Time Evolution Of Temperature Research Articles

A limit-cycle model for internal transport barrier oscillations

A 0-D model for the time evolution of the electron temperature T and current density j is derived (following a systematic procedure) from the cylindrical 1-D electron heat transport and current density diffusion equations. The stationary regimes (stable fixed points) of the deduced dynamical system are analysed and it is shown that the model reproduces well the cases of total diffusion (no sources), of a pure Ohmic (OH) discharge and of a constant external heating scenario. Moreover, it is seen that, as the fraction of externally driven non-inductive current applied off-axis is increased, the system moves from an OH regime into an internal transport barrier (ITB) regime, where j is reversed and the negative magnetic shear reduces the heat diffusivity, thus increasing T at the core. When the external power deposition is made proportional to both T and j, limit-cycle oscillations, which resemble those of the O-regime at Tore Supra, are found. The 1-D transport equations are also solved numerically and an ITB oscillatory regime with features similar to the experiments is found, namely, a period of oscillation that is of the order of the resistive time scale, along with a decrease of the oscillation's amplitude with increasing frequency.

Relation Between Mean Fluid Temperature and Outlet Temperature for Single U-Tube Boreholes

Ground-coupled heat pump (GCHP) systems usually utilize buried vertical heat exchangers, named borehole heat exchangers (BHEs). The accurate design or simulation of a GCHP system requires the calculation of the time-dependent outlet temperature from the BHEs, Tout. However, the most widely employed BHE simulation models yield the time evolution either of the mean temperature of the BHE-ground surface, Tsm, or of that of the fluid, Tfm. In transient regime, it is not easy to relate Tout to either Tsm or Tfm. In this paper we determine, through 3D finite element simulations, simple expressions of a dimensionless coefficient φ allowing the calculation of Tout by means of a simulation model that yields Tfm. These expressions hold for single U-tube BHEs, both in quasi-steady and in unsteady working conditions. We validate our 3D simulation code by comparison with an analytical BHE model. Then, we present applications of our expressions of φ to calculate the time-dependent values of Tout through a BHE model that yields those of Tfm. Finally, we show that the values of φ in quasi-steady working conditions can be used for a simple calculation of the effective borehole thermal resistance.

Cooling theory faced with old warm neutron stars: role of non-equilibrium processes with proton and neutron gaps

ABSTRACT Recent observations have found several candidates for old warm neutron stars whose surface temperatures are above the prediction of the standard neutron star cooling scenario, and, thus, require some heating mechanism. Motivated by these observations, we study the non-equilibrium beta process in the minimal cooling scenario of neutron stars, which inevitably occurs in pulsars. This out-of-equilibrium process yields the late-time heating in the core of a neutron star, called the rotochemical heating, and significantly changes the time evolution of the neutron star surface temperature. To perform a realistic analysis of this heating effect, we include the proton-singlet- and neutron-triplet-pairing gaps simultaneously in the calculation of the rate and emissivity of this process, where the dependence of these pairing gaps on the nucleon density is also taken into account. We then compare the predicted surface temperature of neutron stars with the latest observational data. We show that the simultaneous inclusion of both proton and neutron gaps is advantageous for the explanation of the old warm neutron stars since it enhances the heating effect. It is then found that the observed surface temperatures of the old warm millisecond pulsars, J2124−3358 and J0437−4715, are explained for various choices of nucleon gap models. The same set-up is compatible with the observed temperatures of ordinary pulsars, including old warm ones, J0108−1431 and B0950+08, by choosing the initial rotational period of each neutron star accordingly. In particular, the upper limit on the surface temperature of J2144−3933 can be satisfied if its initial period is $\gtrsim 10\, \mathrm{ms}$.

