Negative Temperature Gradient Research Articles

Quantification of the near-surface wind conditions of the African coast: A comparative approach (satellite, NCEP CFSR and WRF-based)

The temporal and spatial variations of the near-surface wind conditions across the African coast are enormous due to local flow perturbations from changes in sea surface roughness or/and the weather system processes driven mainly by the Atlantic and Indian Ocean Currents. Over the past decades, the patterns of the near surface wind speed and directional flow have significantly changed across the globe. To quantify the long-term changes of the surface wind conditions off the African coasts, the spatial distributions of historical wind climates and analyzed surface temperature from remote sensing and two atmospheric models are presented. Thus, the offshore wind conditions variability derived across 4 coastal zones are quantified through a comparative approach. Over period of 2001–2010, the trends of regional-scale wind conditions from the numerical model of NCEP CFSR and satellite observations of CCMP are assessed. For identification of geographical viable locations with concentrated energy resource and negative temperature gradient, the surface wind conditions are adjusted to offshore turbine generator (V80 2 MW) operating height of 100 m. Based on statistical evaluation of the offshore wind condition, graphical representations of the historical wind climate are presented. Furthermore, the monthly and seasonal sectorwise winds at 10 and 100 m ASL for 2002 are compared in determining how local perturbations had caused a drift in offshore wind flows within the boundary height of 100 m. On local-scale evaluation, the near-surface wind conditions derived from WRF are validated with NCEP and CCMP datasets. The long-term historical wind conditions in time and space revealed that the satellite, WRF and NCEP models are reliable tools in replication of the coastal wind conditions across the coasts of Africa. Results also indicate the southeast coast to be an energetic region with concentrated mean wind energy flux between 300 and 1580 W/m2 (8.10–13.70 m/s), but subjects to coastal variations of strong weather processes. No persistent wind pattern was found when considering the variability of near-surface wind conditions from a low to high latitude.

Investigation of Heat and Moisture Transport in Bananas during Microwave Heating Process

The numerical method was used to investigate heat and moisture transport during dehydration of bananas from microwave heating. COMSOL multi-physics software was employed to perform the simulation task. A banana is defined as a porous medium. It has constituents of water, vapor, air as the liquid phase and a solid porous matrix. The numerical results of this study were validated with experimental data. The profiles of moisture, vapor and pressure are discussed in this study. Moreover, the effects of the ripening stages of the banana are examined. A higher heat flux was observed from the beginning period along with the increasing time steps until 50 s. Heat generation decreased during 50 s to 60 s, coinciding with a small rise in temperature, but the temperature gradient remained constant. The temperature distribution of both unripe and ripe banana samples was non-uniform. At the center of the banana, the temperature increased rapidly and reached its highest temperature with the negative temperature gradient toward the boundary surface. More heat generation was observed around the center region of the banana. This was due to higher moisture in comparison with the boundary surface. Heat and moisture were transported from the center of the banana to its surface. The water convective flux peaked around 11 mm from the center. The vapor pressure peaked at the center for all cases. Less heat generation within unripe bananas was observed due to the lower moisture content.

The effect of grain boundaries on instability at the crystal/melt interface during the unidirectional growth of Si

The instability of crystal/melt interfaces including numerous Σ3, small-angle and large-angle grain boundaries during the unidirectional growth of Si was investigated, using an in situ observation system. Planar crystal/melt interfaces including Σ3 or small-angle grain boundaries were found to undergo local morphological transformation at the grain-boundary positions during high-velocity growth. The data also confirmed that the critical growth velocity for the appearance of instability at a crystal/melt interface including grain boundaries is significantly lower than that for a single crystal Si/melt interface. The ambient temperature field at the crystal/melt interface was calculated, taking into account the effective thermal conductivities of grain boundaries and the results show that a negative temperature gradient readily forms in the case that grain boundaries are present.

