Non-isothermal Temperature Research Articles

Apparent kinetics of nonisothermal high temperature oxidative degradation of ethylene homopolymers: effects of residual catalyst surface chemistry and structure

The effects of two supported residual catalysts—one Ziegler-Natta and another metallocene—on the nonisothermal thermooxidative degradation of the resulting ethylene homopolymers were investigated using TGA experiments and kinetic modeling. The rigorous constitutive kinetic model (developed in this study), unlike the analytical Horowitz and Metzger model, fitted very well to the entire TGA curve, without distribution of activation energy Ea, for n (overall degradation order) = 1 for both polymers. Neither n nor Ea varied as a function of fractional weight loss of the polymer. Hence, the proposed unified molecular level concept of surface chemistry and structure of the residual catalysts held all through the degradation process. The above feature of n and Ea also indicates the suitability of the model formulation and the effectiveness of the parameter-estimation algorithm. Random polymer chain scission, with the cleavage of the −C−C− and the −O−O− (hydroperoxide) bonds, prevailed. The types of residual catalyst surface chemistry and structure varied the bond cleavage process. The metallocene Zr residual catalyst caused more thermooxidative degradation in MetCat HomoPE than what the Ti one did in Z-N HomoPE. The rigorous constitutive model-predicted apparent kinetic energy Ea, and frequency factor Z also support this finding. The proposed degradation mechanism suggests that the Zr residual catalyst more (i) decreased the activation energy required to decompose the −C−C− and the −O−O− bonds, and (ii) eliminated β-hydrogen (by the carbonyl functionalities) from the polymer chains. These findings were attributed to the differences in surface chemistry and structure of the residual catalysts. Therefore, the current study presents a rigorous constitutive kinetic model that duly illustrates the influence of the characteristic surface chemistry and structure of the residual catalysts on the high temperature oxidative degradation of polyethylenes.

CURE SIMULATION OF LARGE RUBBER COMPONENTS: A COMPARISON OF COMPRESSION AND EXTRUSION MOLDING

ABSTRACT Curing rubber is a complex process that involves the insertion of cross-links to convert the rubber into a useful functional material. The estimation of the cure time needed for product manufacture of small or thin walled products is often arrived at by means of a rheometer trace. Although this has been recognized as adequate for thin walled products, the production of large rubber articles requires a more rigorous analysis of cure kinetics for an essentially non-isothermal process. Often finite element analysis is used to generate non-isothermal temperature histories in a thick component, and then an appropriate cure kinetic equation is solved to predict the state of cure. In addition to generating the capability for cure time prediction, there is a need in the industry to minimize cycle time, improving productivity and therefore costs involved in product manufacture. For large products, the viability of the use of extrusion molding, where the rubber is extruded into a heated mold at the same temperature as the mold, has been demonstrated in previous reported work in this laboratory. The present work explores, via simulation, the feasibility of using extrusion molding as a manufacturing method for large components. The cure simulation module of Autodesk Moldflow has been used to compare the state of cure of a laminated bearing manufactured by conventional compression molding and extrusion molding. Previous experimental data on the temperature histories of a large laminated bearing manufactured using compression molding are compared with simulation data. Simulation data are then presented on manufacturing the bearing using extrusion molding. The aim is to demonstrate the usefulness of extrusion molding for very large components and to illustrate the advantages of using simulation codes to assist in shortening the cycle time in product manufacture.

ESTIMATION OF THE THERMOCHEMICAL NONISOTHERMAL INACTIVATION BEHAVIOR OF BACILLUS COAGULANS SPORES IN NUTRIENT BROTH WITH OREGANO ESSENTIAL OIL

The aim of this work was to validate the prediction of the nonisothermal thermochemical inactivation of Bacillus coagulans spores in nutrient broth, adjusted to 4 °Brix and pH 4.2, with 400 ppm of oregano essential oil (EO), using the Weibull dynamic model proposed by Peleg. First, the spores were heat treated at four constant temperatures. Afterwards, empirical secondary models were employed to describe the influence of temperature on the primary parameters. Finally, primary and secondary models were used to simulate microorganism inactivation under two nonisothermal temperatures, ranging from 90 to 95C every 1 min; and from 90 to 95C for 5 min at each temperature. Even if a limited experimental data was employed for the nonisothermal analysis, it appears that the proposed model can be used to estimate the nonisothermal inactivation of B. coagulans spores in nutrient broth with 400 ppm of oregano EO.

