Volumetric Heating Rate Research Articles

Impacts of energetic particles from T Tauri flares on inner protoplanetary discs

ABSTRACT T Tauri stars are known to be magnetically active stars subject to strong flares observed in X-rays. These flares are likely due to intense magnetic reconnection events during which a part of the stored magnetic energy is converted into kinetic energy of supra-thermal particles. Since T Tauri stars are surrounded by an accretion disc, these particles may influence the disc dynamics and chemistry. This work continues on a previous stationary model, which showed that energetic particles accelerated during flares can produce a strong ionization rate at high column densities in the inner accretion disc. The present model includes non-stationary sequences of flaring events sampled by a Chandra X-ray survey of nearby young stellar objects. We calculate the averaged ionization rate expected in a radius range 0.08–0.6 au from the central star. We confirm that energetic particles produced by the flares dominate the ionization of the disc up to column densities of $10^{25}~\rm {cm^{-2}}$. We further study the main consequences of this additional source of ionization on the viscosity, the accretion rate, the volumetric heating rate, and the chemical complexity of inner protoplanetary discs.

Ultrafast crystallization and sintering of Li1.3Al0.3Ti1.7(PO4)3 glass through flash sinter‐crystallization

AbstractFlash sinter‐crystallization (FSC) is a new technique for concurrently crystallizing and sintering glasses, derived from flash sintering. In this study, we explore, for the first time, the use of FSC as a processing method for producing Li1.3Al0.3Ti1.7(PO4)3 (LATP) glass ceramics. Using FSC, LATP with NaSICON structure is produced at a furnace temperature as low as 460°C and a processing time of 5 min. The FSC‐processed samples with different current density limits were compared with those conventionally sinter‐crystallized (CSC) at 950°C for 1 h. We show that FSC can significantly improve the densification of LATP glass ceramics due to the volumetric high heating rate. Furthermore, the LATP samples processed by FSC exhibit superior total ionic conductivity than those processed by CSC, also surpassing the reported results for LATP with similar levels of densification. Therefore, our results suggest that FSC is a promising method for processing glass ceramics, particularly for materials with high crystallization kinetics like LATP, opening up new possibilities for the production of solid electrolytes.

Thermal behavior of CMC solutions under simulation of radio frequency pasteurization

Pasteurization and enzyme-inactivation are an economical and convenient way to provide safety and shelf-life stability. However, long heating time and non-uniform temperature distribution are the main issues of traditional thermal processing for enzyme-inactivation. Because of the volumetric heating and high heating rate, radio frequency (RF) treatment is considered as one of the most promising physical enzyme-inactivating methods. A 6 kW, 27.12 MHz RF heating system was applied to explore the effect of cylindrical container dimension and solution concentration on the thermal behavior of high-viscosity liquid food. Carboxymethylcellulose (CMC) solution as a non-Newtonian fluid was selected as a model liquid food in this study. The target temperature for enzyme inactivation was 70 °C. The experimental results showed that the electrode gap, container length, and container diameter affected the heating rate and uniformity of the liquid food. Furthermore, when the concentration of CMC solution increased from 0.5% to 2.0%, the heating rate of the solution firstly increased and then decreased, while the heating uniformity index of the solution increased from 0.008 ± 0.001 to 0.056 ± 0.002. The simulation results showed that the higher electric field strength led to a higher heating rate, temperature, and velocity of natural convection of the solution at the ends of the container. Then, the recirculation zones from the ends to the center of the container were formed, which was diminished with the increasing concentration solution, resulting in the increased maximum temperature difference of solution. The results of this research may provide useful data for subsequent continuous flow studies and information on potential RF enzyme-inactivation in high-viscosity liquid foods.

Temperature and Differential Emission Measure Profiles in Turbulent Solar Active Region Loops

We examine the temperature structure of static coronal active region loops in regimes where thermal conductive transport is driven by Coulomb collisions, by turbulent scattering, or by a combination of the two. (In the last case collisional scattering dominates the heat transport at lower levels in the loop where temperatures are low and densities are high, while turbulent scattering dominates the heat transport at higher temperatures/lower densities.) Temperature profiles and their corresponding differential emission measure distributions are calculated and compared to observations, and earlier scaling laws relating the loop apex temperature and volumetric heating rate to the loop length and pressure are revisited. Results reveal very substantial changes, compared to the wholly collision-dominated case, to both the loop scaling laws and the temperature/density profiles along the loop. They also show that the well-known excess of differential emission measure at relatively low temperatures in the loop may be a consequence of the flatter temperature gradients (and so increased amount of material within a specified temperature range) that results from the predominance of turbulent scattering in the upper regions of the loop.