Long-term field test of temperature gradients on the composite girder of a long-span cable-stayed bridge

Bridges are inevitably affected by daily, seasonal and annual air temperature and solar radiation. The thermal effects on bridges, especially for long-span cable-stayed bridges with composite girders, are significant and complicated. The evaluation of temperature distribution has been a primary concern to bridge engineers and researchers. This article presents a more than one-year temperature database of a long-span cable-stayed bridge with a small cantilever length-to-web depth ratio in the composite girder. Uniform temperature, linear temperature difference, thermal curvature, and self-equilibrated thermal stress are considered to imply the characteristics of the temperature distribution in such composite girders. Two profiles (profile 1 and profile 2) for positive vertical temperature gradient and one profile (profile 3) for negative vertical temperature gradient are proposed. The extreme temperature differences with a 100-year return period are determined for each profile with extreme value analysis. Among the three profiles, profile 2 is unique for composite girders with a small cantilever length-to-web depth ratio. Based on parametric studies, profile 2 is revised with the cantilever length-to-web depth ratio for wide applications. Finally, comparisons of vertical temperature gradients are made between the investigated composite girder and the recommendations in Chinese Specification.

Numerical analyses of rigid and flexible pavements responses under heavy vehicles’ loading

In an attempt to better understand the interaction between heavily loaded trucks and the pavement structure; rigid and flexible pavements’ responses (stresses, strains and deflections) were evaluated under simulated loading of 11-axle trucks (MI-20, MI-18, MI-14, MI-13) at gross vehicle weights (GVW) of 164,000 lb with different axle configurations, which are allowed in the state of Michigan. These responses were compared against results of a standard 5-axle semi-trailer at GVW nearing the common 80,000 lb standard in most states. Using these heavy truck types, the combined effects of truck loading, pavement thickness, joint spacing, material properties and thermal conditions on the pavement damages were evaluated. The major fatigue and faulting damages for rigid pavements as well as fatigue damage and subgrade rutting for flexible (asphalt) pavements are analysed. The finite element method (FEM) based program ISLAB2000 and multilayer elastic theory (MLET) based program JULEA were used to compute rigid and flexible pavements responses, respectively. Results show that the standard 5-axle truck yields up to 50% more fatigue damage potential under positive temperature gradient across slab (during daytime) even at a much lower gross vehicle weight than that of Michigan (MI) trucks. However, the 11-axle MI trucks provide up to 45% higher fatigue damage potential under negative temperature gradient (during nighttime). In comparison with the standard truck, the 11-axle MI trucks yield up to 17% less faulting damage for the typical rigid pavement with a thickness of 8 mm and up to 18% more faulting for larger pavement thickness. In flexible pavements, the standard truck exhibits up to 39% higher asphalt concrete fatigue damage than MI trucks. However, up to 80% more subgrade rutting damage for typical flexible pavements is observed for MI trucks with the multi-axles group configuration and larger GVW than the standard truck.

Strong seasonal connectivity between shallow groundwater and soil frost in a humid alpine meadow, northeastern Qinghai-Tibetan Plateau

The freeze-thaw cycle in the active soil layer plays a crucial role in cold-region hydrological processes, yet the effect of vertical water migration caused by the soil frost on shallow groundwater remains poorly quantified. The shallow groundwater level (GWL), soil frost depth and main environmental controls were monitored in a humid alpine meadow on the northeastern Qinghai-Tibetan Plateau from 2012 to 2017. GWL fluctuated with two seasonal maxima and minima during soil frost-centric year from November to October. GWL declined remarkably from the strong peak (3.9 ± 0.2 m, Mean ± S.D.) in mid-January to the strong minimum (4.8 ± 0.1 m) in mid-May, and then increased to the second peak (4.2 ± 0.2 m) in late August. This seasonal variability in GWL was mainly attributed to the freeze-thaw processes of the lower layer soil frost from November to late June both at a ∼45-day delay, respectively. The clear increasing GWL from mid-November to mid-January was probably related to the melted upper layer soil frost, which was detained in subsoil layers because of the high thermal isolating effect in topsoil Mattic Epipedon (dense organic-rich turf) and the associated negative subsoil profile temperature gradient from mid-May to late August. The seasonal N-type in GWL was thus hysteretically determined by the soil freeze-thaw processes and the related subsoil profile temperature gradient. Annually, GWL was significantly correlated with air temperature (R2 = 0.88, P = 0.003, N = 6), suggesting the shallow groundwater recharges would be weakened under the warming scenario. Annual GWL was not directly connected with annual precipitation (P = 0.81), likely owing to the high water holding capacity of the topsoil Mattic Epipedon and the similarity between precipitation input and evapotranspiration loss. This critical buffering function of the topsoil Mattic Epipedon in vertical moisture movement should be taken into consideration when modeling regional water dynamics in humid alpine meadows.

