Non-isothermal Systems Research Articles

Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell–Stefan type

In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell–Stefan structure.

Experimental study on corrosion and precipitation in non-isothermal Pb-17Li system for development of liquid breeder blanket of fusion reactor

The corrosion characteristics of RAFM steel JLF-1 in a non-isothermal Pb-17Li flowing system were investigated by means of the corrosion test using a non-isothermal mixing pot. The corrosion test was performed at 739K with a temperature gradient of 14K for 500 hours. The corrosion tests at a static and a flowing conditions in an isothermal Pb-17Li system were also performed at the same temperature for the same duration with the non-isothermal test. Then, the effect of mass transfer both by the flow and the temperature gradient on the corrosion behaviors was featured by the comparison of these results. The corrosion was caused by the dissolution of Fe and Cr from the steel surface into the flowing Pb-17Li. The specimen surface revealed a fine granular microstructure after the corrosion tests. A large number of pebbleshaped protrusions were observed on the specimen surface. This microstructure was different from the original martensite microstructure of the steel, and might be formed by the influence of the reaction with Li component in the alloy. The formation of the granular microstructure was accelerated by the flow and the temperature gradient. Some pebble-shaped protrusions had gaps at their bases. The removal of these pebble-shaped granules by the flowing Pb-17Li might cause a small-scale corrosion-erosion. The results of metallurgical analysis indicated that a large-scale corrosion-erosion was also caused by their destruction of the corroded layer on the surface. The non-isothermal mixing pot equipped a cold trap by a metal mesh in the low temperature region. The metal elements of Fe and Cr were recovered as they precipitated on the surface of the metal mesh. It was found that a Fe-Cr binary intermetallic compound was formed in the precipitation procedure. The overall mass transfer coefficient for the dissolution type corrosion in the non-isothermal system was much bigger than that in the isothermal system. This model evaluation indicated that the temperature gradient accelerated the corrosion.

Thermal energy storage system operating with phase change materials for solar water heating applications: DOE modelling

Phase change materials have gathered wide acceptance globally due to its effective and economically efficient storage properties. It is emerging to find potential applications in both renewable and fossil energy systems. This paper analyzes the performance and models an experimental design for heat transfer enhancement of a thermal energy storage system by using honey and paraffin waxes. Experiments were conducted in a fabricated thermal energy storage cylindrical tank embedded with copper tubes that in turn filled with these waxes in a liquid state. This non-isothermal system was fabricated to improve the water heat transfer rate from the solar tank unit to waxes in the thermal chamber. The conservation of heat energy was achieved through implementation of this system, this offer a better solution to a conventional storage tank. Performance appraisal of results from experimentation during the processes of charging and discharging of phase change materials has been performed and examined. Good thermal energy storage characteristics of heat transfer, absorption and rejection were observed. The design of experiments modelling work- artificial neural network showed good agreement with experimental results. Mainly, it was found that the factor time has contributed more than 40% of the heat improvement in this storage system during charging and discharging process of paraffin and honey waxes. On the other side, the least number of residuals was observed for the honey wax heat absorption during charging process.

Thermodynamic and morphological characterization of Turing patterns in non-isothermal reaction-diffusion systems.

The effect of temperature on the bifurcation diagram and Turing instability domain under non isothermal conditions is studied in the reversible Gray-Scott model. After adding the energy balance to the cubic autocatalytic model, the thermostat temperature and heat transfer coefficient are used as control parameters in the Turing pattern formation. The patterns obtained in the domain of the thermal parameter are characterized by quantifying the overall entropy generation rate and two topological indices; Shannon entropy and Minkowski functionals. The results show that it is possible to induce transitions between Turing patterns of different morphologies by regulating the temperature, and that these transitions take place at a lower entropy generation value compared to other parameters, such as kinetic constants and reactant fluxes. Finally, a correlation between entropy generation and topological indices shows that a difference between direct and inverse patterns is mainly morphological and not energetic.

Diffusion in dense non-isothermal Coulomb plasma

We generalize our previous work on diffusion of ions in isothermal plasmas to handle non-isothermal systems. This approach, combined with the method of effective potentials for computing diffusion coefficients, allows us to formulate the diffusion problem in Coulomb systems of arbitrary coupling. The results are applied to study heat-blanketing envelopes of neutron stars in diffusive equilibrium.

Development of an equilibrium theory solver applied to pressure swing adsorption cycles used in carbon capture processes

Abstract An equilibrium theory simulator (Esim) for the simulation of cyclic adsorption processes is presented. The equations are solved with a Godunov upwind flux scheme that does not require either the evaluation of characteristics or shock equations or the imposition of a numerical entropy condition to track shocks. Esim is able to simulate non-trace and non-isothermal adsorption systems with any adsorption isotherm. Esim has been validated against gPROMS based simulations that use the full set of governing equations (including mass and heat transfer resistances and axial dispersion) carried out under conditions close to the limits where equilibrium theory is valid. Esim enables the establishment of bounds for the optimal performance of an equilibrium driven separation and requires only the measurement of adsorption isotherms.

