Non-isothermal Case Research Articles

Kinetics of crystallization in selenium molybdate glass

In this work we have studied isothermal and non-isothermal crystallization kinetics in Ag2O modified selenium molybdate glass employing differential scanning calorimetry. Activation energies for crystallization and glass transition were estimated following Ozawa and Kissinger methods. The value of the Avrami exponent was determined from the experimental results and was related to the nature of crystal nucleation and growth. The Matusita model was employed to extract non-isothermal crystallization parameters. The applicability of the Johnson–Mehl–Avrami (JMA) model to both isothermal and non-isothermal cases was tested. We showed that the JMA model gave the best description of isothermal crystallization, whereas the Sestak–Berggren (SB) model described the non-isothermal transformation kinetics adequately.

Leaf hydraulics I: Scaling transport properties from single cells to tissues

In leaf tissues, water may move through the symplast or apoplast as a liquid, or through the airspace as vapor, but the dominant path remains in dispute. This is due, in part, to a lack of models that describe these three pathways in terms of experimental variables. We show that, in plant water relations theory, the use of a hydraulic capacity in a manner analogous to a thermal capacity, though it ignores mechanical interactions between cells, is consistent with a special case of the more general continuum mechanical theory of linear poroelasticity. The resulting heat equation form affords a great deal of analytical simplicity at a minimal cost: we estimate an expected error of less than 12%, compared to the full set of equations governing linear poroelastic behavior. We next consider the case for local equilibrium between protoplasts, their cell walls, and adjacent air spaces during isothermal hydration transients to determine how accurately simple volume averaging of material properties (a ‘composite’ model) describes the hydraulic properties of leaf tissue. Based on typical hydraulic parameters for individual cells, we find that a composite description for tissues composed of thin walled cells with air spaces of similar size to the cells, as in photosynthetic tissues, is a reasonable preliminary assumption. We also expect isothermal transport in such cells to be dominated by the aquaporin-mediated cell-to-cell path. In the non-isothermal case, information on the magnitude of the thermal gradients is required to assess the dominant phase of water transport, liquid or vapor.

Unified isothermal and non-isothermal modelling of neat PEEK crystallization

A differential generalized Avrami’s law is used to model crystallization kinetic of PEEK in considering that PEEK crystallization results from the contribution of two distinct mechanisms. The form of this equation allows to predict with good accuracy both isothermal and non-isothermal crystallization kinetics. Nevertheless, isothermal model parameters are not entirely satisfactory for predicting non-isothermal crystallization and the identification of kinetic parameters is needed for both isothermal and non-isothermal cases. The results show that the Avrami exponents and Arrhenius activation energies remain constant for both conditions and therefore suggest that these parameters are only material dependent. On the other hand, the other kinetic parameters depend on the crystallization condition and vary with temperature and/or cooling rate.

Role of entropy generation on thermal management due to thermal convection in porous trapezoidal enclosures with isothermal and non-isothermal heating of wall

One of the important objectives of thermal systems engineering is to analyze the utilization of thermal energy in an efficient manner. Analysis on entropy generation may give an insight about thermal efficiency of various thermal systems. Entropy generation analysis during natural convection in a porous trapezoidal structures of various inclination angles (φ) with isothermal (case 1) and non-isothermal (case 2) hot bottom wall has been performed. Simulations have been done to obtain solutions in terms of isotherms (θ), streamfunction (ψ) and entropy generation maps (Sθ and Sψ) for various ranges of modified Darcy number (Da), Prandtl number (Pr) at modified Rayleigh number, Ra=106. It is observed that Sθ,max occurs near bottom corners for case 1 whereas that occurs near middle part of the left and right portions of the bottom wall for case 2. The entropy production due to fluid flow irreversibilities (Sψ,max) occurs either at the top wall, or side walls or along the interface between two counter-rotating cells. It is found that, square cavities may be the optimal geometry in comparison to trapezoidal cavities for both cases. Also, trapezoidal cavities with φ=60° may be the alternative optimal design in comparison with φ=45° for all Pr fluids.