Optimization of Structure Parameters of Airfield Jointed Concrete Pavements under Temperature Gradient and Aircraft Loads

Daily changing temperature causes significant thermal stress in concrete pavement. Tensile stress obtained can exceed flexural tensile strength when the concrete slabs are subjected to large temperature gradient and traffic loads, resulting in pavement damages. In this paper, maximum tensile stresses in concrete slabs with different slab sizes, thicknesses, and length to width (L/W) ratios were investigated by using the finite element (FE) method. The important parameters in the design of concrete pavement are the flexural tensile strength and the fatigue limit. By analyzing the comparison results between the maximum tensile stress and the fatigue limit, the optimum slab size and the critical thickness were determined. The results indicate that the maximum tensile stress obtained is higher for larger slab size with thin thickness. Furthermore, to reduce cutting work and the amount of dowel bars, the optimum slab sizes of the regional airport concrete pavement are recommended as 4 m × 4 m to 6 m × 6 m. The critical thicknesses of 4 m × 4 m slab and 6 m × 6 m slab are determined as 28.2 cm and 34.7 cm, respectively, based on the most unfavorable coupling between positive and negative temperature gradients and the Boeing 737–800 aircraft load. Moreover, the maximum tensile stress increases as the L/W ratio increases. When the slab length is less than 6 m, it is better to use square slab in airport jointed concrete pavement (JCP).

Control of Stratification in Drying Particle Suspensions via Temperature Gradients.

A potential strategy for controlling stratification in a drying suspension of bidisperse particles is studied using molecular dynamics simulations. When the suspension is maintained at a constant temperature during fast drying, it can exhibit "small-on-top" stratification with an accumulation (depletion) of smaller (larger) particles in the top region of the drying film, consistent with the prediction of current theories based on diffusiophoresis. However, when only the region near the substrate is thermalized at a constant temperature, a negative temperature gradient develops in the suspension because of evaporative cooling at the liquid-vapor interface. Since the associated thermophoresis is stronger for larger nanoparticles, a higher fraction of larger nanoparticles migrate to the top of the drying film at fast evaporation rates. As a result, stratification is converted to "large-on-top". Very strong small-on-top stratification can be produced with a positive thermal gradient in the drying suspension. Here, we explore a way to produce a positive thermal gradient by thermalizing the vapor at a temperature higher than that of the solvent. Possible experimental approaches to realize various thermal gradients in a suspension undergoing solvent evaporation and thus to produce different stratification states in the drying film are suggested.

Specific kinetic triplet estimation of Tahe heavy oil oxidation reaction based on non-isothermal kinetic results

Although the oxidation mechanisms and kinetics characteristics of heavy oils have been involved in enormous studies, little attention is paid to the specific kinetics triplet and activation energy distribution in detailed temperature ranges. In this study, the non-isothermal oxidation kinetics characteristics of the Tahe heavy oil, including kinetics triplet, activation energy distribution (E-α curve) and thermodynamic parameters under specific temperature subzones, were investigated by thermo-analysis techniques and Popescu method. And it indicated that six sequential temperature subzones were identified with different mechanism function, G(α), and rate constant, k(T). Besides, it can be seen from the E-α curve that the first obvious increasing peak was attributed to the negative temperature gradient region (NTGR) and the second mild peak corresponded to the initiation stage of the combustion process, between which positive temperature coefficient and negative temperature coefficient zones were located at the valley. Additionally the calculated thermodynamic parameters (△S*, △H*, △G*) indicated that the non-isothermal oxidation process for Tahe heavy oil is the non-spontaneous reaction and needs heat to occur under atmospheric pressure.

Simulation of Temperature Distribution and Microstructure Evolution in the Molten Pool of GTAW Ti-6Al-4V Alloy.

In this paper, a three-dimensional (3D) finite element model was established by ABAQUS software to simulate the welding temperature field of a Ti-6Al-4V alloy under different welding currents based on a Gaussian heat source model. The model uses thermo-mechanical coupling analysis and takes into account the effects of convection and radiation on all weld surfaces. The microstructure evolution of the molten pool was calculated using the macro-micro coupling cellular automaton-finite different (CA-FD) method. It was found that with the increase of the welding current, the temperature in the central region of the moving heat source was improved and the weld bead became wider. Then, the dendritic morphology and solute concentration of the columnar to equiaxed transition (CET) in the weld molten pool was investigated. It is shown that fine equiaxed crystals formed around the columnar crystals tips during solidification. The coarse columnar crystals are produced with priority in the molten pool and their growth direction is in line with the direction of the negative temperature gradient. The effectiveness of the model was verified by gas tungsten arc welding experiments.

