An analytical solution of temperature response in multilayered materials for transient methods

Transient methods, such as those with pulse- or stepwise heating, have often been used to measure thermal diffusivities of various materials including layered materials. The objective of the present study is to derive an analytical solution of the temperature rise in a multilayered material, the front surface of which is subjected to pulse- or stepwise heating. The Laplace transformation has been used to obtain the analytical solution. This solution will enable us to establish the appropriate measurement method for thermophysical properties of the multilayered material. It is also shown that the present solution can be extended to functionally gradient materials (FGM), in which thermophysical properties as well as compositions change continuously.     

Data-driven identification for approximate analytical solution of first-passage problem

The first-passage problem plays a significant role in engineering performance evaluation and design optimization. To address general stochastic dynamical systems, a data-driven method is proposed to identify approximate analytical solutions for the first-passage problem which explicitly includes parameters of the system, excitation, and those related to the initial and boundary conditions. The method consists of two successive processes. First, the probability density of the first-passage time is assumed to satisfy the modified Weibull distribution and its expansion expression is constructed by using the rule of dimensional consistency. Second, by comparing the expansion with the probability density of the first-passage time estimated from random state data, the coefficients are determined by solving a set of overdetermined linear algebraic equations. Two representative examples, including the Duffing oscillator and a 2-DOF nonlinear dynamical system, are discussed in detail to illustrate the application and efficiency of the data-driven method. The efficacies of the approximate analytical solutions for the external parameters are also verified.     

Photo-assisted Fenton type processes for the degradation of phenol: a kinetic study

In this study the application of advanced oxidation processes (AOPs), dark Fenton and photo-assisted Fenton type processes; Fe(2+)/H(2)O(2), Fe(3+)/H(2)O(2), Fe(0)/H(2)O(2), UV/Fe(2+)/H(2)O(2), UV/Fe(3+)/H(2)O(2) and UV/Fe(0)/H(2)O(2), for degradation of phenol as a model organic pollutant in the wastewater was investigated. A detail kinetic modeling which describes the degradation of phenol was performed. Mathematical models which predict phenol decomposition and formation of primary oxidation by-products: catechol, hydroquinone and benzoquinone, by applied processes were developed. The study also consist the modeling of mineralization kinetic of the phenol solution by applied AOPs. This part, besides well known reactions of Fenton and photo-Fenton chemistry, involves additional reactions which describe removal of iron from catalytic cycle through formation of ferric complexes and its regeneration induced by UV radiation. Phenol decomposition kinetic was monitored by HPLC analysis and total organic carbon content measurements (TOC). Complete phenol removal was obtained by all applied processes. Residual TOC by applied Fenton type processes ranged between 60.2 and 44.7%, while the efficiency of those processes was significantly enhanced in the presence of UV light, where residual TOC ranged between 15.2 and 2.4%.     

Mechanochemical degradation treatment of TBBPA: A kinetic approach for predicting the degradation rate constant

Persistent organic pollutants (POPs) have been banned from production and use. The brominated flame retardant TBBPA is a type of POP and has been widely used in plastics to enhance their fire resistance. However, because the natural degradation of TBBPA is a difficult process, it is particularly important to propose an appropriate treatment method. Hence, the mechanochemical degradation of TBBPA is a feasible method because it does not require high temperature heating and does not produce secondary pollutants after the reaction is completed. In this study, we performed a series of TBBPA degradation experiments with a planetary ball mill and confirmed the degradation efficiency and the rate under various conditions. Then, we conducted a discrete element method (DEM) simulation to compute the collision energies in the ball mill. By comparing the degradation rate and collision energies, we revealed that the mechanochemical degradation rate of TBBPA can be predicted by a normal collision energy computed by DEM simulation. This kinetic approach enables us to predict the rate constant and consequently, the energy consumption for the mechanochemical treatment. The predictability of these parameters will encourage the further application of mechanochemical reaction in the field of POPs treatment.     

On the analytical solution of a nonstationary kinetic equation for a point heat source

A nonstationary kinetic equation for a point heat source in a gas is analytically solved. The dependence of the temperature and concentration of gas molecules on the distance from the source is considered. The results are compared to experimental data on the spreading of acoustic oscillations.     