Global existence of weak solutions to the non-isothermal nematic liquid crystals in 2D

In this article, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on ▪2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many “singular” times, at which the energy concentration occurs and the director field losses its second order derivatives.

A bulk kinetic, burial history and thermal modeling study of the Albian Kazhdumi and the Eocene-Oligocene Pabdeh formations in the Ahvaz anticline, Dezful Embayment, Iran

The Ahvaz anticline which is located in the middle region of the Dezful Embayment is certainly one of the most important oilfields in Iran. Burial history reconstruction and one-dimensional thermal maturity modeling of the Late Jurassic to Present-day successions have been conducted in the Ahvaz anticline. The petroleum generation bulk kinetic parameters of the Kazhdumi and Pabdeh formations were computed by a non-isothermal open system pyrolysis at different heating rates. Bulk kinetic experiments reveal that a relatively narrow distribution of activation energies, range from 40 to 52kcal/mol for the Kazhdumi samples and from 42 to 54kcal/mol for Pabdeh shales, are directly related to the homogeneity in the organic matter. The principal activation energies of 46kcal/mol and 48kcal/mol, frequency factors of 4.36×10+11s−1 and 1.91×10+12s−1 and hydrogen indexes (HI) of 123 and 351mg/g TOC have been computed for the Kazhdumi and Pabdeh formations, respectively. The lithology composition (percentages of shale, marl, gypsum, limestone and sandstone) of the Late Jurassic-Present formations in the selected wells was determined by using cutting samples and wireline well log data. The computed kinetic parameters and derived lithology composition of strata were applied to thermal maturity modeling. Thermal maturity modeling and burial history reconstruction which is calibrated by vitrinite reflectance data and formation temperature indicate that the palaeo-heat flow ranges from 37mW/m2 to 41mW/m2.The Kazhdumi Formation entered the main stage of oil generation during the Late Miocene (6.5Ma) and the Pabdeh Formation reached early stage of oil window from the Early Pliocene (3.5Ma). Our results provide the bulk petroleum generation kinetic parameters description of the Kazhdumi and Pabdeh formations and demonstrate the thermal maturation state of source rocks, especially the Albian shales, that has been recognized as most important source rock in the Dezful Embayment.

Thermomechanics of damage and fatigue by a phase field model

ABSTRACTIn this paper, we present an isothermal model for describing damage and fatigue by the use of the Ginzburg–Landau (G–L) equation. Fatigue produces progressive damage, which is related with a variation of the internal structure of the material. The G–L equation studies the evolution of the order parameter, which describes the constitutive arrangement of the system and, in this framework, the evolution of damage. The thermodynamic coherence of the model is proved. In the last part of the work, we extend the results of the paper to a nonisothermal system, where fatigue contains thermal effects, which increase the damage of materials.

Thermodynamic Model Formulations for Inhomogeneous Solids with Application to Non-isothermal Phase Field Modelling

Abstract The purpose of the current work is the comparison of thermodynamic model formulations for chemically and structurally inhomogeneous solids at finite deformation based on “standard” non-equilibrium thermodynamics [SNET: e. g. S. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, 1962] and the general equation for non-equilibrium reversible–irreversible coupling (GENERIC) [H. C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley Interscience, 2005]. In the process, non-isothermal generalizations of standard isothermal conservative [e. g. J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial energy. J. Chem. Phys. 28 (1958), 258–267] and non-conservative [e. g. S. M. Allen and J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979), 1085–1095; A. G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983] diffuse interface or “phase-field” models [e. g. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Modern Phys. 49 (1977), 435–479; N. Provatas and K. Elder, Phase Field Methods in Material Science and Engineering, Wiley-VCH, 2010.] for solids are obtained. The current treatment is consistent with, and includes, previous works [e. g. O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D 43 (1990), 44–62; O. Penrose and P. C. Fife, On the relation between the standard phase-field model and a “thermodynamically consistent” phase-field model. Phys. D 69 (1993), 107–113] on non-isothermal systems as a special case. In the context of no-flux boundary conditions, the SNET- and GENERIC-based approaches are shown to be completely consistent with each other and result in equivalent temperature evolution relations.

