration and adsorbed fraction throughout the column. Comparison is made with experimental data for the adsorption of toluene on activated carbon (dominated by physical adsorption) and Cr(III) on zeolite NaX (dominated by ion exchange). For toluene the nonlinear model provides good agreement but it is less accurate for Cr(III). The linear model apparently works well for Cr(III) but only at the expense of violating the model assumptions. This motivates extending the travelling wave solution to a Sips sink model, which has a power law dependence on local concentration. Comparison with data provides excellent agreement in all cases and also indicates why the previous models fail. Following from the investigation of the linear sink model, we prove that previously accepted results frequently fail due to a violation of assumptions made in their derivation. Specifically we challenge the belief that widely used models such as Bohart–Adams, Yoon–Nelson, Bed Depth Service Time, etc can accurately predict breakthrough data. Their success instead may be attributed to: at times, having a similar shape to the breakthrough curve rather than being the correct solution; treating measurable quantities as fitting parameters and a willingness to accept that constant parameters vary. In contrast to these previous models, the travelling wave solution of the present paper, based on a Sips sink, provides analytical solutions consistent with the model assumptions for a wide range of experimental data. [ABSTRACT FROM AUTHOR]

• The thermodynamic compatibility of initial conditions is investigated. • Analytical solutions of the Guyer-Krumhansl equation is provided. • The maximum principle for the Guyer-Krumhansl equation is proved. • The results are supported by computational calculations. In the literature, one can find numerous heat conduction models with different backgrounds. In general, a heat equation beyond Fourier consists of additional time and spatial derivatives, which makes it more challenging to solve the mathematical model correctly. In the present paper, we revisit the famous Guyer-Krumhansl heat equation for which it has been reported earlier that can lead to negative temperatures by violating the maximum principle. We show that for proper initial and boundary conditions with thermodynamic compatibility, the maximum principle is fulfilled. Our work further emphasizes the importance of the thermodynamic origin of heat equations and their compatibility with the second law. Furthermore, we use two different approaches how to determine the initial state in a thermodynamically compatible way. Computational simulations support our results. [ABSTRACT FROM AUTHOR]

• The application of the cold plate device to thermal management has evolved in the past fifty years from the cooling of computer chips to aviation thermal management, which is the application of interest in this paper. Numerical solution procedures for performance analysis of the device are currently being used in a commercial software package for automotive and aviation thermal management. A major objective of the present paper is to report on an elaborate and successful experimental work carried out at The Boeing Aerospace company for the purpose of validating the software package. For this purpose, powder fusion additive manufacturing (AM) procedures were used to build metallic cold plate test articles. The excellent agreement between the software predictions and measured performance provides confidence in the implementation of the software package. Additional relevant results are provided in the paper on the thermalhydraulic performance analysis of cold plates for aviation thermal management. This study, which has been motivated by the recent applications of the cold plate device in aviation thermal management, reports on physics-based mathematical models derived from the conservation laws of mass, momentum, and energy, and empiricism-based models. One of the objectives of the present work is to report on an elaborate and successful experimental work carried out on an additively manufactured device for the purpose of rigorously validating the numerical predictions. The excellent agreement between the numerical predictions and measured performance provides much needed confidence in the implementation, in the software package, of the offset-strip fin passage correlations, as well as in the software implementation of user-defined wavy fin correlations for aerospace heat exchangers and cold plates operating with ram air at Reynolds numbers below 8000. The contributions of this work can also be found in the development of a new and accurate thermal-hydraulic analysis procedure, referred to in this paper as plate-fin analogy. Results from this procedure are compared with those from thermal resistance network. The comparative study in this paper of the bulk and discrete enthalpy flux method is also new, as is the relative assessment of four off-set strip fin thermal-hydraulic models. [ABSTRACT FROM AUTHOR]

• Normal mode stability analysis performed on counjugate heat transfer (CHT) 1D problem. • Stability analysis reveals existence of lower stability bound for coupling coefficient in Robin-Dirichlet interface boundary conditions. • Validity of stability analysis results is verified empirically. • Stability analysis is extended to more general CHT problems. This paper aims to evaluate and validate a mathematical coupling model, based on a normal mode stability analysis, for steady conjugate heat transfer problems. In order to achieve this goal, an aerothermal computational code was designed specifically ex novo to meet the needs of the current study. A large number of numerical simulations were carried out within the framework of the Dirichlet-Robin fluid-solid interface procedure and with conditions strictly identical to those adopted in the mathematical model. These coupled computations have been synthesized in five representative cases. The computed results show that the stability limit and the numerical Biot number derived from the coupling model are very reliable parameters. Many other physical and numerical aspects, such as the splitting of the coupling period are also considered in this work from which some interesting and promising results are obtained. At the end of this paper, we assess the general potential, limits and constraints of the mathematical model and its extension to multidimensional cases is discussed. [ABSTRACT FROM AUTHOR]