Multiphysics simulation and validation of microwave melting characteristics of AA6061 by finite element analysis

Microwave processing of metallic material is an emerging process compared to conventional ones. In the present work microwave heating of bulk specimen of AA6061 is studied experimentally and numerically to understand heating behaviour of metal sample and tooling materials in an electromagnetic field. A three-dimensional model of the process has been generated using the COMSOL Multiphysics tool. The electric field distribution has been observed with a maximum value of 4.29 × 104 (V/m) in the centre of the cavity. The average volumetric heating rate has been reached to above 700°C within 600 s. The resistive losses have been observed with the value of 2.37 × 106 (W/m3) due to electromagnetic field distribution and tooling material properties. Temperature profiles obtained through experimental trials and simulation studies have been analysed and found in almost similar propensity within 5% of error.

A blackbox optimization of volumetric heating rate for reducing the wetness of the steam flow through turbine blades

This paper proposes to use a blackbox optimization to obtain the optimal volumetric heating required to reduce the wetness at the last stages of steam turbines. For this purpose, a global multiobjective optimization is utilized through the automatic linking of genetic algorithm and CFD code, where the blackbox function evaluations are performed by CFD runs. The logarithm of number of droplets per volume (LND), the droplet average radius (DAR), and the integral of local entropy (ILE) at the end of the cascade (after the condensation location) are minimized, while the volumetric heating rate is the optimization parameter. The Eulerian–Eulerian approach is implemented to model the two-phase wet steam turbulent flow and the numerical results are validated against well-established experiments. Since higher volumetric heating rates reduce DAR and LND, while increase ILE, according to optimization results, there is an optimum for the volumetric heating rate to reach the best performance of steam turbines. For case studies presented in this work, the optimal volumetric heating rates of 5.21×108 and 4.67×108 W/m2 are obtained for two different cases of supersonic and subsonic outlets, respectively. Particularly, these rates improve DAR by 45.7% and 57.5%, and LND by 6.0% and 7.8% for respective cases.

Scaling Laws for Dynamic Solar Loops

The scaling laws which relate the peak temperature T M and volumetric heating rate E H to the pressure P and length L for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide range of studies. Here we extend these scaling laws to dynamic loops, where enthalpy flux becomes important to the energy balance, and study impulsive heating/filling characterized by upward enthalpy flows. We show that for collision-dominated thermal conduction, the functional dependencies of the scaling laws are the same as for the static case, when the radiative losses scale as T -1/2, but with a different constant of proportionality that depends on the Mach number M of the flow. The dependence on the Mach number is such that the scaling laws for low to moderate Mach number flows are almost indistinguishable from the static case. When thermal conduction is limited by turbulent processes, however, the much weaker dependence of the scattering mean free path (and hence thermal conduction coefficient) on temperature leads to a limiting Mach number for return enthalpy fluxes driven by thermal conduction between the the corona and chromosphere.

Frequency Dependence of Initial Heat Generation in Granular Magnetite Nanoparticles

The frequency dependence of heat generation in granular magnetite nanoparticles was studied using vibrating sample magnetometry and the nanoTherics Magnetherm™ hyperthermia testing system. First, the particle size and its distribution were obtained by fitting the M-H curve to the classical Langevin function weight-averaged with a modified log-normal size distribution function. Next, the ac power dissipation model for monodispersed nanoparticles was extended to the polydispersed case, and the volumetric heating rate was predicted as a function of the frequency of the applied field under the assumption of the Neel relaxation mechanism. Finally, the temperature increase caused by the application of an ac magnetic field was measured experimentally at frequencies of 50, 112, 261, 335, 474 and 523 kHz, with the root-mean-squared field fixed to 250 Oe, and the results were compared with those from theoretical calculation. The frequency dependence of the initial heating rates was found to be in good agreement with the results predicted by using the polydispersed power dissipation model.

A combo system consisting of simultaneous persulfate recirculation and alternating current electrical resistance heating for the implementation of heat activated persulfate ISCO

A combo system capable of simultaneous persulfate recirculation and low temperature electrical resistance heating (ERH) was developed for subsurface remediation of organic contaminants using heat-activated persulfate. First, dual-function injection/extraction-electrode wells were designed, and a laboratory-scale combo system was custom-build. Experiments in water tanks and sand tanks were then carried out to investigate the performance of the combo system, and study the impact of main operating parameters (persulfate dosage, recirculation rate, and phase voltage) on volumetric delivery and dispersion of heat and persulfate, and consequent volumetric oxidation of phenanthrene-spiked sand, a model compound of HOCs. The results indicate that the addition of persulfate salts could significantly improve volumetric heating rate, and application of recirculation brought more uniform elevation in temperature and enhanced volumetric degradation of phenanthrene in the recirculation-impacted zone. Overall, this study developed a promising combo system for the implementation of heat-activated persulfate ISCO.