Relaxation Dynamics and Crystallization Study of Sildenafil in the Liquid and Glassy States

In this paper, the physical stability and molecular dynamics of amorphous sildenafil are investigated in both the liquid and glassy states. We have established that the amorphous sildenafil is resistant to recrystallization at temperatures below the glass transition temperature Tg during the experimental period of its storage (i.e., above 6 months), however, it easily undergoes cold crystallization at T > Tg. To determine the crystallization mechanism, the isothermal and non-isothermal studies of the cold crystallization kinetics of the drug are performed by using the broadband dielectric spectroscopy (BDS) and the differential scanning calorimetry (DSC), respectively. The cold crystallization mechanism has been found to be similar in both the isothermal and non-isothermal cases. This mechanism has been analyzed from the point of view of the molecular mobility of sildenafil investigated in the supercooled liquid and glassy states by using the BDS measurements in the wide temperature range. This analysis has been enriched with a new approach based on a recently reported measure of dynamic heterogeneity given by a four-point dynamic susceptibility function. No tendency to recrystallization of glassy sildenafil at T < Tg is also discussed in relation to molecular dynamics of sildenafil in the glassy state. The relatively small molecular mobility reflected in one secondary relaxation as well as the predicted large time scale of structural relaxation of glassy sildenafil suggests that amorphous sildenafil should not recrystallize during its long-term storage at room temperature.

Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)–Reynolds (Re)–Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 103 to 105 at Re=1 and 100 for three different fluids of Pr=0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45o. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re2≫1) or mixed convection regime (Gr/Re2∼O(1)) in convection dominated heat transport regime (Pr×Re≳1). Number of steady states are observed to be more in natural convection dominated regime at Re=1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall.

Comparison of coarse grid lattice Boltzmann and Navier Stokes for real time flow simulations in rooms

Coarse grid lattice Boltzmann models (LBM) and computational fluid dynamics (CFD) are compared in building simulations. Three simulations are used to assess the different numerical models: (i) a 2D isothermal flow case, (ii) a 3D isothermal flow case and (iii) a 2D non-isothermal flow case. Both models predicted the correct flow patterns and temperature field and could be used for real time (RT), near real time (NRT) and faster than real time (FRT) simulations without loss of accuracy on multi-core processors. The results indicate that the coarse grid CFD is both faster and more time accurate than the LBM for unsteady simulations.

Spatial decay for several phase-field models

In this paper, we study the spatial behavior of three phase-field models. First, we consider the Cahn-Hilliard equation and we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal phase-field equation (i.e., the Allen-Cahn equation), we prove the nonexistence and the fast decay of solutions and, for the nonisothermal case governed by the Fourier law, we obtain a Phragm en-Lindel of alternative of exponential type, respectively.

Penalization technique to model wall-component impact on heat and mass transport in the tokamak edge

The original and computationally efficient volume penalization technique Ref. [1], proposed for an isothermal plasma to recover the Bohm boundary condition at the plasma–obstacle interface, is extended to model 3D obstacles. It is then generalized to handle electron and ion temperatures in a 1D model. Results in 3D simulations show that the geometry of secondary limiter has an influence on the density and particle flux profiles, breaking its toroidal symmetry and introducing profile gaps of magnitude of 20%. On the other hand, the generalization of the penalization scheme to the non-isothermal case demands to deal with new Neumann conditions on the heat fluxes. Those boundary conditions require the introduction of new mask functions to ensure that the Bohm boundary condition remains satisfied.

Properties of large-scale flow structures in an isothermal ventilated room

In the present work experimental and numerical investigations of the large-scale structures of isothermal air flow in a highly simplified model room are reported and discussed. We compare the measured velocity distribution with direct numerical simulations (DNSs) for the reference Reynolds number Reref = 2.4 × 104, which is based on the maximum inlet velocity and the height of the room. This comparison shows a high similarity concerning the flow structures. Furthermore, we investigate the dependence of the spatial and temporal behavior of flow structures on the Reynolds number from measurements covering a Reynolds number range of 1.0 × 104 ≤ Re ≤ 7.0 × 104. The major finding is that there is a coherent oscillation of the large-scale flow structures, which depends on the Reynolds number. Our findings show that the frequencies of the oscillations are in a good agreement with an empirical model, which describes the auto-oscillation of two colliding planar jets with respect to the Reynolds number and the geometry relations of the inlets. Moreover, the present work indicates that the chosen flow geometry is well suited as a simplified model for problems of room ventilation and can serve as a base for forthcoming studies of non-isothermal cases.