Computational analysis of non-isothermal temperature distribution on natural convection in nanofluid filled enclosures

In this study, the problem of steady state natural convection in an enclosure filled with a nanofluid has been analyzed numerically by using heating and cooling by sinusoidal temperature profiles on one side. The governing partial differential equations, in terms of the dimensionless stream function–vorticity and temperature, are solved numerically using the finite volume method for various inclination angles 0 ∘ ≤ ϕ ≤ 9 0 ∘ , different types of nanoparticles (TiO 2 and Al 2O 3) and fractions of nanoparticles 0 ≤ φ ≤ 0.1 , whereas the range of the Rayleigh number Ra is 10 3–10 5. It is found that the addition of nanoparticles into water affects the fluid flow and temperature distribution especially for higher Rayleigh numbers. An enhancement in heat transfer rate was registered for the whole range of Rayleigh numbers. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers.

On the ability of the spectroscopic Sunyaev-Zeldovich effect measurements to determine the temperature structure of galaxy clusters

(abridged) We explore in this paper the ability of spatially resolved spectroscopic measurements of the SZ effect (SZE) to determine the temperature profile of galaxy clusters. We derive a general formalism for the thermal SZE in galaxy clusters with a non-uniform temperature profile that can be applied to both cool-core clusters and non-cool core cluster with an isothermal or non-isothermal temperature structure. We derive an inversion technique through which the electron distribution function can be extracted from spectroscopic SZE observations over a wide frequency range. We study the fitting procedure to extract the cluster temperature from a set of simulated spatially resolved spectroscopic SZE observations in different bands of the spectrum, from 100 to 450 GHz. The results of our analysis for three different cluster prototypes (A2199 with a low-temperature cool core, Perseus with a relatively high-temperature cool core, Ophiuchus with an isothermal temperature distribution) provide both the required precision of the SZE observations and the optimal frequency bands for a determination of the cluster temperature similar or better than that obtainable from X-ray observations. The precision of SZE-derived temperature is also discussed for the outer regions of clusters. We also study the possibility to extract, from our method, the parameters characterizing the non-thermal SZE spectrum of the relativistic plasma contained in the lobes of radio galaxies as well as the spectrum of relativistic electrons co-spatially distributed with the thermal plasma in clusters with non-thermal phenomena. We find that the next generation SZE experiments with spectroscopic capabilities can provide precise temperature distribution measurements (...)

Simulation of cottonseed cake melt flow in metering zone of a single screw extruder

Research on the extrusion of natural polymers (food, feed, etc.) is relatively new due to the complex physicochemical transformations of raw materials, although plastics melt conveying and transport have been well studied. The structure and composition, rheological behavior as well as extrusion processing of natural polymer are much more complicated. In this study, a quasi-three-dimensional (3D) fluid flow model for non-Newtonian, non-isothermal and undeveloped temperature was developed, the model prediction being in reasonably good agreement with the experiment. Results show that the influence of moisture content, among other process variables, is the most significant, followed by screw speed. Some interaction exists between these two variables and the screw speed effect becomes marginal at high moisture contents. In addition, viscosity change in the channel was studied.