The Magnetic Properties of Heating Events on High-temperature Active-region Loops

Abstract Understanding the relationship between the magnetic field and coronal heating is one of the central problems of solar physics. However, studies of the magnetic properties of impulsively heated loops have been rare. We present results from a study of 34 evolving coronal loops observed in the Fe xviii line component of 94 Å filter images obtained by the Atmospheric Imaging Assembly (AIA)/Solar Dynamics Observatory (SDO) from three active regions with different magnetic conditions. We show that the peak intensity per unit cross section of the loops depends on their individual magnetic and geometric properties. The intensity scales proportionally to the average field strength along the loop (B avg) and inversely with the loop length (L) for a combined dependence of . These loop properties are inferred from magnetic extrapolations of the photospheric Helioseismic and Magnetic Imager (HMI)/SDO line-of-sight and vector magnetic field in three approximations: potential and two nonlinear force-free (NLFF) methods. Through hydrodynamic modeling (enthalpy-based thermal evolution loop (EBTEL) model) we show that this behavior is compatible with impulsively heated loops with a volumetric heating rate that scales as .

Subresolution activity in solar and stellar coronae from magnetic field line tangling

The heating of coronal loops is investigated to understand the observational consequences in terms of the thermodynamics and radiative losses from the Sun as well as the magnetized coronae of stars with an outer convective envelope. The dynamics of the Parker coronal heating model are studied for different ratios of the photospheric forcing velocity timescale $t_p$ to the Alfv\'en crossing time along a loop $t_A$. It is shown that for $t_p/t_A \gtrsim$ 10--24 the heating rate and maximum temperature are largest and approximately independent of $t_p/t_A$, leading to a strong emission in X-rays and EUV. On the opposite decreasing $t_p/t_A$ to smaller values leads to lower heating rates and plasma temperatures, and consequently fading high-energy radiative emission once $t_p/t_A \lesssim$ 1--3. The average volumetric loop heating rate is shown to scale as $\ell_p u_p B_0^2/4\pi L^2$, where $\ell_p$ and $u_p$ are respectively the convective granule length-scale and velocity, $B_0$ is the intensity of the strong magnetic field threading the loop, and $L$ the loop length. These findings support a recent hypothesis explaining ultracool dwarf observations of stars with similar magnetic field strength but radically different topologies displaying different radiative emission.

The Earth’s mantle in a microwave oven: thermal convection driven by a heterogeneous distribution of heat sources

Convective motions in silicate planets are largely driven by internal heat sources and secular cooling. The exact amount and distribution of heat sources in the Earth are poorly constrained and the latter is likely to change with time due to mixing and to the deformation of boundaries that separate different reservoirs. To improve our understanding of planetary-scale convection in these conditions, we have designed a new laboratory setup allowing a large range of heat source distributions. We illustrate the potential of our new technique with a study of an initially stratified fluid involving two layers with different physical properties and internal heat production rates. A modified microwave oven is used to generate a uniform radiation propagating through the fluids. Experimental fluids are solutions of hydroxyethyl cellulose and salt in water, such that salt increases both the density and the volumetric heating rate. We determine temperature and composition fields in 3D with non-invasive techniques. Two fluorescent dyes are used to determine temperature. A Nd:YAG planar laser beam excites fluorescence, and an optical system, involving a beam splitter and a set of colour filters, captures the fluorescence intensity distribution on two separate spectral bands. The ratio between the two intensities provides an instantaneous determination of temperature with an uncertainty of 5% (typically 1K). We quantify mixing processes by precisely tracking the interfaces separating the two fluids. These novel techniques allow new insights on the generation, morphology and evolution of large-scale heterogeneities in the Earth’s lower mantle.