• A mathematical model based on non-equilibrium formulation was established. • The simulation results show better accordance with the experimental results compared with the model based on equilibrium formulation. • The heat and mass transfer during the drying stage were analyzed. • The effects of different operating parameters on the drying time were investigated. Spray freeze drying has been expanding its influence in many fields. However, the long duration dramatically hinders its further development. A model established based on non-equilibrium formulation was established in this paper. The accuracy of the model proposed with that established based on equilibrium formulation was compared. And the history of temperature, vapor concentration and ice saturation were then investigated. Lastly, the effects of product thickness, particle diameter on the drying time were investigated. The simulation results reproduce well with the experimental data, and show a better agreement with the increase rate of experimentally measured temperature curve than that based on equilibrium formulation. In addition, the temperature increases from the bottom to the top region while the vapor concentration distribution presents the opposite trend. The ice saturation first obtains a slight increase and then decreases. Lastly, the drying time decreases as: (i) the product thickness decreases, (ii) the packing porosity increases and (iii) the chamber temperature increases. The mathematical model proposed in this paper could offer better understanding of the process and guide the design and optimization for the process. [ABSTRACT FROM AUTHOR]

• The desirable operating conditions to achieve high operational efficiency are obtained. • The performance of the IEC under different operating conditions is investigated. • The mathematical model is validated against published data. • The optimal dimensions that give good efficiency in climates with moderate humidity are highlighted. [Display omitted] This paper presents a study investigating and analyzing the effect of heat and mass exchanger (HMX) dimensions and the flow parameters on the indirect evaporative cooler (IEC) system's performance. For this purpose, a mathematical model based on heat and mass transfer concepts was developed, and the model was verified using experimental and simulation results from published papers. Simulations were performed based on different operating and structural conditions affecting the outlet air temperature, cooling capacity, coefficient of performance, and wet-bulb efficiency. Results showed that the optimal dimensions that give good efficiency in climates with moderate humidity, the length of the duct should be between 0.6 to 1.0 m , the width of the channel between 0.3 to 0.5 m , and the channel gap between 0.004 to 0.008 m. It has also been observed that the increasing working air velocity has a positive effect on cooling performance, and its velocity should not be less than 1 m / s. As for increasing the product air velocity, it reduces the heat exchange period, which is undesirable, so it should not exceed 1 m / s. The prescribed flow rate ratio between product and working air should be 0.3 to 0.5. This analysis provides desirable operating conditions to achieve high operational efficiency as well as optimal dimensions for designing such a cooler. [ABSTRACT FROM AUTHOR]

• The mathematical model is useful for analyzing the heat exchanger performance. • The most probable variant of heat exchanger operation is established. • There is a risk of frost accumulation within the fixed-bed regenerator. The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established. [ABSTRACT FROM AUTHOR]

• Mathematical models of ion transport through specific ion channels are discussed. • Various mathematical kinetic models for specific membrane carriers are presented. • Models of electrical fluxes carried by symporters, antiporters, and pumps are presented. • This work provides tools for simulation of ion transport across the cell membrane. Mathematical modeling of membrane transporters and ion channels helps researchers obtain a thorough understanding of the complex regulation process between membrane transporters, estimate the changes and uncertainties of their mechanisms, and study how disorders in these procedures may cause disease. A unified mathematical framework that includes most available models for ion channels and transporters can help scientists choose the appropriate model more conveniently. In this regard, this work presents a comprehensive, up-to-date set of currently available mathematical equations for modeling ion channel and membrane transporter mechanisms. This paper aims to provide a mathematical framework for modeling molecule transport, such as nutrients, inorganic ions, drugs, and toxins, across the cell through membrane transporters and ion channels. Our purpose is to substantially save the time and resources needed to find the mathematical models available for different classes of membrane transporters and improve communication between scientists with different backgrounds interested in this field. [ABSTRACT FROM AUTHOR]