• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.12
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• pp.1710-1719
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• 1997

An approximate analytical solution for the initial transient process of close-contact melting occurring between a phase change material kept at its melting temperature and an isothermally heated flat surface is derived. The model is so developed that it can cover both rectangular and circular cross-sectional solid blocks. Normalization of simplified model equations in reference to the steady solution enables the solution to be expressed in a generalized form depending on the liquid-to-solid density ratio only. A selected result shows an excellent agreement with the previously reported numerical data, which justifies the present approach. The solution appears to be capable of describing all the fundamental characteristics of the transient process. In particular, dependence of the solid descending velocity oft the density ratio at the early stage of melting is successfully resolved. The effects of other parameters except the density ratio on the transient behaviors are efficiently represented via the steady solution implied in the normalized result. A simple approximate method for estimating the effect of convection on heat transfer across the liquid film is also proposed.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.7
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• pp.468-473
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• 2010

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• ETRI Journal
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• v.29 no.1
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• pp.50-58
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• 2007

Robust adaptive beamforming based on worst-case performance optimization is investigated in this paper. It improves robustness against steering vector mismatches by the approach of diagonal loading. A closed-form solution to optimal loading is derived after some approximations. Besides reducing the computational complexity, it shows how different factors affect the optimal loading. Based on this solution, a performance analysis of the beamformer is carried out. As a consequence, approximated closed-form expressions of the source-of-interest power estimation and the output signalto-interference-plus-noise ratio are presented in order to predict its performance. Numerical examples show that the proposed closed-form expressions are very close to their actual values.

• ETRI Journal
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• v.24 no.4
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• pp.280-289
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• 2002

In this work, we present a novel approach to the bit allocation problem that aims to minimize overall distortion subject to a bit rate constraint. The optimal solution can be found by the Lagrangian method with dynamic programming. However, the optimal bit allocation for block-based interframe coding is practically unattainable because of the interframe dependency of macroblocks caused by motion compensation. To reduce the computational burden while maintaining a result close to the optimum, i.e., near optimum, we propose an alternative method. First, we present a partitioned form of the bit allocation problem: a "frame-level problem" and "one-frame macroblock-level problems." We show that the solution to this new form is also the solution to the conventional bit allocation problem. Further, we propose a bit allocation algorithm using a "two-phase optimization technique" with an interframe dependency model and a rate-distortion model.

• Journal of computational fluids engineering
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• v.14 no.3
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• pp.86-94
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• 2009

The non-conservative form of momentum equations is often used for some two-phase flow codes instead of a conservative form because of numerical convenience. Another non-conservative form, so called, a semi-conservative form can improve the numerical solution of these codes maintaining the numerical convenience. It is close to the conservative form but still maintains the feature of the non-conservative form. A semi-conservative form of the momentum equations and a non-conservative form of the momentum equations are implemented in CUPID[1] code. The numerical results of the semi-conservative and the non-conservative forms are compared against analytical solutions and the solutions of the FLUENT code that uses the conservative form. The results clearly showed that the semi-conservative form of the momentum equations provides better solutions than the non-conservative form, especially for heterogeneous two-phase flows.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.10a
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• pp.499-509
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• 2005

We have many foundations which were constructed on the karstic areas where solution cavities and fractured zone may form under, or close to foundations. The fact that the ground under the pier foundations was reinforced with the three axial high pressure jet grouting is confirmed through out about two hundred design reports. It is necessary that evaluation of a simple application of high pressure jet grouting method on the karstic areas containing solution cavities. In this study, the improved situation and reinforcing methods of the ground under the pier foundations are proposed based on the evaluation of design reports for the express highway and No.38 national roads.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.661-665
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• 1996

An inverse kinemetics problem of a reclaimer which digs and transports ironstones or coals in the raw yard is investigated. Because of the special features of the reclaimer of which scooping buckets are attached around the rotating drum at the end of boom, kinematic redundancy occurs in determining the joint varialbes For a given reclaiming point in space the forward kinematics yields 3 equations, however the number of involved variables in the equations are four. A plane equation approximating the surface near a reclaiming point is obtained by considering 8 adjacent points surrounding the reclaiming point. One extra equation to overcome redunduncyis further obtained from the condition that the normal vector at a reclaiming point is perpendicular to the plane. An approximate solution for a simplified problem is first discussed, Numerical solution for the oritinal nonlinear porblem with a constraint equation is also investigated. Finally a closed form solution which is not exact but sufficiently close enough is proposed by exploiting geometric constraint.

• Korean Journal of Materials Research
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• v.24 no.1
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• pp.25-32
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• 2014

In this study, nano-sized cobalt oxide powder with an average particle size below 50 nm was prepared from a cobalt chloride solution by the spray pyrolysis process. The influences of reaction temperature on the properties of the generated powder were examined. The average particle size of the particles formed based on the spray pyrolysis process at a reaction temperature of $700^{\circ}C$ is roughly 20 nm. Moreover, most of these particles cannot appear with an independent type, thereby coexisting in a droplet type. When the reaction temperature increases to $800^{\circ}C$, the average particle size not only increases to roughly 40 nm but also shows a more dense structure while the ratio of particles which shows a polygonal form significantly increases. As the reaction temperature increases to $900^{\circ}C$, the distribution of the particles is from roughly 70 nm to 100 nm, while most of the particle surface is more intricately close and forms a polygonal shape. When the reaction temperature increases to $1000^{\circ}C$, the particle size distribution of the powder shows an existing form from 80 nm to at least 150 nm in an uneven form. As the reaction temperature increases, the XRD peak intensity gradually increases, yet the specific surface area gradually decreases.

• Bulletin of the Korean Chemical Society
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• v.18 no.9
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• pp.961-965
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• 1997

1H NMR spectra of 3,3-dimethylpiperidine (1) at -70 to 30 ℃ exhibit gradual change from slow to rapid exchange between two alternate chair forms. The exchange rate constant was determined as a function of temperature by simulating the line shape of the signal from the two methyl groups using the modified Bloch equations. The resulting free energy of activation is ΔG* = 44.4±1.9 kJ mol-1 at 298 K. The 1H NMR spectrum of a D2O or dimethylsulfoxide-d6 (DMSO-d6) solution containing 1 and [SiW11CoⅡO39]6- exhibits separate signals for the free ligand and the complex, indicating that the ligand exchange is slow on the NMR time scale. In D2O the piperidine ring is frozen as a chair form even at room temperature with the cobalt ion bonded to the axial position of the nitrogen atom. When DMSO-d6 is added to the D2O solution, the NMR spectral change suggests that a rapid exchange occurs between the chair form and another conformer. It is proposed that the conformation of ^b1^b coordinated to [SiW11CoⅡO39]6- in DMSO-d6 is close to a twist form.