DIAGNOSTICS OF CORONAL HEATING IN ACTIVE-REGION LOOPS

ABSTRACT Understanding coronal heating remains a central problem in solar physics. Many mechanisms have been proposed to explain how energy is transferred to and deposited in the corona. We summarize past observational studies that attempted to identify the heating mechanism and point out the difficulties in reproducing the observations of the solar corona from the heating models. The aim of this paper is to study whether the observed extreme ultraviolet (EUV) emission in individual coronal loops in solar active regions can provide constraints on the volumetric heating function, and to develop a diagnostic for the heating function for a subset of loops that are found close to static thermal equilibrium. We reconstruct the coronal magnetic field from Solar Dynamics Observatory/HMI data using a nonlinear force-free magnetic field model. We model selected loops using a one-dimensional stationary model, with a heating rate dependent locally on the magnetic field strength along the loop, and we calculate the emission from these loops in various EUV wavelengths for different heating rates. We present a method to measure a power index β defining the dependence of the volumetric heating rate E H on the magnetic field, , and controlling also the shape of the heating function: concentrated near the loop top, uniform and concentrated near the footpoints. The diagnostic is based on the dependence of the electron density on the index β. This method is free from the assumptions of the loop filling factor but requires spectroscopic measurements of the density-sensitive lines. The range of applicability for loops of different length and heating distributions is discussed, and the steps to solving the coronal heating problem are outlined.

DEPENDENCE OF OCCURRENCE RATES OF SOLAR FLARES AND CORONAL MASS EJECTIONS ON THE SOLAR CYCLE PHASE AND THE IMPORTANCE OF LARGE-SCALE CONNECTIVITY

ABSTRACT We investigate the dependence of the occurrence rates of major solar flares (M- and X-class) and front-side halo coronal mass ejections (FHCMEs), observed from 1996 to 2013, on the solar cycle (SC) phase for six active McIntosh sunspot group classes: Fkc, Ekc, Dkc, Fki, Eki, and Dki. We classify SC phases as follows: (1) ascending phase of SC 23 (1996–1999), (2) maximum phase of SC 23 (2000–2002), (3) descending phase of SC 23 (2003–2008), and (4) ascending phase of SC 24 (2009–2013). We find that the occurrence rates of major flares and FHCMEs during the descending phase are noticeably higher than those during the other phases for most sunspot group classes. For the most active sunspot group class, Fkc, the occurrence rate of FHCMEs during the descending phase of SC 23 is three times as high as that during the ascending phase of SC 23. The potential of each McIntosh sunspot group class to produce major flares or FHCMEs is found to depend on the SC phase. The occurrence rates (R) of major flares and FHCMEs are strongly anti-correlated with the annual average latitude of the sunspot groups (L): for major flares and for FHCMEs. This finding indicates the possible role of large-scale coronal connectivity, e.g., trans-equatorial loops, in powerful energy releases. Interestingly, this relationship is very similar to that between the volumetric coronal heating rate and X-ray loop lengths, indicating common energy release mechanisms.

Microwave heating characteristics of magnetite ore

The heating characteristics of magnetite ore under microwave irradiation were investigated as a function of incident microwave power, particle size, and magnetite ore mass. The results showed that the heating rate of magnetite ore is highly dependent on microwave power and magnetite ore mass. The maximum heating rate was obtained at a microwave irradiation power of 1.70 kW with a mass of 25 g and particle size between 53-75 µm. The volumetric heating rate of magnetite ore was investigated by measuring the temperature at different depths during microwave irradiation. Microwave irradiation resulted in modification of the microstructure of the magnetite ore, but new phases such as FeO or Fe2O3 were not formed. In addition, the crystal size decreased from 115 nm to 63 nm after microwave irradiation up to 1573 K.

Characterization of the electrocaloric effect and hysteresis loss in relaxor ferroelectric thin films under alternating current bias fields

We report characterization and analysis of the frequency-dependent temperature responses in thin films exhibiting the electrocaloric (EC) effect under AC bias fields using a high-precision lock-in technique. The temperature response detected by an embedded thin-film resistance thermometer is analyzed using the steady-periodic solutions of a 3D heat conduction model to extract the equivalent volumetric heat sources/sinks, which represent the combined effects of electrocaloric cooling/heating and hysteresis loss. The dependence of the measured heat source strengths on the bias field frequency and amplitude is consistent with our model prediction and independently measured dielectric properties. The volumetric heating rate due to hysteresis loss is estimated to be as much as 15% of the EC heating/cooling rates for solution-cast relaxor ferroelectric polymer films studied here. Our experimental approach enables a systematic study of the electrocaloric performance of thin films and deleterious impact of hysteresis loss.