Thermal radiation and chemical reaction effects on a porous media flow with heat generation

The present study investigates the effects of thermal radiation and chemical reaction on the unsteady free-convection flow over a vertical infinite porous plate under the action of a transverse magnetic field, suction velocity and heat sources. The incompressible Newtonian fluid model is considered and the convective, diffusive and reactive processes are incorporated to describe the time evolution of fluid temperature and mass concentration within the flow. These led to a coupled system of partial differential equations alongside the relevant conditions. A decoupled finite difference scheme is formulated for the dimensionless model, and the resulting linear system are solved, using the Gauss Seidel algorithm, for the field variables. The stability and convergence of the method are proved, and the results are numerically verified using the method of manufactured solutions. The numerical results are presented and the effects of the various flow parameters on the field variables are discussed. It is observed that an increase in the radiation parameter decreases the temperature, while an increase in the chemical reaction parameter leads to an increase in the concentration

Thermal Explosion Characteristics of a Gelled Hypergolic Droplet

When a sphere of one reactant is placed in the medium of another reactant with which it is hypergolic, a chemical reaction (modeled here as a zeroth-order one-step irreversible Arrhenius reaction) occurs at the common interface of the two reactants, and the heat generated at the interface then is transmitted away from it by thermal conduction. Depending on the nature of the problem, the system may approach an explosive mode, or it may settle into a steady-state mode. The critical condition defining the transition between these two states is determined analytically. In particular, explicit formulas for the ignition delay time for the explosive mode are provided for two limits, one in which an appropriately defined Damköhler number is large and the other in which it is closer to the critical conditions. This is accomplished here by deriving and solving an integral equation for the time evolution of the interface temperature, employing activation-energy asymptotics.

Experimental Characterization of the Supersonic Transitional Wake Downstream of a Single Roughness Element

An experimental campaign was carried out to investigate the characteristics of the transitional supersonic wake downstream of a single roughness element. Two Mach numbers were tested, 1.6 and 2.3, and two roughness heights, 0.1 mm and 1 mm. Unsteady and steady wall temperature measurements were taken along and across the roughness wake. The spatial trends of adiabatic wall temperature and heat flux, and the spectral time evolution of temperature were documented in this paper. The initial wall temperature was varied during the temperature measurements, and the resulting steady and unsteady effects on the roughness wake were investigated. The streamwise trends of heat-flux and adiabatic-wall temperature confirmed the transitional nature of the roughness wake. Spectral analysis showed that roughness height and initial wall temperature had the same type of effect on the wake wall-temperature fluctuations. The effect of roughness height was more sensible at Mach 2.3, ant that of the initial wall temperature was more evident with the smallest roughness also tested at Mach 2.3.

Sand casting of sheet lead: numerical simulation of metal flow and solidification

Sandcast lead sheets are characterised by their superior aesthetic performance and mottled surface. Lead sheet casting is widely used in the construction industry for roofing and flashing applications, while the roots of this process can be tracked back to the Roman times. In this study, two-dimensional computational fluid dynamics (CFD) simulations have been performed to simulate the melt flow and solidification stages of the lead sandcasting process. The effects of process parameters such as pouring temperature, screed velocity and clearance between the screed and the sandbed on the final quality of the lead sheet are investigated. Lead sheet quality has been quantified by measuring the variance and the average value of the final sheet thickness over the sandbed length. The developed CFD model has been validated against experimental results by comparing the time evolution of the lead-sandbed interface temperature against data collected by thermocouples during the real-time process. The numerical results show that all of the aforementioned parameters affect the final quality of the cast product and suggest that superior quality lead sheets can be produced for a range of relatively low values of the pouring temperature and slow strickle motion.

CFD-based fire spread visualization for improvement of road tunnel safety

Teaching and training of operators of road and highway tunnels are necessary to increase their preparedness for incidents accompanied by fire and ensure safe tunnel operation. For such purposes Tunnel Traffic & Operation Simulator (TTOS) is used in Slovakia. TTOS is capable to simulate various types of emergency situations in 1 km long twin tube virtual highway tunnel with longitudinal ventilation including scenarios of car accidents accompanied by fire. However, TTOS does not provide information about the fire dynamics and smoke stratification. In this paper, the use of the well-known CFD-based Fire Dynamics Simulator for creating a series of didactic videos is illustrated. The videos demonstrate the smoke propagation and time evolution of temperature, air flow velocity and visibility for selected fire scenarios. They have been implemented into the TTOS environment and became available for tunnel operators.

