• Title/Summary/Keyword: three different solutions

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Kinetic and multi-parameter isotherm studies of picric acid removal from aqueous solutions by carboxylated multi-walled carbon nanotubes in the presence and absence of ultrasound

  • Gholitabar, Soheila;Tahermansouri, Hasan
    • Carbon letters
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    • v.22
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    • pp.14-24
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    • 2017
  • Carboxylated multi-wall carbon nanotubes (MWCNTs-COOH) have been used as efficient adsorbents for the removal of picric acid from aqueous solutions under stirring and ultrasound conditions. Batch experiments were conducted to study the influence of the different parameters such as pH, amount of adsorbents, contact time and concentration of picric acid on the adsorption process. The kinetic data were fitted with pseudo-first order, pseudo-second-order, Elovich and intra-particle diffusion models. The kinetic studies were well described by the pseudo-second-order kinetic model for both methods. In addition, the adsorption isotherms of picric acid from aqueous solutions on the MWCNTs were investigated using six two-parameter models (Langmuir, Freundlich, Tempkin, Halsey, Harkins-Jura, Fowler-Guggenheim), four three-parameter models (Redlich-Peterson, Khan, Radke-Prausnitz, and Toth), two four-parameter equations (Fritz-Schlunder and Baudu) and one five-parameter equation (Fritz-Schlunder). Three error analysis methods, correlation coefficient, chi-square test and average relative errors, were applied to determine the best fit isotherm. The error analysis showed that the models with more than two parameters better described the picric acid sorption data compared to the two-parameter models. In particular, the Baudu equation provided the best model for the picric acid sorption data for both methods.

Effects of Optical Brightening Agent on the Chemical Degradation Characteristics of Paper Cellulose (형광증백제가 종이 셀룰로오스의 화학적 열화특성에 미치는 영향)

  • Lee, Jae-Hun;Choi, Kyoung-Hwa;Cho, Byoung-Uk
    • Journal of Korea Technical Association of The Pulp and Paper Industry
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    • v.47 no.6
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    • pp.66-72
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    • 2015
  • This study was conducted to investigate the effects of optical brightening agents (OBA) on the chemical degradation characteristics of paper cellulose during humid heating aging. Three different types of OBAs were applied to a filter paper by dipping it in OBA solutions whose concentrations were controlled to 1% and 2%. The filter papers with an OBA were artificially aged at $80^{\circ}C$ and 65% RH, and the changes in pH of paper and viscosity of cellulose were evaluated. Their functional groups were also analyzed by ATR-FTIR (at-tenuated total reflectance fourier transform infrared spectroscopy). It was found that OBAs influenced the chemical degradation of paper cellulose during humid heating aging. Higher concentration of OBA solutions accelerated the degradation of paper cellulose. Especially, after aging for 12 days, the paper cellulose treated with the tetra-type OBA were the most significantly aged among the three types of OBAs. It was assumed that pH of OBA solutions affected the aging characteristics.

Three-dimensional crack analysis by fractional linear mapping (선형분수사상을 이용한 3차원 균열해석)

  • 안득만
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.1
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    • pp.61-78
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    • 1995
  • In this study the method of analysis for three-dimensional plane crack problem by fractional linear mapping is given. Using this method we can obtain the exact solutions of significantly different configurations of the crack. In the example image crack configurations by mapping of elliptic crack are illustrated. And the stress intensity factors along the image crack tips are calculated.

ON THE SOLVABILITY OF A NONLINEAR LANGEVIN EQUATION INVOLVING TWO FRACTIONAL ORDERS IN DIFFERENT INTERVALS

  • Turab, Ali;Sintunavarat, Wutiphol
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.1021-1034
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    • 2021
  • This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

Direct Calculation Method for Excited-state Diffusion-influenced Reversible Reactions with an External Field

  • Reigh, Shang Yik;Kim, Hyo-Joon
    • Bulletin of the Korean Chemical Society
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    • v.33 no.3
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    • pp.1015-1019
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    • 2012
  • The direct calculation method is generalized to the excited-state diffusion-influenced reversible reaction of a neutral and a charged particle under an external field with two different lifetimes and quenching in three dimensions. The present method provides an alternative way to calculate the binding probability density functions and the survival probabilities from the corresponding irreversible results. The solutions are obtained as the series solutions by the diagonal approximation due to the anisotropy of the unidirectional external field. The numerical results are found to be in good agreement with those of the previous study [S. Y. Reigh et al. J. Chem. Phys. 132, 164112 (2010)] within a weak field limit. The solutions of two approaches show qualitatively the same overall behavior including the power laws at long times.