THE COSMOLOGICAL IMPACT OF LUMINOUS TeV BLAZARS. II. REWRITING THE THERMAL HISTORY OF THE INTERGALACTIC MEDIUM

The Universe is opaque to extragalactic very high-energy gamma rays (VHEGRs, E>100 GeV) because they annihilate and pair produce on the extragalactic background light. The resulting ultra-relativistic pairs are assumed to lose energy through inverse Compton scattering of CMB photons. In Broderick et al. (2011, Paper I of this three paper series), we argued that instead powerful plasma instabilities in the ultra-relativistic pair beam dissipate the kinetic energy of the TeV-generated pairs locally, heating the intergalactic medium (IGM). Here, we explore the effect of this heating upon the thermal history of the IGM. We collate the observed extragalactic VHEGR sources to determine a local VHEGR heating rate and correct for the pointed nature of VHEGR observations using Fermi observations of high and intermediate peaked BL Lacs. Because the local extragalactic VHEGR flux is dominated by TeV blazars, we tie the TeV blazar luminosity density to the quasar luminosity density, and produce a VHEGR heating rate as a function of redshift. This heating is relatively homogeneous for z<~4 with increasing spatial variation at higher redshift (order unity at z~6). This new heating process dominates photoheating at low redshift and the inclusion of TeV blazar heating qualitatively and quantitatively changes the structure and history of the IGM. TeV blazars produce a uniform volumetric heating rate that is sufficient to increase the temperature of the mean density IGM by nearly an order of magnitude, and at low densities by substantially more, naturally producing an inverted equation of state inferred by observations of the Ly-alpha forest, a feature that is difficult to reconcile with standard reionization models. Finally, we close with a discussion on the possibility of detecting this hot low-density IGM, but find that such measurements are currently not feasible. (abridged)

Ohmic heating of dairy fluids—effects of local electric field on temperature distribution

AbstractThis paper presents the heat transfer model of a continuous flow ohmic heating process. The model fluid used was a mixture of reconstituted skimmed milk and whey protein concentrate solution. Two‐dimensional numerical simulations of an annular ohmic heater were performed using a general purpose partial differential equation solver, FlexPDE. The momentum, energy, and electrical equations were solved for a laminar flow regime. Two models were used to determine the volumetric heating rate, one taking into account the local electric field by solving the Laplace equation while another model assumes an average voltage gradient applied between the two electrodes. Results show that while the wall temperature distribution is different for the two cases, the bulk fluid temperature and the average outlet temperature are the same. The predicted temperatures generally agree well with the measured temperatures. Copyright © 2009 Curtin University of Technology and John Wiley &amp; Sons, Ltd.

Joule heating and anomalous resistivity in the solar corona

Abstract. Recent radioastronomical observations of Faraday rotation in the solar corona can be interpreted as evidence for coronal currents, with values as large as 2.5×109 Amperes (Spangler, 2007). These estimates of currents are used to develop a model for Joule heating in the corona. It is assumed that the currents are concentrated in thin current sheets, as suggested by theories of two dimensional magnetohydrodynamic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calculated volumetric heating rate is compared with an independent theoretical estimate by Cranmer et al. (2007). This latter estimate accounts for the dynamic and thermodynamic properties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cranmer et al estimate by at least a factor of 3×105. The currents inferred from the observations of Spangler (2007) are not relevant to coronal heating unless the true resistivity is enormously increased relative to the Spitzer value. However, the same model for turbulent current sheets used to calculate the heating rate also gives an electron drift speed which can be comparable to the electron thermal speed, and larger than the ion acoustic speed. It is therefore possible that the coronal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.

Forward Modeling of Active Region Coronal Emissions. II. Implications for Coronal Heating

In Paper I, we introduced and tested a method for predicting solar active region coronal emissions using magnetic field measurements and a chosen heating relationship. Here, we apply this forward-modeling technique to 10 active regions observed with the Mees Solar Observatory Imaging Vector Magnetograph and the Yohkoh Soft X-ray Telescope. We produce synthetic images of each region using four parameterized heating relationships depending on magnetic field strength and geometry. We find a volumetric coronal heating rate (dEH/dV, not to be confused with dEH/dA quoted by some authors) proportional to magnetic field and inversely proportional to field-line loop length (BL−1) best matches observed coronal emission morphologies. This parameterization is most similar to the steady-state scaling of two proposed heating mechanisms: van Ballegooijen's "current layers" theory, taken in the AC limit, and Parker's "critical angle" mechanism, in the case where the angle of misalignment is a twist angle. Although this parameterization best matches the observations, it does not match well enough to make a definitive statement as to the nature of coronal heating. Instead, we conclude that (1) the technique requires better magnetic field measurement and extrapolation techniques than currently available, and (2) forward-modeling methods that incorporate properties of transiently heated loops are necessary to make a more conclusive statement about coronal heating mechanisms.