• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.311-327
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• 2011

This paper is devoted to simplified Tikhonov regularization for two kinds of parabolic equations, i.e., a sideways parabolic equation, and a two-dimensional inverse heat conduction problem. The measured data are assumed to be known approximately. We concentrate on the convergence rates of the simplified Tikhonov approximation of u(x, t) and its derivative $u_x$(x, t) of sideways parabolic equations at 0 $\leq$ x < 1, and that of two-dimensional inverse heat conduction problem at 0 < x $\leq$ 1, respectively.

• Journal of Power System Engineering
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• v.3 no.3
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• pp.14-21
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• 1999

The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(${\xi}<{\eta}_l$). It is shown that due to the thermal relaxation time, the hyperbolic heat conduction equation has thermal wave characteristics as the damped wave equation has wave nature.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.7
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• pp.952-957
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• 2001

In the glass forming process, the phenomena of hyperbolic heat conduction in the hot mold with an inner defect are studied analytically. It is shown that the temperature predicted by the parabolic model is underestimated compared to the one by the hyperbolic model. As the rmal wave is reflected from the area with defects and then arrives at the surface supplied by the heat flux, it is expected that there exists thermal shock in the materials. The area with defects is assumed to be adiabatic since its thermal conductivity is much lower compared to the one of the material. The results also indicate that the sudden temperature -jump in the mold surface can cause diverse problems such as glass defect (embryo mark, etc), oxidation of mold and coating, and change of material properties.

• Journal of the Korean Society of Safety
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• v.23 no.3
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• pp.87-92
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• 2008

A finite element method which is discontinuous in time is developed for the solution of the classical parabolic model of heat conduction problems. The approximations are continuous with respect to the space variables for each fixed time, but they admit discontinuities with respect to the time variable at each time step. The method is superior to other well-known approaches to these problems in that it allows a wider range of moving boundary value problems to be dealt with, such as are encountered in complex engineering operations like ground freezing. The method is applied to one-dimensional and two-dimensional heat conduction problems in this paper, although it could be extended to more higher dimensional problems. Several example problems are discussed and illustrated, and comparisons are made with analytical approaches where these can also be used.

• Solar Energy
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• v.20 no.1
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• pp.81-89
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• 2000

In the present study, the characteristics of conductive and convective heat transfer occurred in a circular absorber of PTC (parabolic trough concentrator) for medium temperature solar energy utility were numerically investigated. A circular tube was considered as an absorber and the shape of PTC modeled in this study was based on the system that was installed in Korea Institute of Energy Research. Not only convection inside the tube but also conduction through the wall of the tube were analyzed, simultaneously. Circumferentially non-uniform heat flux that was simulated from the non-uniform solar disc model proposed by Jose was applied as thermal boundary condition on the tube surface. And, hydrodynamically fully developed laminar velocity profile was used as the inlet boundary condition and it was assumed that the working fluid was water. And, local heat fluxes at the interface of the tube and the working fluid were calculated for different wall thickness and thermal conductivity of the tube at various Reynolds number. Based on the results, the effects of thermal conduction of the tube on the local heat transfer were investigated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.4
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• pp.528-536
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• 1999

This work studies the effects of transient reflectance on the thermal responses of a metal(gold) thin-film during ultrashort laser heating. The heating process is calculated using the conventional conduction model (parabolic one-step: POS), parabolic two-step model (PTS) with and without variable properties, hyperbolic two-step model (HTS). Results from the HTS model are very similar to those from the PTS model, since the laser heating time in this study is greater than the electron relaxation time. PTS model with variable properties, however, results in totally different temperature profiles compared to those from POS models or calculation with constant properties. Transient reflectances are estimated from electron temperature distributions and based on the linear relationship between the electron temperature and complex dielectric constants. Reflectance of the front surface can be changed with respect to dielectric constants, while those of the rear surface remain unchanged.

