• Journal of the Korean Geotechnical Society
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• v.28 no.11
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• pp.17-31
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• 2012

No analytical solution exists for evaluating in-situ hydraulic conductivity of vertical cutoff walls by analyzing slug test results with consideration of transient flow. There is an analytical solution proposed to interpret a slug test performed in a partially penetrated well within an aquifer. However, this analytical solution cannot be directly applied to the cutoff wall because the solution has been developed exclusively for an infinite aquifer instead of a narrow cutoff wall. To consider the cutoff wall boundary conditions (i.e, constant head boundary and no flux boundary condition), the analytical solution has been modified in this study to take into account the narrow boundaries by introducing the imaginary well theory. Type curves are constructed from the currently derived analytical solution and compared with those of a partially penetrated well within an aquifer. The constant head boundary condition provides faster hydraulic head recovery curve than the aquifer case. On the other hand, no flux boundary condition leads to slower hydraulic head recovery. The bigger the shape factor and deviation of the well and the smaller the width of the vertical cutoff wall are, the more effect of boundary condition was observed. The type curves obtained from the analytical solution for a cutoff wall are similar to those made by the numerical method in the literature.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.997-998
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• 2007

This paper deals with analytical solution concerning the image method using the magnetic charge instead of 3D FEA(finite element analysis) in the slotless single air-gap motor. The theory of analytical method and the design procedures are introduced. The reliability and validity of proposed analytical solution are verified through the comparison with the results of commercial 3D FE software. In addition, calculation time between proposed analytical solution and 3D FEA is compared. Finally, characteristics, such as Back-EMF and phase resistance, between calculated and experimental results are compared. From the verification with 3D FEA and experimental results, it is proved that presented analytical method provided very effective and precise results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.11
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• pp.3655-3665
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• 1996

An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.165-173
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• 1998

Analytical solutions to predict the movement rate of submerged mound are derived using the convection coefficient and the joint distribution function of wave heights and periods. Assuming that the sediment is moved onshore due to the velocity asymmetry of Stokes' second order nonlinear wave theory, the micro-scale bedload transport equation is applied to the sediment conservation. The nonlinear convection-diffusion equation can then be obtained which governs the migration of submerged mound. The movement rate decreases exponentially with increasing the water depth, but the movement rate tends to increase as the spectral width parameter, $ u$ increases. In comparison of the analytical solution with the measured data, it is found that the analytical solution overestimates the movement rate. However, the agreement between the analytical solution and the measured data is encouraging since this over-estimation may be due to the inaccuracy of input data and the limitation of sediment transport model. In particular, the movement rates with respect to the water depth predicted by the analytical solution are in very good agreement with the estimated result using the discritization technique with the hindcast wave data.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.17-25
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• 2003

Simple methods are developed to predict temperatures of a satellite box during launch stage. The box is mounted on outer surface of satellite and directly exposed to space thermal environment for the time period from fairing jettison to separation. These simple methods are to solve a 1st order ordinary differential equation (ODE) which is simplified from the governing equation after applying several assumptions. The existence of analytical solution for the 1st order ODE is determined depending on treatment of time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (Jess than $1^{\circ}C$ along the time line) when they are applied to STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against space environment during the launch stage for the case that the detailed thermal analysis is not available.

• Journal of Welding and Joining
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• v.13 no.3
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• pp.116-124
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• 1995

This paper presents an analytical solution to predict the transient temperature distribution in fillet arc welding including the effect of molten metal. The solution is obtained by solving a transient three-dimensional heat conduction equation with convection boundary conditions on the surfaces of a plate, and mapping the infinite plate onto the fillet weld geometry with energy equation. The electric heat input on the fillet weld and on the infinite plate is assumed to have a combination of two bivariate Gaussian distribution. To check the validity of the solution. FCA welding experiments were performed under various welding conditions. The actual isotherms of the weldment cross-sections at various distances from the arc start point are compared with those of simulation result.

• Biotechnology and Bioprocess Engineering:BBE
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• v.5 no.1
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• pp.65-70
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• 2000

An approximated analytical solution of mathematical model for the three phase fluidized bed bioreactor (TFBBR) was proposed using the linearization technique to describe oxygen utilization rate in wastewater treatment. The validation of the model was done in comparison with the experimental results. Satisfactory agreement was obtained in the comparison of approximated analytical solution and numerical solution in the oxygen concentration profile of a TFBBR. The approximated solutions for three modes of the liquid phase flow were compared. The proposed model was able to predict the biomass concentration, dissolved oxygen concentration the height of efficient column, and the removal efficiency.

• International Journal of Air-Conditioning and Refrigeration
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• v.6
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• pp.14-26
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• 1998

This paper deals with approximate analytical solutions for the two-region one-dimensional model describing the charging process of stratified thermal storage tanks at variable inlet temperature with momentum-induced mixing. An arbitrarily increasing inlet temperature is decomposed into inherent step changes and intervals of continuous change. Each continuous interval is approximated as a finite number of piecewise linear functions, which admits an analytical solution for perfectly mixed region. Using the Laplace transform, the temperature profiles in plug flow region with both the semi-infinite and adiabatic ends are successfully derived in terms of well-defined functions. The effect of end condition on the solution proves to be negligible under the practical operating conditions. For a Quadratic variation of inlet temperature, the approximate solution employing a moderate number of pieces agrees excellently with the exact solution.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.1
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• pp.31-36
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• 2015

To describe turbulent wake behind a submarine, it is very important to know turbulent kinetic energy distributions in the wake. To get the distribution is to solve the turbulent kinetic energy equation, and to solve the equation, it is needed both information of ${\lambda}$ and ${\sigma}$ which define physical characteristics of the wake. This paper gives analytical solution of the equation, which is driven from $8^{th}$ order polynomial fitting, as a function of given ${\lambda}$, even though there is no information of ${\sigma}$. In comparison between numerical solution(i.e. exact solution) and analytical solution, the relative errors between them are less than to 5% in the range of 0 < ${\xi}$ < 0.95 in most given ${\lambda}$.

• Journal of Korean Port Research
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• v.5 no.1
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• pp.71-81
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• 1991

This study deals with the analytical and numerical solution for the combined wave reflection and diffraction near the impermeable rigid upright breakwater, subject to the excitation of a plane simple harmonic wave coming from infinity. Three cases are presented : a) the analytical solution near a thin semi-infinite breakwater, b) the analytical solution near the semi-infinite breakwaters of arbitrary edge angles, $30^{\circ},\;45^{\circ},\;and\;90^{\circ}$, c) the numerical solution near a detached thin breakwater the results are presented in amplification factor and wave height diagrams. Moreover, the amplification factors near the structure(2 wavelength before and behind the structure) are compared for the given cases. A finite difference technique for the numerical solution was applied to the integral equation obtained for the wave potential.