A key to tune the grain size gradient of the TiC coating on titanium by interstitial carburization: The timing for pressing

Herein, we fabricated TiC coatings on titanium via the interstitial carburization technique. By hot-pressing the titanium substrate with cast iron at 1100 °C, the interstitial carbon atoms in the cast iron diffused into titanium, forming a TiC coating. The timing of starting pressing affected the spatial distribution of TiC grain size, namely starting pressing at 1100 °C generated coatings with a clear gradient microstructure, while starting pressing at room temperature generated coatings with a relatively homogeneous microstructure. The TiC grain size in the gradient coating increased from 0.3 μm to 1.1 μm with increasing distance from the surface, giving rise to a nanohardness gradient varying from 25 GPa to 32 GPa. The relatively homogeneous microstructure resulted in a constant nanohardness of 32 GPa in the coating. Both coatings exhibited an extremely high micro-hardness of 2100–2300 HV and strong adhesion with the substrate. These findings provide a route for controlling the spatial distribution of the carbide grain size by designing the time evolution of temperature and pressure. These results should be applicable to more substrate materials and may also be valuable for other hot-pressing based technologies.

Corrections to the Landau kinetic equation for a weakly dissipative randomly driven system and the fluctuation-dissipation theorem

This paper is devoted to the derivation of a kinetic equation for many-body one-component dissipative systems in an external random field. The system under consideration was discussed in the recent paper by Sliusarenko et al. [J. Math. Phys. 56, 043302 (2015)], where a generalization of the Vlasov kinetic equation was obtained. The potential interaction is assumed to be small (the corresponding small parameter λ), the dissipation interactions and the correlation functions of the external random field are considered as small quantities estimated by one small parameter μ for the simplicity. The kinetic equation is obtained up to the terms of the orders λ2μ0, λ1μ1, λ0μ2 inclusive. In weakly spatially nonuniform states of the system, this gives corrections to the Landau–Vlasov kinetic equation caused by the dissipation and external random field. In the case λ ≫ μ after the mean free time, the system reaches a state approximately described by the Maxwell distribution. The dissipation and random field will lead to the evolution of the system temperature. A time evolution equation for the temperature in spatially uniform states is derived on the basis of the obtained kinetic equation by a generalized Chapman–Enskog method which takes into account that the kinetic equation is an approximate one. This temperature time evolution equation is investigated up to the terms of the order μ3 inclusive. It is shown that under some conditions the final stage of the system evolution is a steady state. A fluctuation-dissipation theorem for this state is discussed. In this steady state, the system is described by a distribution function that contains corrections to the Maxwell distribution.

Pyroelectric ultrasound sensor model

Ultrasound is typically measured using phase-sensitive piezoelectric sensors. Interest in phase-insensitive sensors has grown recently, with proposed applications in ultrasound attenuation tomography of the breast. The advantage of phase-insensitive imaging is that it does not suffer from degradation of image quality due to phase-aberration and narrow directional response. A numerical model of a phase-insensitive pyroelectric ultrasound sensor is presented. The model consists of three coupled components run in sequence: acoustic, thermal, and electrical. The acoustic simulation models the propagation and absorption of the incoming ultrasound wave. The negative divergence of the time-averaged acoustic intensity is used as a heat source in the thermal simulation for the time-evolution of temperature in the sensor. Both the acoustic and thermal simulations are performed using the k-Wave MATLAB toolbox with an assumption that shear waves are not supported in the medium. The final component of the model uses a pyroelectric circuit model which outputs the sensor response based on the temperature change in the sensor. The modelled pyroelectric sensor response and directional dependence are compared to empirical data. A physical model for the directionality of the sensor response is then proposed.

Thermal discrete element method for transient heat conduction in granular packing under compressive forces

A thermal discrete element method is introduced in granular packs. This method is applicable to 3D packing in either static or dynamic states coupled with the ordinary discrete element method code. This method resolves the local heat fluxes and temperature of particles relying on particles conductivity and the deformation of particles at various contact points. Using this method, the time evolution of temperature is studied within packed beds under various compressive forces. Our results match very well with the analytical solution as if the value of the effective conductivity is properly adjusted, which is found to be related to the pressure exponentially. We have also shown that the compression of the granular packing exponentially increases the thermal characteristic time of the bed.