The Study of Zonal Circulation of Venus’s Atmosphere by Data Analysis of Radio Occultation Measurements Made by Venera-15 and -16 Satellites

The vertical profiles of temperature and pressure obtained from radio occultation measurements made by satellites Venera-15 and -16 from October 1983 to September 1984 are used for the analysis of wind speed in Venus’s atmosphere. The altitude and latitude dependences of zonal wind speed in the middle atmosphere of the planet’s northern and southern hemispheres are identified at altitudes from 50 to 80 km over the latitude interval of 60°–85°. Zonal speeds were determined assuming cyclostrophic atmosphere balance. The existence of jet flows, whose maximal speed is ~100 m/s and axis is placed at an altitude near 60 km within the latitude zone of 73°–75° N, is confirmed in the northern polar atmosphere of the planet. The results of wind speed measurements in the southern hemisphere clearly show that the jet flows exist at an altitude around 62 km at latitudes from 70° to 72° S, and their zonal speed reaches a maximum of ~115 m/s. It is found that these jets at high latitudes are stipulated by negative latitudinal temperature gradients at altitudes below the jet flow axes in Venus’s polar atmosphere.

Cellular Automaton Modeling of Silicon Facet Formation during Directional Solidification

Silicon facet formation during directional solidification is simulated by cellular automaton (CA) modeling in which anisotropic interfacial energy and kinetics are considered. Numerical simulations were performed with different anisotropy strengths of interfacial energy and they show good agreement with analytical equilibrium shapes obtained by the Gibbs-Thomson equation. We also compare our results of anisotropic kinetics with in situ observation experiments and the results of the phase model to verify the accuracy of our model. Simulation results of facet formation show that perturbation is promoted to the corner by the negative temperature gradient of the interface and the heat accumulation location leads to the disappearance of small corners.

Detonation onset in a thermally stratified constant volume reactor

Understanding detonation development from a flame kernel initiated by a pre-ignition event is important for modern internal combustion (IC) engines operating at boosted conditions. To provide fundamental insights into the effects of bulk gas temperature stratification on the characteristics of detonation development, one-dimensional high fidelity simulations were conducted for a constant volume reactor filled with a thermally stratified reactive stoichiometric hydrogen/air mixture. A linear temperature variation in the upstream end-gas was introduced to represent the thermal stratification of the bulk mixture, and the evolution from the initial deflagration flame front to detonation development was examined. The results showed that the bulk-gas temperature gradient has a significant effect on the run-up time and intensity of the developing detonation. Detailed analyses further revealed that the mechanism of detonation development is qualitatively different for the positive and negative temperature gradient cases. In the former, the detonation development is initiated by the end-gas autoignition at the wall, while the latter exhibits detonation development following the process of the self-acceleration of the flame similar to the deflagration-to-detonation transition. This behavior is attributed to the longer residence time in the end-gas allowing the reinforcement by the interaction of incident and reflected pressure waves during the flame propagation, and results in the peak pressure even higher than the case with the same level of positive temperature gradient. Furthermore, yet another detonation development pattern was observed for the negative temperature gradient condition in the presence of a uniform temperature region just ahead of the flame. In this case, autoignition was found to start in the middle of the bulk end-gas, and subsequently leads to the transition to detonation. The results demonstrate the importance of the bulk gas conditions in predicting the detonation development, which corroborate the existing theoretical framework.

