• Biotechnology and Bioprocess Engineering:BBE
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• 제7권6호
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• pp.362-366
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• 2002

A mathematical model has been developed for describing the oxygen concentration during the exponential growth of microorganisms, in a static solid substrate bed supported on a tray fermentor. The model equations comprise of one partial differential equation for mass transfer and an ordinary differential equation of growth. After nondimensionlisation, analytical solution tn the model has been obtained by the method of Laplace transforms. An expression for critical thickness of bed is deduced from the model equation. The significance of the model in the design of tray fermentors is discussed. The validity of the discussion is verified by taking an illustration from the literature.

• 한국정밀공학회지
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• 제26권10호
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• pp.81-88
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• 2009

Bellows is used to control temperature of a Joule-Thomson micro cryocooler. It is made of Nickelcobalt alloy that retains mechanical properties from cryogenic temperature to temperature of 570K. The geometry of bellows is an axisymmetric shell and Nitrogen with high pressure was charged at temperature of 293K. During cool-down process, the pressure and volume of Nitrogen are changed and must be satisfied with state equation. At cryogenic temperature, Nitrogen can exist as a part liquid and part vapor. Pressure-density-temperature behavior under this vaporliquid phase equilibrium is closely given by the Modified-Benedict-Webb-Rubin(MBWR) state equation. To evaluate deformation of bellows for temperature change, the numerical calculation of the volume within bellows and finite element analysis of bellows under internal pressure were iteratively performed until MBWR state equation is satisfied. The numerical results show that deformation of the bellows can be analyzed by the present method in a wide range of temperature including cryogenic temperature.

• 전기학회논문지
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• 제66권4호
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• pp.643-650
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• 2017

This pap4er analyzes resonance characteristics of a slave motor that is not controlled by load and parameter differences between Dual motors during parallel operation in middle-low speed. Dual SPMSMs(Surface mounted Permanent Magnet Synchronous Motor) connected in parallel to a single inverter controlled by the master and slave control in this paper. Based on the stability analysis of the SPMSM for a variation of torque angle, the 6th nonlinear state equation of the torque angle variation in the SIMM(Single Inverter Multi Motor) structure is derived according to a mathematical model for the dual motors. In general, an analysis of the 6th order nonlinear state equation is complex. Therefore, a resonance frequency generated from the slave motor is found from the characteristic equation of the 2nd order system obtained by linearization and model reduction near steady state operation point. Through simulations and experiments, it is confirmed that the stability analysis of the SPMSMs and state equation models are useful for the variation of the torque angle analyzed in this paper.

• Journal of Magnetics
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• 제22권1호
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• pp.104-108
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• 2017

Induction motors have wide applicability in many fields, both in industrial sectors and households, for their advantages of a high efficiency and robust structure. The introduction of power-source-containing harmonics into the induction motor winding lowers its efficiency and increases its temperature, greatly affecting its operation characteristics. In this study, we performed an electromagnetic field analysis using the time-difference finite-element method with the purpose of analyzing the steady-state current characteristics of an induction motor. Additionally, we calculated the steady-state current with a method combining an electromagnetic field equation and a circuit equation. In the electromagnetic field analysis, the nonlinearity was taken into account using the Newton-Raphson method, and a backward time-difference method was employed for the time derivative term. Then, we compared the steady-state current of the induction motor obtained by calculation with the experimentally measured values, thus validating the proposed algorithm. Furthermore, we analyzed the impacts of the shape and material of the rotor conductor bar of the induction motor on the steady-state current of the main winding.

• Bulletin of the Korean Chemical Society
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• 제11권3호
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• pp.231-235
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• 1990

The activation energy of dissociative adsorption of oxygen on polycrystalline nickel surface is calculated from adsorption isotherms obtained using X-ray photoelectron spectroscopy. Negative value of this activation energy (-5.9 kJ/mol) indicates that the adsorption takes place through an undissociated precursor state. An adsorption energy for this precursor state is calculated assuming the precursor state as a moleculary physisorbed state ($E_{ad}$ = -7.9 kJ/mol). Finally, an adsorption isotherm equation is derived as a function of the gas exposure, which agrees with the experimental isotherms reasonably good.

• Structural Engineering and Mechanics
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• 제18권3호
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• pp.377-388
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• 2004

Based on the basic equations of elasticity, free-edge effects on stresses in cross-ply laminated plates are found by using the state space method. The laminates are subjected to uniaxial-uniform extension plate, which is a typical example of general plane strain problem. The study takes into account material constants of all individual material layers and the state equation of a laminate is solved analytically in the through thickness direction. By this approach, a composite plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The solution provides a continuous displacement and inter-laminar stress fields across all material interfaces and an approxiamte prediction to the singularity of stresses occurring in the boundary layer region of a free-edge. Numerical solutions are obtained and compared with the results obtained from an alternative numerical method.

• 대한수학회보
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• 제43권4호
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• pp.791-804
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• 2006

This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.

• 한국수소및신에너지학회논문집
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• 제30권5호
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• pp.385-394
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• 2019

The analysis of temperature behavior of a hydrogen tank during refueling is of significance to clarify the safety of the compressed hydrogen storage in vehicles since the temperature at a tank rises with inflow of hydrogen. A mass balance and an energy balance were combined to obtain analytical model for temperature change during the hydrogen refueling. The equation was coupled to Peng-Robinson-Gasem (PRG) equation of state (EOS) for hydrogen. The PRG EOS was adopted after comparison with other four different cubic EOSs. A parameter of the model was determined to fit data from experiments of various inlet flow rates and temperatures. The temperature and pressure change with refueling time were obtained by the developed model. The calculation results revealed that the extent of precooling was more effective than the flow rate control.

• Bulletin of the Korean Chemical Society
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• 제27권10호
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.245-249
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• 2003

Vapor-liquid equilibrium data were obtained for system of propane + R227ea (Heptafluoropropane) over the temperature range from 253.15 K to 323.15 K at 10 K intervals. Experiments were performed in a circulation type apparatus by injecting vapor through liquid pool using a magnetic pump. This system forms azeotrope in the temperature range of this study. The experimental results were correlated with the Peng-Robinson (PR) equation of state and Redlich-Kwong-Soave (RKS) equation of state using the van der Walls one-fluid mixing rule and were compared with each other.