Characterization of a spherical probe in gas at rest upon ionization of alkali metals: The nonisothermal case

The characteristics of a spherical probe have been calculated in collisional plasma at rest where the ionization of atoms of an alkali additive and recombination of generated charged particles with consideration for the instability of plasma temperature around the probe occur. The results evidence a strong reduction of the probe current and impairment of agreement between the probe and the spectral measurements of concentration of charged particles. It is concluded that it is necessary to analyze the detailed chemical kinetics of the multicomponent gaseous mixture around the probe.

Computer Modeling and Simulation for 3D Crystallization of Polymers. II. Non-Isothermal Case

A 3D computer modeling and simulation has been used to predict crystallization kinetics and crystal morphology in polymers under the non-isothermal condition. A parametric study is used to explore the influences of thermal conditions on the crystallization. The results indicate that cooling rate has a strong impact on the crystallization kinetics as well as the morphology. The initial temperature only affects the crystallization kinetics and has no impact on the final morphology. It is observed that the distribution of spherulite size in non-isothermal case is much broader than that in the isothermal case.

The influence of talc as a nucleation agent on the nonisothermal crystallization and morphology of isotactic polypropylene: The application of the Lauritzen–Hoffmann, Avrami, and Ozawa theories

AbstractA new method is proposed, which can be used to analyze the influence of different additives and fillers on the nonisothermal crystallization of polymers. The composites of talc in isotactic polypropylene (i‐PP) were prepared using a corotating twin‐screw extruder. The compounds were subsequently dried and injection molded. PP morphology and talc dispersion were visualized using optical microscopy and computed tomography. Wide‐angle X‐ray scattering and small‐angle X‐ray scattering measurements provided an insight into the crystal structure of PP. The data obtained from nonisothermal DSC measurements were fitted to the Avrami model for the nonisothermal case. The calculated Avrami's exponent (n), which takes into account the influence of talc on the nucleation and growth of the PP crystals, was used in the combination of Lauritzen–Hoffman and Ozawa models to calculate the nucleation parameter (Kg). A good agreement was found between the model predictions and literature values. The examination shows that the developed model extension gives an expected trend in the case of i‐PP filled with talcs from the same origin but with different particle sizes. Furthermore, it is shown that delaminated talc with a higher specific surface is more efficient in nucleation of i‐PP. Thus, the introduced model extension could be a useful tool for comparing of nucleation ability of different additives in the crystallization of polymers. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Laminar Film Condensation Heat Transfer on a Vertical, Non-Isothermal, Semi-Infinite Plate

This paper gives similarity transformations for laminar film condensation on a vertical flat plate with variable temperature distribution and finds analytical solutions for arbitrary Prandtl numbers and condensation rates. The work contrasts with Sparrow and Gregg's assertion that wall temperature variation does not permit similarity solutions. To resolve the long debatable issue regarding heat transfer of non-isothermal case, some useful formulas are obtained, including significant correlations for varying Prandtl numbers. Results are compared with the available experimental data.

Inflow turbulence generation for large eddy simulation in non-isothermal boundary layers

Many studies have presented the importance of turbulent inflow data for large eddy simulation, and several techniques have been proposed for generating inflow fluctuations for LES in a neutral boundary layer, but few studies have considered non-isothermal cases. In this study, first wind tunnel experiments were conducted to generate both unstable and stable turbulent thermal boundary layers in a thermally stratified wind tunnel at Tokyo Polytechnic University. The decrease of turbulence due to the effect of buoyancy was clearly observed in a stable boundary layer. Then a precursor method using a long domain and a recycling procedure using a short domain to generate the turbulence statistics corresponding to the experimental data were investigated for both unstable and stable conditions. The characteristics of the generated flow (mean profiles and fluctuation profiles) by both methods agreed relatively well with those of the wind tunnel experimental data. When a recycling procedure was adopted to generate turbulence statistics in a stable boundary layer, large damping was necessary to decrease the turbulence level. For the temperature field, giving only a mean profile (no temperature fluctuation) as an inflow boundary condition of the driver region was the simplest way. Even if the inflow temperature fluctuation was not given, temperature fluctuation gradually developed in the downstream direction with velocity fluctuation in the turbulent boundary layer.