Diffusive heat blanketing envelopes of neutron stars

We construct new models of outer heat blanketing envelopes of neutron stars composed of binary ion mixtures (H - He, He - C, C - Fe) in and out of diffusive equilibrium. To this aim, we generalize our previous work on diffusion of ions in isothermal gaseous or Coulomb liquid plasmas to handle non-isothermal systems. We calculate the relations between the effective surface temperature Ts and the temperature Tb at the bottom of heat blanketing envelopes (at a density rhob= 1e8 -- 1e10 g/cc) for diffusively equilibrated and non-equilibrated distributions of ion species at different masses DeltaM of lighter ions in the envelope. Our principal result is that the Ts - Tb relations are fairly insensitive to detailed distribution of ion fractions over the envelope (diffusively equilibrated or not) and depend almost solely on DeltaM. The obtained relations are approximated by analytic expressions which are convenient for modeling the evolution of neutron stars.

Wave propagation and strain localization in a fully saturated softening porous medium under the non‐isothermal conditions

The thermo-hydro-mechanical (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium are analyzed. The characteristic polynomial corresponding to the governing equations of the THM system is derived, and the stability analysis is conducted to determine the necessary conditions for stability in both non-isothermal and adiabatic cases. The result from the dispersion analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Meanwhile, the dispersion analysis on the adiabatic case leads to a new analytical expression of the internal length scale. Our limit analysis on the phase velocity for the non-isothermal case indicates that the internal length scale for the non-isothermal THM system may vanish at the short wavelength limit. This result leads to the conclusion that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs. Numerical experiments are used to verify the results from the stability and dispersion analyses. Copyright © 2016 John Wiley & Sons, Ltd.

Assessment of interaction potential in simulating nonisothermal multiphase systems by means of lattice Boltzmann modeling

The pseudopotential lattice Boltzmann model (PP-LBM) is a very popular model for simulating multiphase systems. In this model, phase separation occurs via a short-range attraction between different phases when the interaction potential term is properly chosen. Therefore, the potential term is expected to play a significant role in the model and to affect the accuracy and the stability of the computations. The original PP-LBM suffers from some drawbacks such as being capable of dealing with low density ratios only, thermodynamic inconsistency, and spurious velocities. In this paper, we aim to analyze the PP-LBM with the view to simulate single-component (non-)isothermal multiphase systems at large density ratios and in spite of the presence of spurious velocities. For this purpose, the performance of two popular potential terms and of various implementation schemes for these potential terms is examined. Furthermore, the effects of different parameters (i.e., equation of state, viscosity, etc.) on the simulations are evaluated, and, finally, recommendations for a proper simulation of (non-)isothermal multiphase systems are presented.

Dynamic non-isothermal trickle bed reactor with both internal diffusion and heat conduction: Sugar hydrogenation as a case study

A generic approach was applied to develop a comprehensive Trickle Bed Reactor (TBR) model. The model was based on exact definition of the required equations and development of a program code (in gPROMS ModelBuilder environment) to solve them simultaneously. The model consisted of dynamic mass and energy balances in three phases of heterogeneously catalyzed reaction system. The fluid dynamics was expressed in simple terms (dispersion model, semi-empiric expressions for pressure drop and liquid hold-up) to guarantee a fast running program code. Even though a large number of articles have been published on the topic, only few of these studies penetrate into all details of the system. Most of them focus on the description of few selected physical phenomena. Including most or even all phenomena in a single model is seldom done. Most often, the published reactor models consider two dimensions only, because of mathematical simplicity (i.e. TBR axial and radial coordinates or only TBR axial coordinate and particle radius). Here an attempt was made to present a generic simulation model for tubular reactors working in non-isothermal three-phase systems (gas–liquid–solid) where three dimensions are simultaneously taken into account (TBR axial and radial coordinate and particle radius). All the model development and calculations were made by using the powerful software, which allows solving a large set of partial differential equations and algebraic equations. An example case study of hydrogenation of arabinose to arabitol on a ruthenium catalyst was included.

Non-isothermal modeling of glycerol oxidation reaction and estimation of thermodynamic parameters

The paper presents determination of adiabatic temperature rise during the oxidation of glycerol to glyceraldehyde with hydrogen peroxide in order for estimating its potential hazardous behavior. Estimation of enthalpy of the reaction was carried out by using thermodynamic tables and the bond energy method. The Nonisothermal reaction system for glycerol oxidation was described on the basis of a dynamic modeling proposal, considering the energy balance in the reactor to describe the final stage in the process of glycerol oxidation. The objectives of the present study were determination of the physic-mathematical model for glycerol oxidation, performance of the linearization of the proposed model and determination of transfer function for control purposes.