Numerical simulation of effect of operating conditions on flash reduction behaviour of magnetite under H2 atmosphere

The flash reduction behaviour of in-flight magnetite particles under hydrogen atmosphere is investigated by an Eulerian-Lagrangian model to explore the effect of operating conditions. In addition to quantitatively analysing the variations of the reduction degree and residence time of particles at the reactor exit, the reduction state of particles moving in the reactor is depicted by time evolutions of particle temperature, reduction rate, and reduction degree. Results show that the heating time of particles is too short to affect the reduction process. Higher temperature, H2 partial pressure, and operating pressure are conducive to the flash reduction because of a higher reaction rate. Although water vapour promotes the heat transfer inside the reactor, it weakens the reduction rate. Increasing particle feeding rate has a negative effect, with the effect becoming more significant as total gas flow declines. This study can provide a theoretical basis for flash ironmaking technology in hydrogen atmosphere.

Real time optimization of temperature field in induction heating

Abstract Many induction heating processes must be controlled in accordance with the prescribed time evolution of temperature of the heated body (bodies). This requires a correct setting of field currents (amplitudes and frequencies) in the heating inductors that can vary either continuously or by steps. The paper presents a novel model of induction annealing of cylindrical aluminum billets based on solution of nonstationary forward and inverse tasks. The methodology is described in detail and illustrated with a typical example. Some of the results were verified experimentally.

Heating and evaporation of ethanol/iso-octane droplets considering non-ideal mixtures and finite rate transfer

In this paper, the heating and evaporation process of ethanol/iso-octane droplets is deeply investigated through analytical solutions and considering thermodynamic models for non-ideal mixtures. The study is based on the Effective Thermal Conductivity Model (ECM) and Effective Diffusivity Model (EDM), which take into account the finite thermal/mass diffusivities inside the droplets and also consider the effect of droplet internal recirculation. Three sets of cases are considered: ideal liquid and gas phases, non-ideal liquid and gas phases and ideal gas phase together with the non-consideration of the Poynting factor for the liquid phase. The activity coefficients for the non-ideal liquid phase are calculated through the UNIFAC model and the fugacity coefficients for the non-ideal gas phase are calculated from the Virial equation of state. A parametric study is performed with focus on relevant conditions to direct injection internal combustion engines, within an ambient pressure range from 1 to 20 bar, initial ambient gas temperature range from 453 K to 673 K and initial ethanol volume fraction inside the droplet varying from 0 to 1. The thermodynamic analysis of the mixture, the time evolution of the droplet surface temperature and mass fraction together with the droplet lifetimes are presented for several different conditions. The obtained results show that the effect of the non-ideality of both phases has a significant impact on the results when analyzing ethanol/iso-octane mixtures. From cases analyzed considering both phases as ideal mixtures the deviation of the droplet lifetime reached maximum values (in absolute value) of 15.6% at 1 bar, 10.5% at 10 bar and 14.9% at 20 bar and for the ideal gas approach (non-ideal liquid) the deviation reached maximum values (in absolute value) of 3.9% at 10 bar and 9.4% at 20 bar, when compared to the non-ideal approach. These deviations certainly can lead to significant deviations in the prediction of the mixture formation in direct injection engines.

Relativistic second order dissipative hydrodynamics from an effective fugacity quasiparticle model

In this work, a second-order relativistic viscous hydrodynamic model has been presented based on the effective fugacity quasiparticle model (EQPM). The hydrodynamic model has been derived from the effective relativistic second-order transport equation under the EQPM for a multiparticle (two-component) system and solving it in Grad's 14-moment method. The EQPM describes the strongly interacting thermal system of QCD interactions through its fugacity parameters extracted from updated lattice equations of state. The proper time evolution of temperature and pressure anisotropy is observed to be affected significantly due to the inclusion of the EQPM compared to an ideal system.

Radiation flux study of hohlraum used to create uniform and strongly coupled warm dense matter

A hohlraum used to create uniform and strongly coupled warm dense matter and its radiation flux study on the SG-III prototype laser facility are described. Time evolution of the radiation temperature from laser entrance hole (LEH) and the incident radiation temperature at the target surface are obtained using flat response X-ray diode detectors. Then, a calculation of the radiation flux evolution for this hohlraum is carried out using a view-factor method, and the calculated results agree well with the experimental data within the error bar. Using the incident radiation at the target surface as a source, the validity to create uniform and strongly coupled warm dense matter by this hohlraum is verified.