An Interdisciplinary Approach to Industry-Based Complex Problem-Solving: Sustainable Policy Solutions to the Malaysian Water Crisis

  • Richards, Cameron;Padfield, Rory
    • Asian Journal of Innovation and Policy
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    • v.5 no.1
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    • pp.55-77
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    • 2016
  • This paper focuses on how an integrated or systemic approach is needed to both investigate and connect different kinds of interdisciplinary inquiry and knowledge within and beyond universities to encourage more productive collaboration with the other three ‘macro stakeholders’ - government, business, and the wider community. In this way universities can and should provide a greater leadership role in sustainability, innovation and policy studies. Such a framework is needed to also help to change the view of many that academics should just play a supporting role of providing specialised technical expertise only to the other macro stakeholders. The interdisciplinary and collaborative framework developed here is applied to the on-going water crisis in Malaysia - an exemplary complex problem-solving basis for seeking sustainable policy solutions to diverse challenges. As further discussed, this was applied also in practice to a multi-stakeholder seminar on addressing the difficult policy challenges of the Malaysian water industry and sector.

Free Vibration of a Thin Plate with Small Deflections by Semi-Analytical Approach (반해석적 방법에 의한 작은 변위를 가지는 얇은판의 자유진동해석)

  • 최덕기
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.8
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    • pp.1967-1973
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    • 1994
  • The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

Limit Loads for Pipe Bends under Combined Pressure and in-Plane Bending Based on Finite Element Limit Analysis (압력과 모멘트의 복합하중을 받는 곡관에 대한 유한요소 한계하중 해석)

  • Oh Chang-Sik;Kim Yun-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.5 s.248
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    • pp.505-511
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    • 2006
  • In the present paper, approximate plastic limit load solutions fur pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The present FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the present FE results. The proposed limit load solutions would be a basis of defective pipe bends and be useful to estimate non-linear fracture mechanics parameters based on the reference stress approach.

Shape Design of Passages for Turbine Blade Using Design Optimization System (최적화설계시스템을 이용한 터빈블레이드 냉각통로의 형상설계)

  • Jeong Min-Joong;Lee Joon-Seong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.7 s.238
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    • pp.1013-1021
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    • 2005
  • In this paper, we developed an automatic design optimization system for parametric shape optimization of cooling passages inside axial turbine blades. A parallel three-dimensional thermoelasticity finite element analysis code from an open source system was used to perform automatic thermal and stress analysis of different blade configuration. The developed code was connected to an evolutionary optimizer and built in a design optimization system. Using the optimization system, 279 feasible and optimal solutions were searched. It is provided not only one best solution of the searched solutions, but also information of variation structure and correlation of the 279 solutions in function, variable, and real design spaces. To explore design information, it is proposed a new interpretation approach based on evolutionary clustering and principal component analysis. The interpretation approach might be applicable to the increasing demands in the general area of design optimization.

Study on Transient Temperature Distribution in Annular Fin of Uniform Thickness (均一두께 의 원통핀 에서 過渡溫度 分布 에 관한 硏究)

  • 손병진;박희용;이흥주
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.6 no.3
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    • pp.247-255
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    • 1982
  • The heat diffusion equation for an annular fin is analyzed by Laplace transformation. The fin has a uniform thickness, with its end insulated, and three different temperature profiles at the base such as step change, harmonic and exponential functions. The exact solutions for the temperature and heat flux of the fins are obtained with the infinite series. The series solutions converge rapidly for large values of dimensionless time, but slowly for small values. Therefore some approximate solutions are presented here to fine the temperature distribution and heat flux for small values of dimensionless time. Furthermore a simple approximate heat flux, .OMEGA.=1.13c.tau.$^{1}$2/ is found in the range of .tau. .leg. o.1/c for the exponential function at the base.