Long-term creep of polyphenylene sulfide (PPS) subjected to complex thermal histories: The effects of nonisothermal physical aging

The long-term viscoelastic behavior of polymeric materials used below the glass transition temperature ( T g ) is greatly affected by physical aging. In contrast to isothermal physical aging, long-term response under nonisothermal history has received far less attention. This paper reports experimental results and analytical methods of long-term creep behavior of polyphenylene sulfide (PPS) subjected to complex thermal histories in a temperature range below T g . To characterize the effects of aging, creep tests were performed using a dynamic mechanical analyzer (DMA). Besides the long-term data, short-term creep tests in identical thermal conditions were also analyzed; these were utilized with effective time theory to predict long-term response under both isothermal and nonisothermal temperature histories. The long-term compliance after a series of temperature changes was predicted by the effective time theory using the KAHR- a te model to obtain nonisothermal physical aging shift factors. Comparison of theoretical predictions with experimental data shows good agreement for various thermal histories.

Concentration Dependence of Crystalline Poly(L-lactide) Prepared by Freeze-drying Solutions

Poly(L-lactide) was freeze-dried from p-xylene solutions with varying concentrations. The samples were characterized by differential scanning calorimetry. It was found that the sample produced from the dilute solution exhibited higher non-isothermal crystallization temperature and faster crystallization rate. There was a critical concentration corresponding with the critical overlap concentration proposed by De Gennes in the polymer solutions. In the solution below the critical concentration, the PLLA chains were isolated from each other, resulting in an acceleration of melt crystallization for the recovered samples. It appears that the chain entanglement is a barrier to the melt crystallization of polymer.

VERTICAL STRUCTURE IN PLUTO'S ATMOSPHERE FROM THE 2006 JUNE 12 STELLAR OCCULTATION

Pluto occultations are historically rare events, having been observed in 1988, 2002, 2006, and, as Pluto moves into the crowded Galactic plane, on several occasions in 2007. Here we present six results from our observations of the 2006 June 12 event from several sites in Australia and New Zealand. First, we show that Pluto's 2006 bulk atmospheric column abundance, as in 2002, is over twice the value measured in 1988, implying that nitrogen frost on Pluto's surface is 1.2-1.7 K warmer in 2006 than 1988 despite a 9% drop in incident solar flux. We measure a half-light shadow radius of 1216 ± 8.6 km in 2006, nominally larger than published values of 1213 ± 16 km measured in 2002. Given the current error bars, this latest half-light radius cannot discriminate between continued atmospheric growth or shrinkage, but it rules out several of the volatile transport scenarios modeled by Hansen & Paige. Second, we resolve spikes in the occultation light curve that are similar to those seen in 2002 and model the vertical temperature fluctuations that cause them. Third, we show that Pluto's upper atmosphere appears to hold a steady temperature of ~100 K, as predicted from the methane thermostat model, even at latitudes where the methane thermostat is inoperative. This implies that energy transport rates are faster than radiational cooling rates. Fourth, this occultation has provided the first significant detection of a non-isothermal temperature gradient in Pluto's upper atmosphere also reported by Elliot et al., possibly the result of CO gas in Pluto's upper atmosphere. Fifth, we show that a haze-only explanation for Pluto's light curve is extremely unlikely; a thermal inversion is necessary to explain the observed light curve. And sixth, we derive an upper limit for the haze optical depth of 0.0023 in the zenith direction at average CCD wavelengths.

Gelation Crystallization of Poly(L-Lactide) in Solvents of Varying Molecular Size

The crystallization behaviour of poly(L-lactide) (PLLA) samples prepared in large-molecule solvents, such as poly(ethylene glycol) (PEG), was studied by differential scanning calorimetry (DSC) and X-ray diffraction. The results indicate that those samples recovered from large-molecule solvents exhibit higher crystallinity, non-isothermal crystallization temperature and faster crystallization rate than the ones crystallized in a small-molecule solvent. The crystallinity of samples from PLLA/PEG gel is about 73% measured by the DSC. The molar size of the solvent has a large influence on the formation of helical conformations and, thereby on the crystallization rate of PLLA in solution.

Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations

A mathematical analysis has been carried out on momentum and heat transfer characteristics in an incompressible electrically conducting viscoelastic boundary layer fluid flow over a linear stretching sheet. Momentum boundary layer equation takes into account the effect of transverse magnetic field and electric field. Thermal boundary layer equation takes into account the viscous dissipation and Ohmic dissipation due to transverse magnetic field and electric field. Highly non-linear momentum boundary layer equation and thermal boundary layer equation are converted into similarity equations and then solved numerically by employing fifth order Runge–Kutta–Fehlberg method with shooting. The results are analysed for the situation when stretching boundary is prescribed by non-isothermal temperature, namely, prescribed surface temperature (PST) which varies quadratically with the flow directional coordinate x. The effects of various physical parameters like viscoelastic parameter, Prandtl number, local Reynolds number, Eckert number Hartmann number and electric parameter on various momentum and heat transfers characteristics are analysed. Some of the important findings of this paper are (i) The combined effect of increasing the values of local Reynolds number Rex and local electric parameter (E1) is to decrease skin-friction coefficient Cf largely. (ii) In presence of magnetic field the effect of electric field is to decrease temperature near the stretching boundary and increase the same significantly away from the stretching sheet. (iii) If electric field is present and the Prandtl number is lower then there would be a significant decrease of temperature near the boundary sheet in case of viscoelastic fluid. (iv) The presence of electric field reverses the direction of heat transfer on the boundary stretching sheet more significantly in case of viscoelastic fluid.

A Study of Diffusion- and Interface-Controlled Migration of the Austenite/Ferrite Front during Austenitization of a Case-Hardenable Alloy Steel

Migrating austenite/ferrite interfaces in the ferrite regions of an alloy steel, containing 0.20 wt pct C, 0.87 wt pct Mn, and 0.57 wt pct Cr, with a ferrite/pearlite microstructure have been observed during austenitization by a high-temperature confocal scanning laser microscope in order to determine the mechanisms of transformation. The samples were subjected to isothermal (790 °C to 850 °C) and nonisothermal (0.5 °C to 20 °C/s) temperature profiles. The kinetic rates extracted from the observations were compared to models for long-range diffusion-controlled and interface reaction-controlled migration. The transition between the two mechanisms was found to occur at T 0, which defines the temperature and composition at which a partitionless phase transformation is possible. Occurrence of the partitionless, interface-controlled transformation was confirmed by an analysis of carbon distribution and microstructure before and after a sample was subjected to a particular thermal profile. The mobility of such interfaces was found to be in the range 1.6·10−13 to 2·10−12 m4·J−1·s−1, which is consistent with previous studies on interface-controlled migration of the reverse reaction, α to γ, during cooling of dilute substitutional iron alloys. The diffusion-controlled migration, at temperatures below T 0, was found to occur in two stages: an initial stage, at which the growth rate can be predicted by a semi-infinite diffusion model; and a second stage, at which the growth slows more rapidly, possibly due to the overlap of diffusion fields.

Prediction of vitamins loss during non-isothermal heat processes and storage with non-linear kinetic models

Abstract The isothermal degradation kinetics of vitamins in stored and heated foods can be described by the Weibullian–power law model, C ( t ) / C 0 = exp [ − b ( T ) t n ] and the temperature dependence of b(T) by the log logistic equation, b ( T ) = log e { 1 + exp [ k ( T − T c ) ] } . The resulting three degradation parameters, n, Tc and k, can be used to predict the vitamins' degradation patterns under a variety of non-isothermal temperature histories, using a rate model that unlike the traditional Arrhenius and log linear model does not require that the logarithmic degradation rate must be only a function of temperature and hence time independent. Instead, the described model has been constructed on the assumption that the momentary logarithmic degradation rate is the isothermal rate at the momentary temperature, at a time that corresponds to the vitamin's momentary concentration. In all the examined cases, the proposed model's predictions were in agreement with the experimental observations.