Thermal evolution of the Scandian hinterland, Naver nappe, northern Scotland

The Northern Highlands Terrane of Scotland hosts several thrust nappes that were deformed and metamorphosed during the Silurian Scandian orogeny. Quantitative petrological analysis of metamorphic assemblages indicates that the hinterland-positioned Naver nappe experienced decompression heating from 8–9 kbar and 600°C to 6–7 kbar and 700°C. Monazite–xenotime thermometry and geochronology delineate a detailed temperature–time history for the Naver nappe. Monazite often exhibits compositional zoning, which is used to establish multiple temperature–time points in several samples. These data indicate that the Naver nappe experienced relatively fast heating ( c. 50°C myr −1 ) and relatively slow cooling (15–20°C myr −1 ), with peak temperatures occurring at c. 425 Ma. This temperature–time evolution is compatible with the early Emsian (407–403 Ma) deposition of unmetamorphosed conglomerates that rest on high-grade metamorphic rocks in the Naver nappe, but requires an acceleration in the cooling rate to 40–50°C myr −1 at 420–410 Ma. Geochronological constraints from this study and previous work suggest that deformation and metamorphism in the hinterland of the Scandian orogen in northern mainland Scotland are younger than the c. 430 Ma deformation in the foreland-positioned Moine thrust zone. We postulate that heat from pervasive granitic intrusions in the Naver nappe weakened the crust, allowing deformation to retreat to the hinterland of the orogen. Supplementary material: A description of our analytical methods, all U–Pb-trace element data, additional figures explaining our petrological analysis and other relevant data are available at: https://doi.org/10.6084/m9.figshare.c.4458041

Post-250 Ma thermal evolution of the central Cathaysia Block (SE China) in response to flat-slab subduction at the proto-Western Pacific margin

The flat-slab subduction model has been proposed to explain the complex Mesozoic–Cenozoic geotectonic record of SE China as part of the Western Pacific margin. Here we investigate the post-250 Ma thermal history of the Shaoguan-Longnan region to evaluate the time-temperature evolution of local sedimentary and magmatic rocks in the context of the flat-subduction model. Our multi-chronological approach includes zircon U-Pb geochronology, 40Ar/39Ar dating of K-feldspar and biotite, (U-Th)/He dating of zircon and apatite, and fission-track dating of apatite from basement and/or sedimentary rocks, as well as vitrinite reflectance analysis of coal seams. Zircon U-Pb dating revealed Early Silurian and Late Jurassic crystallization ages for the Fuxi (ca. 438 Ma) and Liyuan (ca. 162 Ma) granites, respectively. Syn-/pre-depositional single-grain zircon (U-Th)/He ages from Lower Jurassic sandstones record a Middle Triassic exhumational cooling, interpreted to reflect the Indosinian Orogeny, possibly caused by a flat-slab subduction event. Late Jurassic biotite 40Ar/39Ar age (ca. 156 Ma) obtained from the Late Triassic Mengdong granite, together with maximum vitrinite reflectance values of 1.7%–2.3% measured from a Lower Jurassic coal sample, document a thermal maximum in the Late Jurassic, likely related to the prior regional magmatism arising from delamination of the subducting Paleo-Pacific plate. K-feldspar 40Ar/39Ar plateau age from the Fuxi granite (ca. 125 Ma), and zircon (U-Th)/He mean ages (152–115 Ma) record a protracted cooling through the K-feldspar Ar and the zircon He partial retention zones during the Cretaceous. The Cretaceous cooling is in accord with the prediction of regional uplift and erosion in response to foundering of the flat-slab and consequent lithospheric rebound. The rapid cooling during the Paleocene–Eocene, recorded by apatite fission-track central ages (72–39 Ma) and apatite (U-Th)/He mean ages (38–33 Ma), is interpreted to reflect Cenozoic rifting in the leadup to the opening of the South China Sea.

A quasi-static model for hot-electron interaction with self-generated magnetic fields

The time evolution of the target temperature and ionization degree during the laser-target interaction is of primary importance to understanding the transition between solid and plasma. When the interaction lasts a few tens of femtoseconds, the target resistivity is not well known as in the Spitzer regime, and therefore approximated information must be used from experiments and/or from models. The calculation of the target temperature and the magnetic fields produced inside the target after the propagation of a fast electron current is performed in this paper accounting for the pulse temporal envelope and making use of a complete resistivity model. Analytic calculations of temporal and spatial varying magnetic fields are also presented. Finally, a novel interpretation of the beam hollowing phenomenon is given based on the outcomes of the model developed.