Visualization of Heat Transport during Natural Convection in a Tilted Square Cavity: Effect of Isothermal and Nonisothermal Heating

Bejan's heatlines approach has been introduced to visualize heat flow during natural convection within a tilted square cavity inclined at an angle of ϕ = 30°. The enclosure is bounded by hot wall AB (case 1: isothermal heating and case 2: nonisothermal heating), isothermally cooled walls DA and BC in the presence of adiabatic wall CD. The results are presented in terms of streamlines, isotherms, heatlines, and local and average Nusselt numbers. The nonisothermal heating case produces the greater heat transfer rate at the center of the wall AB compared to that of the isothermal heating case, whereas the average Nusselt number shows an overall lower heat transfer rate for the nonisothermal heating case.

An analytical model of liquid drop evaporation in gaseous environment

A new analytical model of liquid drop evaporation in gaseous environment is developed based on the solution of species, momentum and energy conservation equations in a radial coordinate system. The model relieves some inconsistencies of previous simplified models and it yields solutions also for the non-isothermal case. The flow field characteristics under isothermal and non-isothermal steady-state conditions are investigated for different evaporating fluids. The unsteady drop evaporation process is predicted and comparison with the existing simplified Maxwell equation and the well known Stefan–Fuchs model is reported and discussed.

The onset of oblique vortex shedding behind a heated circular cylinder in laminar wake regime

Oblique vortex shedding (OVS) behind a heated circular cylinder in air was experimentally investigated. Similar to that in the parallel vortex shedding (PVS), the results show that the non-dimensionalized shedding frequency, Strouhal number, decreases under the influence of cylinder heating for oblique shedding mode. Although the onset Reynolds number of OVS increases with the cylinder temperature, the onset effective Reynolds number remains 63.3 ± 1.3 regardless of the cylinder heating. A general Strouhal-Reynolds-number relationship for OVS has been found based on the effective temperature concept in the present study. The ratio of the critical Reynolds numbers for the onsets of OVS and PVS is found to be an invariant with value of 4/3 for both isothermal and non-isothermal cases despite different length/diameter ratios and end conditions.

Energy optimization in heat integrated water allocation networks

In this paper, linear programming formulations, complemented by concept based pinch analysis results, are developed to target the minimum energy requirements in a heat integrated fixed flow rate water allocation networks. These formulations can be applied for the cases of heat integration through isothermal and non-isothermal mixing in water allocation networks involving single as well as multiple contaminants. The earlier reported approaches are based on linear programming formulation for the case of isothermal mixing and either mixed integer non-linear programming or discontinuous non-linear programming formulations for the case of non-isothermal mixing. It has been observed that the earlier reported methodologies produce sub-optimal results for the case of non-isothermal mixing. However, the proposed methodologies produce the optimum results because of the rigorously proved linear formulation. Utility requirements for isothermal as well as for non-isothermal mixing cases are compared over a range of minimum approach temperatures, to evaluate the energy performance using illustrative examples.

Heatline Analysis for Natural Convection within Porous Rhombic Cavities with Isothermal/Nonisothermal Hot Bottom Wall

Analysis has been carried out for energy distribution and thermal mixing in steady laminar natural convective flow through the porous rhombic cavities with inclination angle φ for various applications such as geothermal, grain storage, electronic cooling, etc. A generalized non-Darcy model without the Forchheimer inertia term is used to predict the flow in porous media. The effect of the Darcy number (Da) and the role of φ on the energy distribution and thermal mixing within porous rhombic cavities with isothermal (case 1) and nonisothermal (case 2) hot bottom walls are illustrated via “heatlines”. Heat transfer is found to be primarily conduction dominant at Da = 10–5 even at a higher Rayleigh number (Ra = 106). The onset of convection occurs at Da = 10–4, and the distorted heatlines from the hot bottom wall take a longer path to reach the cold side walls of the cavity. Larger heat transfer and thermal mixing occurs for Da = 10–3 at Ra = 106 irrespective of φ and Pr. Multiple flow/convective circulations...