Fine‐scale climate variability in a complex terrain basin using a high‐resolution weather station network in southeastern Brazil

Montane climates are shaped by high spatial variability that depends on net radiation and synoptic weather, and much on elevation and topographic features of terrain. We measured near‐ground meteorological variables using a weather station network during 14 months, in a valley‐shaped basin in southeast Brazil, to address the spatiotemporal climate variability at the meso‐γ atmospheric scale. The terrestrial climatic gradients were evident in the cross‐valley direction of the basin, where the valley tended to warm/wet up at day and cool/dry down at night relatively from the slopes. The temperature at noon showed high variability and decreased at a mean gradients of about −0.7 °C (100 m)−1. The nocturnal air temperature increased with height up to a maximum at about 200 m (the thermal belt), and showed seasonal rates higher/less in dry/wet season of +1.1/+0.2 °C (100 m)−1 over the full altitude. The vapour pressure decreased from the valley bottom upwards, in general below −0.5 hPa (100 m)−1, whereas the wind speed increased at a rate of 0.9 m s−1 (100 m)−1. We noted significant differential warming along the valley and mountain sides. The middle valley was circumstantially colder at night and warmer at daytime, relatively to the upper catchment, under mean magnitudes below 1.0 °C. The west slope at upper catchment was slightly warmer at night, and colder in the afternoon, at magnitudes below 0.5 °C, highlighting the control of hills’ aspect at daytime, and the sheltering to flow aloft in east side. The cross‐valley gradients appeared to be well associated with local circulation, where downslope wind and positive temperature gradients, as well as upslope wind and negative temperature gradients strictly coexisted during the morning. The terrestrial gradients and the thermal circulation were in general dampened by cloudiness and mechanical mixing.

Analytical solution to spontaneous imbibition under vertical temperature gradient based on the theory of spontaneous imbibition dynamics

In this work, we have theoretically studied the imbibition process related to a block in a fractured carbonate reservoir under an assumed constant, vertical temperature gradient, GT. An analytical solution to an ordinary differential equation we developed has been obtained using a computer program, and the original Washburn law normally valid for isothermal conditions of spontaneous imbibition has been found to hold true for GT equal to zero. The theoretical results of our study show that the space and time evolution of the imbibition front is strongly dependent on surface tension and dynamic viscosity of the imbibing fluid under a given temperature gradient. We have also validated our model against experimental data from a literature source based on spontaneous imbibition into a Hele Shaw Cell under longitudinal temperature gradient. The general conclusion of our study is that spontaneous imbibition in fractured carbonate reservoirs will be accelerated the higher the temperature of the injected water. This corresponds to a negative temperature gradient where the temperature of the injected water exceeds the ambient temperature of the reservoir.

The Effects of the Spatial Distribution of Direct Anthropogenic Aerosols Radiative Forcing on Atmospheric Circulation

The large uncertainty in estimating the global aerosol radiative forcing (ARF) is one of the major challenges the climate community faces for climate projection. While the global-mean ARF may affect global quantities such as surface temperature, its spatial distribution may result in local thermodynamical and, thus, dynamical changes. Future changes in aerosol emissions distribution could further modulate the atmospheric circulation. Here, the effects of the spatial distribution of the direct anthropogenic ARF are studied using an idealized global circulation model, forced by a range of estimated-ARF amplitudes, based on the Copernicus Atmosphere Monitoring Service data. The spatial distribution of the estimated-ARF is globally decomposed, and the effects of the different modes on the circulation are studied. The most dominant spatial distribution feature is the cooling of the Northern Hemisphere in comparison to the Southern Hemisphere. This induces a negative meridional temperature gradient around the equator, which modulates the mean fields in the tropics. The ITCZ weakens and shifts southward, and the Northern (Southern) Hemisphere Hadley cell strengthens (weakens). The localization of the ARF in the Northern Hemisphere midlatitudes shifts the subtropical jet poleward and strengthens both the eddy-driven jet and Ferrel cell, because of the weakening of high-latitude eddy fluxes. Finally, the larger aerosol concentration in Asia compared to North America results in an equatorial superrotating jet. Understanding the effects of the different modes on the general circulation may help elucidate the circulation’s future response to the projected changes in ARF distribution.