Multi‐Objective Optimization of a Batch Copoly(ethylene‐polyoxyethylene terephthalate) Reactor Using Different Adaptations of Nondominated Sorting Genetic Algorithm

AbstractSummary: A multi‐objective optimization is carried out for a copoly(ethylene‐polyoxyethylene terephthalate) (CEPT) batch reactor using different adaptations of the elitist nondominated sorting genetic algorithm (NSGA‐II). Several two objective function problems are formulated and solved. One objective is to minimize the total copolymerization time and other objective is to minimize the formation of total undesirable side products, namely, acid end group, vinyl ester end group, diethylene glycol ester end group of polyethylene terephthalate, and diethylene glycol. End‐point constraint is incorporated to obtain the specified number‐average degree of copolymerization. The operating temperature history of batch CEPT reactor is the only important decision variable for first optimization problem, whereas operating temperature history and molar ratio of feed to the reactor are taken as decision variables for the second optimization problem. Optimal Pareto frontiers are obtained for both the problems studied. In order to operate the polymerization reactor optimally, it is found that higher isothermal temperature history is needed for short copolymerization time, whereas lower nonisothermal temperature history is required for higher copolymerization time. The results of NSGA‐II technique are analyzed and compared with the jumping gene (JG) and adapted jumping gene (aJG) operator in NSGA‐II separately. It is found that NSGA‐II‐JG is superior to NSGA‐II and NSGA‐II‐aJG.Optimization of a batch copoly(ethylene‐polyoxyethylene terephthalate) reactor.magnified imageOptimization of a batch copoly(ethylene‐polyoxyethylene terephthalate) reactor.

Estimating non-isothermal bacterial growth in foods from isothermal experimental data

To develop a mathematical method to estimate non-isothermal microbial growth curves in foods from experiments performed under isothermal conditions and demonstrate the method's applicability with published growth data. Published isothermal growth curves of Pseudomonas spp. in refrigerated fish at 0-8 degrees C and Escherichia coli 1952 in a nutritional broth at 27.6-36 degrees C were fitted with two different three-parameter 'primary models' and the temperature dependence of their parameters was fitted by ad hoc empirical 'secondary models'. These were used to generate non-isothermal growth curves by solving, numerically, a differential equation derived on the premise that the momentary non-isothermal growth rate is the isothermal rate at the momentary temperature, at a time that corresponds to the momentary growth level of the population. The predicted non-isothermal growth curves were in agreement with the reported experimental ones and, as expected, the quality of the predictions did not depend on the 'primary model' chosen for the calculation. A common type of sigmoid growth curve can be adequately described by three-parameter 'primary models'. At least in the two systems examined, these could be used to predict growth patterns under a variety of continuous and discontinuous non-isothermal temperature profiles. The described mathematical method whenever validated experimentally will enable the simulation of the microbial quality of stored and transported foods under a large variety of existing or contemplated commercial temperature histories.

Steady 2D prominence-like solutions of the MHD equations with field-aligned compressible flow

An exact two-dimensional solution of the ideal magnetohydrodynamic (MHD) equations with compressible flow in a uniform gravitational field is presented and applied to solar prominences. The solution is constructed via a systematic nonlinear separation of variables method used to calculate several classes of MHD equilibria in Cartesian geometry and uniform gravity. This simple model of steady plasma flow along the dipped field lines of a solar prominence is the first 2D MHD model with a nonisothermal temperature distribution which selfconsistently also examines the required heating. Although the model is 2D, a third magnetic/velocity vector field component is included and the highly sheared fields observed in prominences are reproduced. A description is given of the balance of gas pressure gradient, gravity, Lorentz and inertial forces acting along and across the prominence. It is found that the flow may significantly influence the energy balance as in a similar application of this class of solutions to solar coronal loops.

