An improved estimate for the critical parameter value in a thermal explosion

In an earlier paper (Carter et al . 1979), estimates and bounds were derived for the critical initial reactant concentration in a thermal explosion with reactant consumption. In this paper, a greatly improved estimate for the critical concentration is obtained and its accuracy investigated. Arising from this, an excellent approximation is obtained for the relation between the critical value of the parameter a (expressing heat loss rate), the dimensionless adiabatic temperature rise B and the dimensionless ambient temperature ε. For ε = 0, this approximation is much closer to the known exact curve than any previously obtained estimates.

Download Full-text

Cellular Automata Approach to Hydration Heat of Concrete Based on Equivalent Time

Materials Science Forum ◽

10.4028/www.scientific.net/msf.982.181 ◽

2020 ◽

Vol 982 ◽

pp. 181-188

Author(s):

Yi Liu ◽

Yue Ting Yang ◽

Ling Chen ◽

Jing Zeng

Keyword(s):

Cellular Automata ◽

Ambient Temperature ◽

Temperature Rise ◽

Concrete Slab ◽

Hydration Heat ◽

Slab Thickness ◽

Adiabatic Temperature Rise ◽

Equivalent Time ◽

Arrhenius Function ◽

The Relationship

Cellular automata can be used to analyze a physical system which is satisfying differential equations. A cellular automata program for a thermal analysis of hydration heat was developed. Based on the fundamental theory of cellular automata, the heat conduction equation was deduced for validating the cellular automata approach. By introduction of the concept of equivalent time, the variation of the chemical reaction rate of hydration heat with temperature was studied by use of the Arrhenius function. The relationship between the adiabatic temperature rise and equivalent time was determined by analyzing testing data．A parametric analysis of ambient temperature and concrete slab thickness was also conducted. The temperature rise of concrete increases with increasing ambient temperature and thickness of the slab.

Download Full-text

Thermal explosion and the theory of its initiation by steady intense light

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1983.0131 ◽

1983 ◽

Vol 390 (1799) ◽

pp. 265-281 ◽

Cited By ~ 12

Keyword(s):

Ambient Temperature ◽

Thermal Explosion ◽

Critical Value ◽

Critical Conditions ◽

Central Temperature ◽

Self Heating ◽

Thermal Mechanism ◽

Arrhenius Temperature Dependence ◽

Intense Light ◽

Arrhenius Temperature

The initiation of explosion by steady intense light (from lasers or other sources) involves degradation of the radiation to heat, leading to self-heating and thermal runaway. The critical conditions for such a thermal mechanism can still be expressed in terms of the standard dimensionless group δ = qσ a 0 2 AEexp ( -E/RT a )/ k RT a 2 . When δ attains a critical value δ cr , thermal explosion occurs: the critical value depends on the intensity of the radiation. The dependence of δ cr on the light intensity β is computed numerically for an Arrhenius temperature-dependence of rate. The corresponding critical values for the reduced central temperature-excesses θ 0 , cr are also obtained. If the ambient temperature is too high or the activation energy is too low, so that є = RT a /E is not very small, the phenomenon of criticality disappears. Accurate transitional values for the reduced ambient temperature є tr are calculated as a function of the intensity of the light.

Download Full-text

Thermal explosion and times to ignition in systems with distributed temperatures. III. The influence of a steadily increasing (ramped) ambient temperature

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1986.0050 ◽

1986 ◽

Vol 405 (1829) ◽

pp. 213-228 ◽

Cited By ~ 6

Keyword(s):

Ambient Temperature ◽

Thermal Explosion ◽

Critical Value ◽

Rate Of Change ◽

Infinite Cylinder ◽

Order Unity ◽

Ambient Temperatures ◽

External Cooling ◽

Steady Rate ◽

Asymptotic Formulae

In classical treatments of thermal explosion, reactant consumption is ignored and ambient temperatures are assumed constant. We turn here to the very important case where the temperature of the surroundings is varying at a steady rate. The influence of this ramping and the importance of reactant consumption are considered for the whole range of Biot numbers from the Semenov extreme (β = 0) to the Frank-Kamenetskii extreme (β→∞) for arbitrary geometry and for any concentration- and temperature-dependence of reaction rate. External heating modifies the critical value for the Frank-Kamenetskii parameter δ ; δ cr /δ 0 = 1 + P[Qg w - α )/B] ⅔ . Here δ 0 is the critical value without reactant consumption, α is the dimensionless rate of change of ambient temperature (and is negative for external cooling), B is the dimensionless adiabatic temperature rise, and g w is the effective order of reaction. The numbers P and Q are of order unity and are determined here for all important circumstances. Illustrative values are presented for the sphere, the infinite cylinder and the infinite slab. Times to ignition are also evaluated and, for limiting cases, simple asymptotic formulae are given which are good approximations over wide ranges. Many of the new results parallel those for constant ambient temperature but a new branch of solutions is found if α > Qg w where thermal runaway becomes inevitable and criticality is lost.