• International Journal of Air-Conditioning and Refrigeration
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• v.10 no.1
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• pp.1-9
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• 2002

Effects of temperature coefficients fur dielectric constants on transient reflectances and thermal responses have been investigated for a metal(gold) thin-film during ultrashort pulse laser heating. Heating processes are simulated using the conventional conduction model(parabolic one-step, POS), the parabolic tow-step model(PTS), the hyperbolic two-step model(HTS). Results fro the HTS model are very similar to those from the PTS model, since the laser heating time in this study is considerably greater than the electron relaxation time. PTS and HTS models, however, result in completely different temperature profiles from those obtained by the POS model due to slow electron-lattice interactions compared to laser pulse duration. Transient reflectances are directly estimated from the linear relationship between electron temperature and complex dielectric constants, while conventional approaches assume that the change in reflectances is proportional to that in temperatuer. Reflectances at the front surface vary considerably for various dielectric constants, while those at the rear surface remain unchanged relatively.

• Journal of the Korean Institute of Gas
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• v.7 no.4 s.21
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• pp.44-52
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• 2003

In this work dynamic heat transfer in a CPFS (cable penetration fire stop) system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealant. Dynamic heat transfer in the fire stop system is formulated in a parabolic PDE (partial differential equation) subjected to a set of initial and boundary conditions. First, the PDE model is divided into two parts; one corresponding to heat transfer in the axial direction and the other corresponding to heat transfer on the vertical planes. The first PDE is converted to a series of ODEs (ordinary differential equations) at finite discrete axial points for applying the numerical method of SOR (successive over-relaxation) to the problem. The ODEs are solved by using an ODE solver In such manner, the axial heat flux can be calculated at least at the finite discrete points. After that, all the planes are separated into finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The initial condition of each finite element can be obtained from the above solution. The heat fluxes on the vertical planes are calculated by the Galerkin FEM (finite element method). The CPFS system was modeled, simulated, and analyzed here. The simulation results were illustrated in three-dimensional graphics. Through simulation, it was shown clearly that the temperature distribution was influenced very much by the number, position, and temperature of the cable stream, and that dynamic heat transfer through the cable stream was one of the most dominant factors, and that the feature of heat conduction could be understood as an unsteady-state process.

• Fire Science and Engineering
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• v.18 no.1
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• pp.24-30
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• 2004

In this work the dynamic heat transfer occurring in a cable penetration fire stop system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealants. Here was carried out an experiment to observe the heat transfer in the cable penetration fire stop system made of DOW CORNING products. The dynamic heat transfer occurring in the fire stop system is formulated in a parabolic partial differential equation subjected to a set of initial and boundary conditions. And it was modeled, simulated, and analyzed. The simulation results were illustrated in three-dimensional graphics and were compared with experimental data. Through the simulations, it was shown clearly that the temperature distribution was influenced very much by the number, position, and temperature of the cable streams. It also was found that the dynamic heat transfer through the cable streams was one of the most dominant factors, and the feature of heat conduction could be understood as an unsteady-state process. It is certain that these numerical results are useful for making a performance-based design for the cable penetration fire stop system.

• 한국가스학회:학술대회논문집
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• 2003.10a
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• pp.120-125
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• 2003