DNS of Dispersed Multiphase Flows with Heat Transfer and Rarefaction Effects

We propose a method for DNS of particle motion in non-isothermal systems. The method uses a shared set of momentum and energy balance equations for the carrier-and the dispersed phases. Measures are taken to ensure that non-deformable entities (solid particles) behave like rigid bodies. Moreover, deformable entities (e.g. bubbles) as well as rarefaction effects can be accommodated. The predictions of the method agree well with the available data for isothermal solid particles motion in the presence of walls and other particles, natural convection around a stationary particle, solid particles motion accompanied with heat transfer effects and isothermal solid particles motion under rarefied conditions. The method is used to investigate the simultaneous effects of heat transfer and rarefaction on the motion of a solid catalyst particle in an enclosure, the interaction of a solid particle and a microbubble in a flotation cell and a case with more than 1000 particles.

Energy-conserving dissipative particle dynamics with temperature-dependent properties

The dynamic properties of fluid, including diffusivity and viscosity, are temperature-dependent and can significantly influence the flow dynamics of mesoscopic non-isothermal systems. To capture the correct temperature-dependence of a fluid, an energy-conserving dissipative particle dynamics (eDPD) model is developed by expressing the weighting terms of the dissipative force and the random force as functions of temperature. The diffusivity and viscosity of liquid water at various temperatures ranging from 273 K to 373 K are used as examples for verifying the proposed model. Simulations of a Poiseuille flow and a steady case of heat conduction for reproducing the Fourier law are carried out to validate the present eDPD formulation and the thermal boundary conditions. Results show that the present eDPD model recovers the standard DPD model when isothermal fluid systems are considered. For non-isothermal fluid systems, the present model can predict the diffusivity and viscosity consistent with available experimental data of liquid water at various temperatures. Moreover, an analytical formula for determining the mesoscopic heat friction is proposed. The validity of the formula is confirmed by reproducing the experimental data for Prandtl number of liquid water at various temperatures. The proposed method is demonstrated in water but it can be readily extended to other liquids.

Unimolecular Decomposition Pathway for the Vapor-Phase Cracking of Eugenol, A Biomass Tar Compound

To design optimal thermochemical processes for the conversion of biomass into chemicals, fuels, and electrical power, an understanding of the mechanisms for the secondary vapor-phase cracking of tar compounds is crucial. Despite the many studies examining the homogeneous secondary cracking of biomass tar existing in the literature, its thermal decomposition reaction pathways are not completely understood. Much of this lack of understanding is due to the complex, heterogeneous nature of biomass tar. A useful approach is to examine the pyrolysis of model-fuel compounds that are actual components or are representative of compounds found in biomass tar. In this study, we focus on eugenol, a model-fuel compound representative of the lignin-derived components found in biomass tar. We conduct pyrolysis experiments at temperatures of 300–900 °C and one second residence time using a non-isothermal laminar-flow reactor system. We report the variation in the experimental yield of light product gases as functions of the reactor temperature. We examine a reaction pathway for the unimolecular decomposition of eugenol with consideration of the experimental product distributions and analogous reactions based on established decomposition mechanisms of similar compounds. We examine the detailed energetics of the unimolecular decomposition route using computational chemistry calculations at the B3LYP/6-311G+(d,p) level of theory. The results presented in this study would be of relevance to the pyrolysis, gasification, and combustion of biomass.

Superplastic-like forming of Ti-6Al-4V alloy

Superplastic forming of titanium alloys is used for producing structural components, since it is an effective way to manufacture complex-shaped parts in a one-step operation. An optimized sheet-forming process has been designed incorporating a non-isothermal heating system to establish a fast forming process. This work sought to expand the advantages of the technology to the forming of Ti-6Al-4V alloy at 800 °C and shorter cycle time. The minimum thicknesses area was found at the outward corners, showing a maximum percent thinning of 54 %. In addition to stress variations, the cracks resulting from hot drawing and the oxidation on the sheet surface are the other reasons leading to thickness reduction. From the oxidization behavior of Ti-6Al-4V alloy, it was revealed that the decrease in forming temperature from 900 to 800 °C significantly reduced the formation rate of oxide film on the sheet surface. The study also showed that the main microstructure evolution of Ti-6Al-4V alloy under these conditions was recrystallization.

Selection criterion of stable dendritic growth at arbitrary Péclet numbers with convection

A free dendrite growth under forced fluid flow is analyzed for solidification of a nonisothermal binary system. Using an approach to dendrite growth developed by Bouissou and Pelcé [Phys. Rev. A 40, 6673 (1989)], the analysis is presented for the parabolic dendrite interface with small anisotropy of surface energy growing at arbitrary Péclet numbers. The stable growth mode is obtained from the solvability condition giving the stability criterion for the dendrite tip velocity V and dendrite tip radius ρ as a function of the growth Péclet number, flow Péclet number, and Reynolds number. In limiting cases, the obtained stability criterion presents known criteria for small and high growth Péclet numbers of the solidifying system with and without convective fluid flow.