结构动力方程一种新的级数形式的解析解

将结构的位移及速度响应作为状态变量,采用Lyapunov(李雅普诺夫)人工小参数法求解状态方程,导出状态方程的一个新的级数形式的解析解,该解析解还可以推广到非线性动力方程的计算。将秦九韶算法引入级数解的计算,提高了计算的效率和稳定性,同时给出了算法的计算格式和步骤。该算法无需对转换矩阵H求逆,仅使用矩阵向量相乘,计算稳定,精度仅由收敛项数控制,很容易达到任意精度要求,而且适合并行计算及压缩存储。最后通过算例进一步证实了该算法的精度和效率。     

New integral relations for analytical solutions of parabolic-type equations in noncylindrical domains

The theory of the method of Green’s functions in solving boundary-value problems of nonstationary heat conduction in domains with moving boundaries has been developed. A modification of the thermal-potential method for a uniform law of motion of the boundary has been proposed, which leads to integral relations of a new (simplest) form compared to the existing results; this makes it possible to consider numerous particular cases that are of practical interest for many applications. A number of special features of model representations of nonstationary heat transfer in domains with moving boundaries have been revealed.     

An approximate method for solving the integral equation of transport theory

An approximate solution is given for one of the integral equations of transport theory, using the Pade method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.31, No.1, pp.111–115, July, 1976.     

An integral solution for thermal diffusion in periodic multilayer materials: Application to iron/copper multilayers

A closed-form solution for heat transfer through a periodic multilayer material utilizing a transfer matrix technique is presented. The benefit of this technique for periodic multilayer samples is that the use of eigenvector decomposition significantly simplifies the solution. Experimental results, obtained in the vicinity of 1200 K on samples composed of 10 bilayers of nominally 2/3 μm copper and 4/3 μm iron on 75-μm molybdenum substrates, are presented.     

A solution via generalised intergral transform technique for the simultaneous transport processes during combustion of wood cylinders

A non‐linear moving boundary diffusion problem is proposed as a simple model for the heat transfer during combustion of wood cylinders. Such a problem is solved here by applying the generalized integral transform technique. A new filtering strategy, denoted as local‐instantaneous filter, is used in order to accelerate the convergence of the series‐solution obtained with the present hybrid numerical–analytical technique. We show that the use of such filtering approach reduces the stiffness of the system of ordinary differential equations, resultant from the integral transformation of the original problem. Hence, subroutines based on simpler and faster methods can be used for the solution of such systems. Results are presented in the paper for the combustion of cylinders of different sizes and involving different initial moisture contents and densities. The effects on the solution of different models available in the literature for the evaluation of thermal conductivity and specific heat are also addressed on the paper. Copyright © 2000 John Wiley & Sons, Ltd.     

Derivation of a new analytical solution for a general two-dimensional finite-part integral applicable in fracture mechanics

An exact expression is derived for the general finite-part integral over an inclined ellipticaldomain Ω. r denotes the distance of a point in Ω to the singular point $\left({x,y} \right).f = x_{^0 }^i y_0^j \sqrt {Z\left({x_{0,} y_0 }\right)}$ is a general function of the Cartesian co-ordinates x₀,y₀. The boundary of the region Ω represents the equation Z(x₀, y₀)=O. These integrals appear during the numerical solution of plane crack problems in three-dimensional elasticity where they are the dominant part of a hypersingular integral equation. The availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and, simultaneously, lead to quicker numerical results. The considered finite-part integral can be expressed in closed form as function of complete elliptical integrals or Gauss hypergeometric functions, respectively. Formuias for special cases and some i, j values and their numerical verification are given in Appendices II and III.     

A kinetic energy model of two-vehicle crash injury severity

An important part of any model of vehicle crashes is the development of a procedure to estimate crash injury severity. After reviewing existing models of crash severity, this paper outlines the development of a modelling approach aimed at measuring the injury severity of people in two-vehicle road crashes. This model can be incorporated into a discrete event traffic simulation model, using simulation model outputs as its input. The model can then serve as an integral part of a simulation model estimating the crash potential of components of the traffic system. The model is developed using Newtonian Mechanics and Generalised Linear Regression. The factors contributing to the speed change (ΔV_s) of a subject vehicle are identified using the law of conservation of momentum. A Log-Gamma regression model is fitted to measure speed change (ΔV_s) of the subject vehicle based on the identified crash characteristics. The kinetic energy applied to the subject vehicle is calculated by the model, which in turn uses a Log-Gamma Regression Model to estimate the Injury Severity Score of the crash from the calculated kinetic energy, crash impact type, presence of airbag and/or seat belt and occupant age.     