Optimization of the active component distribution through the catalyst bed

A variational problem was formulated to determine the optimal axially non-uniform catalyst activity distribution along the fixed catalyst bed. It was observed that the mass transport limitations or non-isothermal temperature profile are necessary conditions for potential optimization of the catalyst distribution along the bed length. Under isothermal conditions with linear dependence of the reaction rate on concentration at a constant mass transfer coefficient, the uniform distribution is optimal. Analytical solution for the first-order reaction and numerical solutions for power-law kinetics were found.

Characterisation and modelling of precipitate evolution in an Al–Zn–Mg alloy during non-isothermal heat treatments

This paper describes the response of a precipitate microstructure to various types of non-isothermal temperature changes, namely reversion, ramp heating and thermal cycles, met in heat-affected zones (HAZs) of arc-welds, in an Al–Zn–Mg alloy in the T6 and T7 states. During these thermal histories, the precipitate size and volume fraction are quantitatively measured by small-angle X-ray scattering (SAXS). Reversion experiments are characterised by a fast dissolution stage at almost constant average precipitate size, followed by a coarsening stage that affects the surviving precipitates. Ramp heating experiments show a dissolution behaviour, which is temporarily interrupted for low heating rates, either due to phase transition when the initial precipitates are of a metastable nature (the case of T6 initial state), or due to a dynamic competition between the average and critical radii during the temperature increase (the case of the T7 material). The HAZ of arc-welds is characterised by a gradual increase of the dissolved precipitate fraction as one gets closer to the weld line. In the zone immediately before complete dissolution, precipitate coarsening is observed. A simple model, based on the growth/dissolution of precipitates distributed in size classes, has been adapted to the present ternary alloy. This model, calibrated using the reversion experiments, has proven its predictive nature in all the other thermal cycles investigated (ramp heating and welding). The predictions of the model are used in order to improve the physical insight into the range of material behaviour observed in the experiments.

Catalytic combustion over platinum group catalysts: fuel-lean versus fuel-rich operation

Performance data are presented for methane oxidation on alumina-supported Pd, Pt, and Rh catalysts under both fuel-rich and fuel-lean conditions. Catalyst activity was measured in a micro-scale isothermal reactor at temperatures between 300 and 800 °C. Non-isothermal (near adiabatic) temperature and reaction data were obtained in a full-length (non-differential) sub-scale reactor operating at high pressure (0.9 MPa) and constant inlet temperature, simulating actual reactor operation in catalytic combustion applications. Under fuel-lean conditions, Pd catalyst was the most active, although deactivation occurred above 650 °C, with reactivation upon cooling. Rh catalyst also deactivated above 750 °C, but did not reactivate. Pt catalyst was active above 600 °C. Fuel-lean reaction products were CO 2 and H 2O for all three catalysts. The same catalysts tested under fuel-rich conditions demonstrated much higher activity. In addition, a ‘lightoff’ temperature was found (between 450 and 600 °C), where a stepwise increase in reaction rate was observed. Following ‘lightoff’ partial oxidation products (CO, H 2) appeared in the mixture, and their concentration increased with increasing temperature. All three catalysts exhibited this behavior. High-pressure (0.9 MPa) sub-scale reactor and combustor data are shown, demonstrating the benefits of fuel-rich operation over the catalyst for ultra-low emissions combustion.

Concrete Hydration and Mechanical Properties under Nonisothermal Conditions

This paper presents the development of an analytical procedure to determine the heat and degree of hydration due to nonisothermal temperature history using a 3-parameter model. The procedure can also be applied to concrete mechanical properties if they are strongly related to the degree of hydration. To demonstrate this, experiments were conducted to obtain the heat of hydration, chemically bound water, compressive strength, split tensile strength, and Young's modulus of concrete. Experimental results in the literature were also used. It was found that the measured degree of hydration relates uniquely to measured concrete properties. The analytical procedure was then extended to determine a generalized hydration or aging time. Results from the literature were used to confirm the predictive capability of the proposed aging relation. The proposed maturity relation was found to relate uniquely to mechanical properties such as compressive strength and fracture energy.