Download Full-text

Effect of Slag Characteristics on Adiabatic Temperature Rise of Blended Concrete

ACI Materials Journal ◽

10.14359/51733150 ◽

2022 ◽

Author(s):

Hai Zhu ◽

Dhanushika Gunatilake Mapa ◽

Catherine Lucero ◽

Kyle A. Riding ◽

A. Zayed

Keyword(s):

Temperature Rise ◽

Adiabatic Temperature ◽

Adiabatic Temperature Rise

Download Full-text

Kinetic Model of Adiabatic Temperature Rise of Mass Concrete

Science of Advanced Materials ◽

10.1166/sam.2021.3951 ◽

2021 ◽

Vol 13 (5) ◽

pp. 771-780

Author(s):

Shou-Kai Chen ◽

Bo-Wen Xu

Keyword(s):

Temperature Field ◽

Temperature Rise ◽

Initial Conditions ◽

Dynamic Change ◽

Adiabatic Temperature ◽

Model Parameters ◽

Hydration Reaction ◽

Mass Concrete ◽

Adiabatic Temperature Rise ◽

Proposed Model

The adiabatic temperature rise model of mass concrete is very important for temperature field simulation, same to crack resistance capacity and temperature control of concrete structures. In this research, a thermal kinetics analysis was performed to study the exothermic hydration reaction process of concrete, and an adiabatic temperature rise model was proposed. The proposed model considers influencing factors, including initial temperature, temperature history, activation energy, and the completion degree of adiabatic temperature rise and is theoretically mature and definitive in physical meaning. It was performed on different initial temperatures for adiabatic temperature rise test; the data were employed in a regression analysis of the model parameters and initial conditions. The same function was applied to describe the dynamic change of the adiabatic temperature rise rates for different initial temperatures and different temperature changing processes and subsequently employed in a finite element analysis of the concrete temperature field. The test results indicated that the proposed model adequately fits the data of the adiabatic temperature rise test, which included different initial temperatures, and accurately predicts the changing pattern of adiabatic temperature rise of concrete at different initial temperatures. Compared with the results using the traditional age-based adiabatic temperature rise model, the results of a calculation example revealed that the simulated calculation results using the proposed model can accurately reflect the temperature change pattern of concrete in heat dissipation conditions.

Download Full-text

Modelling the critical concentration of mixed filler in mastic with synthetic wax

MATEC Web of Conferences ◽

10.1051/matecconf/201926205008 ◽

2019 ◽

Vol 262 ◽

pp. 05008 ◽

Cited By ~ 1

Author(s):

Grzegorz Mazurek ◽

Marek Iwański

Keyword(s):

Critical Concentration ◽

Hydrated Lime ◽

Critical Value ◽

Filler Concentration ◽

Mathematical Function ◽

Parallel Plates ◽

Proposed Model ◽

Wax Content ◽

Filler Phase ◽

Limestone Dust

This article presents the results of tests of mastic containing mixed filler (limestone dust/hydrated lime) and Fisher-Tropsch synthetic wax. Synthetic wax content was controlled up to 3% (w/w). The ratio of filler in the bitumen was from 0.5 to 3 (w/w), with hydrated lime content of up to 30% w/w. The rheological properties of different mastic compositions were determined with a rheometer equipped with two parallel plates at 60°C using oscillating load. The primary purpose of the article was to determine the nature of mastic stiffness changes in the context of using hydrated lime and synthetic wax as the filler. Consequently, the article proposes a method for evaluation of the critical value of the filler phase in the phase of bitumen modified with synthetic wax. The proposed model of the mathematical function was used to determine the nature of mastic structuring throughout the range of the experiment. The model was also used to determine the critical concentration of the filler in the bitumen phase. It was demonstrated that below the critical filler concentration the mastic behaved in a significantly different manner from the behaviour observed above this critical concentration. When the critical concentration of the filler was exceeded, it resulted in an excessive increase of mastic stiffness, which was considered in the model.

Download Full-text