Adsorption of reactive dye from an aqueous solution by chitosan: isotherm, kinetic and thermodynamic analysis

The adsorption of Remazol black 13 (Reactive) dye onto chitosan in aqueous solutions was investigated. Experiments were carried out as function of contact time, initial dye concentration (100-300mg/L), particle size (0.177, 0.384, 1.651mm), pH (6.7-9.0), and temperature (30-60 degrees C). The equilibrium adsorption data of reactive dye on chitosan were analyzed by Langmuir and Freundlich models. The maximum adsorption capacity (qm) has been found to be 91.47-130.0mg/g. The amino group nature of the chitosan provided reasonable dye removal capability. The kinetics of reactive dye adsorption nicely followed the pseudo-first and second-order rate expression which demonstrates that intraparticle diffusion plays a significant role in the adsorption mechanism. Isotherms have also been used to obtain the thermodynamic parameters such as free energy, enthalpy and entropy of adsorption. The positive value of the enthalpy change (0.212kJ/mol) indicated that the adsorption is endothermic process. The results indicate that chitosan is suitable as adsorbent material for adsorption of reactive dye form aqueous solutions.     

An approximate analytical solution of the problem of propagation of a filtration combustion wave in a porous medium

Within the one-dimensional single-temperature model, approximate analytical expressions are obtained for determination of the heat wave propagation velocity and the maximum temperature at the combustion front. The present results are compared with the results of the Zel’dovich - Frank-Kamenetskii asymptotic theory. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 41–45, January–February, 1998.     

An approximate, analytical approach to the `HRR'-solution for sharp V-notches

The well-known so-called `HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent `n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than /6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail.     

Studies of cryotreatment on the performance of integral diaphragm pressure transducers for space application

The integral diaphragm pressure transducers machined out of precipitation hardened martensite stainless steel (APX4) are widely used for propellant pressure measurements in space applications. These transducers are expected to exhibit dimensional stability and linearity for their entire useful life. These vital factors are very critical for the reliable performance and dependability of the pressure transducers. However, these transducers invariably develop internal stresses during various stages of machining. These stresses have an adverse effect on the performance of the transducers causing deviation from linearity. In order to eliminate these possibilities, it was planned to cryotreat the machined transducers to improve both the long-term linearity and dimensional stability. To study these effects, an experimental cryotreatment unit was designed and developed based on the concept of indirect cooling using the concept of cold nitrogen gas forced closed loop convection currents. The system has the capability of cryotreating large number of samples for varied rates of cooling, soaking and warm-up. After obtaining the initial levels of residual stress and retained austenite using X-ray diffraction techniques, the pressure transducers were cryotreated at 98 K for 36 h. Immediately after cryotreatment, the transducers were tempered at 510 °C for 3 h in vacuum furnace. Results after cryo treatment clearly indicated significant reduction in residual stress levels and conversion of retained austenite to martensite. These changes have brought in improvements in long term zero drift and dimensional stability. The cryotreated pressure transducers have been incorporated for actual space applications.     

An approximate solution of the Boltzmann kinetic equation taking into account crystallite polarization: I: One-dimensional approximation

An approximate solution of the one-dimensional Boltzmann equation for a polycrystalline semiconductor in which the crystallites are much larger than the mean free path of the carriers in the bulk material is given. The electric field intensity inside the crystallites is lower than the external electric field intensity, except in the regions with a thickness of the same order of magnitude as that of the mean free path which are located near the potential barriers. When the mobility through the barriers is strongly limited, the effective mobility is proportional to the distance between the barriers and thus is proportional to the crystallite size.     

A method for approximate calculation of the energy integral for notched and cracked bodies

We propose an approximate method for the calculation of the energyJ-integral for bodies with notches (cracks) subjected to elastoplastic deformations based on an analysis of stress and stress concentration at the tip of the notch (crack). The formulas for theJ-integral are obtained in terms of the theoretical stress concentration factor (stress intensity factor), nominal stresses, radius of the notch tip (crack length), and elastoplastic properties of the material. These formulas enable one to representJ-based design curves with account of the effect for material hardening.Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow; Moscow Institute of Engineering Physics, Moscow. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 3, pp. 82–87, May–June, 1994.     

Biosorption of zinc from aqueous solution using Azadirachta indica bark: equilibrium and kinetic studies

The removal of zinc ions from aqueous solutions on the biomass of Azadirachta indica bark has been studied by using batch adsorption technique. The biosorption studies were determined as a function of contact time, pH, initial metal ion concentration, average biosorbent size and biosorbent dosage. The equilibrium metal uptake was increased and percentage biosorption was decreased with an increase in the initial concentration and particle size of biosorbent. The maximum zinc biosorption occurred at pH 6 and percentage biosorption increases with increase in the biosorbent dosage. Experimental data obtained were tested with the adsorption models like Langmuir, Freundlich and Redlich-Peterson isotherms. Biosorption isothermal data were well interpreted by Langmuir model with maximum biosorption capacity of 33.49mg/g of zinc ions on A. indica bark biomass and kinetic data were properly fitted with the pseudo-second-order kinetic model.