본 연구는 원자력 발전소에 있는 방화벽의 케이블 관통부위에 설치된 CPFS(Cable Penetration Fire Stop)시스템 안에서 일어나는 동적열전달 현상을 3 차원으로 나타낼 수 있는 시험시뮬레이터에 사용될 수학적 모델과 수치계산 알고리즘의 개발에 관한 것이다. CPFS 내에서 일어나는 열전도 현상을 나타내는 지배방정식은 주어진 조건들 하에서 포물선형 편미분방정식(Parabolic PDE)으로 나타난다. 문제를 단순화하기 위해 열의 흐름을 두 성분으로 나누었다 즉, 케이블과 평행한 선을 따라서 일어나는 열전도와 벽면과 평행한 평면 위에서 일어나는 열전도로 나누었다. 먼저 선을 따라 일어나는 동적 열전도 현상을 나타내는 PDE를 연속과완화(SOR: Successive Over-Relaxation)를 적용하여 유한한 불연속점들에 대한 연립 상미분방정식(ODE)으로 전환했고, 그 연립방정식은 ODE Solver 를 이용하여 풀 수 있었다. 둘째로, 각 불연속 점에 위치한 평면 위에서 일어나는 열전도를 계산하기 위해서, 유한요소의 합을 근사식으로 이용하여 PDE를 ODE로 전환해서 계산하는 유한요소법(Finite Element Method)이 이용된다. 여기서 시간과 공간의 함수 T(x, y, z, t)인 온도는 각 선의 점들과 각 평면의 요소들에 대해서 일정한 시간간격으로 초기온도와 경계온도를 업데이트하여 계산을 반복한다. 이러한 일련의 계산결과를 바탕으로 CPFS 시스템 내에서의 온도분포의 동적인 변화를 해석한다. 결론적으로 관통하는 케이블이 CPFS 시스템의 온도분포에 매우 중요한 역할을 한다는 것을 알 수 있다. 시뮬레이션 결과는 CPFS 내의 온도분포를 쉽게 이해할 수 있도록 3 차원 그래픽으로 나타냈으며, 상용소프트웨어 FEMLAB 으로 계산한 결과와 비교해서 개발된 모델과 계산 알고리즘의 정당성을 보였다. 맞이하고 있음을 볼 수 있다. 국내광업이 21C 급변하는 산업환경에 적응하여 생존하기 위해서는 각종 첨단산업에서 요구하는 소량 다품종의 원료광물을 적기에 공급 할 수 있는 전문화된 기술력을 하루속히 확보해야 하며, 이를 위해 고품위의 원료광물 확보를 위한 탐사 및 개발을 적극 추진하고 가공기술의 선진화를 위해 선진국과의 기술제휴 등 자원산업 글로벌화 정책이 절실히 요구되고 있음을 알 수 있다. 또한 삶의 질을 향상시키려는 현대인의 가치관에 부합하기 위해서는 각종 소비제품의 원료를 제공하는 광업의 본래 목적 이외에도 자연환경 훼손을 최소화하며 개발 할 수밖에 없는 구조적인 어려움에 직면할 수밖에 없다. 이처럼 국내광업이 안고 있는 여러 가지 난제들을 극복하기 위해서는 업계와 정부가 합심하여 국내광업 육성의 중요성을 재인식하고 새로운 마음가짐으로 관련 정책을 수립 일관성 있게 추진해 나가야 할 것으로 보인다.의 연구 결과를 요약하면 다음과 같다. 첫째, 브랜드 이미지와 서비스 품질과의 관계에서 브랜드이미지는 서비스 품질의 선행변수가 될 수 있음을 증명하였으며 4개 요인의 이미지 중 사풍이미지를 제외한 영업 이미지, 제품 이미지, 마케팅 이미지가 서비스 품질에 영향을 미치고 있음을 알 수 있다. 둘째, 지각된 서비스 품질과 가격 수용성과의 관계에서, 서비스 품질은 최소 가격에 신뢰서비스 요인에서 정의 영향을 미치고 있으나 부가서비스, 환경서비스에서는 역의 영향을 미침을 알수 있고, 최대 가격에 있어서는 욕구서비스 요인은 정의 영향을 미치지만 부가서비스의 경우에는 역의 영향을 미치고 있음을 알 수 있다. 셋째, 서비스품질과 재 방문 의도와의 관계에 있어서 서비스품질은 재 방문 의도에 영향을 미침을 알 수 있다. 따라서 브랜드 이미지는 서비스품질의 선행변수가 될 수 있으며, 서비스품질은 가격 수용성과 재방문 의도에 영향을 미치고 있음을 알 수