Oil transportation in pipelines with the existence of ice

In the Arctic environment, ambient temperature can drop below the freezing point, which may lead to ice formation in the oil transportation pipelines. Natural hazards can also cause freezing in the liquid transportation system. The formation of ice can cause flow assurance and process safety issues, such as restricting flow path, pipeline plugging, failure of pipeline components, the release of hazardous liquid, and fire. Restricting of flow path causes additional burden to the upstream pumping system, while pipeline plugging leads to shutdown of the pipeline system and causes tremendous cost to remediate plugging. The incidents with hazardous liquid release and fire can also lead to enormous expenses. This paper investigates the risks of ice formation in the pipeline and its effect on the transportation system. The experimental tests were performed in a 2-inch diameter carbon steel flow loop. Pressure, temperature, and differential temperature were measured during the test. The experimental results show that an annular ice deposition layer was observed at the pipe inner wall, which restricted flow path and caused an increased differential pressure. The deposition of ice on the pipe surface required a negative temperature gradient. Ice accumulations were identified at the low spot in front of the flow meter, the inserted thermocouples, and the perforated plate. The deposition and accumulation mechanisms are discussed. Both the ice layer on the pipe surface and ice accumulation at the pipeline components were porous, indicating the formation mechanism was due to small ice crystals sticking to the pipe surface. The study on deposition and plugging mechanism can help provide a guidance to prevent hazardous liquid transportation damages triggered by ice plugging.

Mechanical property and damage evolution of concrete interface of ballastless track in high-speed railway: Experiment and simulation

The interface damage of ballastless tracks in high-speed railway is considered as one of the most critical damage problems, however, the mechanical property and damage evolution of the concrete interface of ballastless tracks are rarely ascertained, and maintenance of the interface damage has been a heavy burden on the modern railway networks. This work aims to reveal the damage constitutive relationship and fatigue performance of the concrete interface of double-clock ballastless track based on experimental tests and simulation analysis. Firstly, by making the composite specimen composed of half track-slab concrete and half supporting-layer concrete and by designing experiment programs for the interface cracking test, the full-field evolution of strain distribution of the specimen under monotonic splitting loading is obtained based on the digital image correlation (DIC) technique, and the key parameters of a cohesive zone model for describing the interface stress-displacement relationship is determined. Subsequently, the interface damage evolution is investigated by applying cyclic splitting loads, and the interface fatigue S-N curve is acquired and validated by comparing with relevant references. It is found that the fatigue life of the concrete interface can be easily predicted with only knowing its secondary growth rate of the opening displacement amplitude. Furthermore, to elucidate the practical application of the experiment data and proposed models, the interface damage evolution of the double-block ballastless track under monotonic and cyclic temperature gradient loads are investigated, respectively. Simulation results show that much attentions should be paid to the negative temperature gradient load (below −60 °C/m) that could cause initiation of interface cracks. The proposed fatigue S-N curve enable a convenient and effective prediction for the interface fatigue damage of ballastless track with different service state under random loading cycles.

In-situ observation of instability of a crystal–melt interface during the directional growth of pure antimony

The instability of a crystal–melt interface during the directional growth of pure antimony was studied using an in-situ observation technique. The morphology of the crystal–melt interface was planar at a low growth velocity, while the interface transitioned to wavy and then zig-zag faceted at 60 μm s−1. Calculating the thermal field at the crystal–melt interface using a diffusion equation showed that the temperature gradient in the melt becomes negative when the moving velocity of the interface is higher than 52 μm s−1. These results demonstrate that perturbations introduced into the planar interface are amplified by a negative temperature gradient and these amplified perturbations result in zig-zag facets.

A theoretical model for delayed hydride cracking velocity considering the temperature history and temperature gradients

Delayed hydride cracking (DHC) threatens the safety of Zircaloy components. The DHC velocity in the stage of stable crack growth needs to be studied. Based on the recent research, with a new idea the theoretical model is developed for the DHC velocity considering the temperature history and temperature gradient. The stress field ahead of the crack tip is calculated based on the fracture mechanics theory of second-order estimate of plastic zone size, and the redistributed stresses are statically equivalent with the stresses obtained from Linear Elastic Fracture Mechanics. It is confirmed that a simple linear function of the equivalent axisymmetric temperature distribution can be effectively and easily calibrated for predictions of the DHC velocity at different temperature gradients along the cracking direction. The developed model is validated to be effective because the predicted velocities agree well with some experimental results for the cases with and without temperature gradients, whether the test temperature is approached by heating or cooling. The theoretical results indicate that (1) with a higher positive temperature gradient along the cracking direction, the DHC velocity increases and a higher crack arrest temperature will occur; while a negative temperature gradient will remarkably depress DHC process; (2) The total hydrogen concentration in the hydrogen source has an important effect on the DHC velocity, and the crack arrest temperature can be evidently lowered for the cases with a small quantity of hydrogen atoms there;(3) At higher temperatures, negative flux contribution from the hydrogen concentration gradient in the hydrogen source is found to be the main mechanism of crack arrest.