• 대한기계학회논문집B
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• 제25권2호
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• pp.195-201
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• 2001

An inverse heat conduction problem(IHCP) arises when unknown heat fluxes and whole temperature field are to be found with temperature measurements of a few points. In this paper, observers are proposed as solution algorithm for the IHCP. A 1-dimensional heat transfer problem is modeled with modal analysis and state space equations. Position of the heat source is estimated through test heat inputs and the autocorrelation among a few of temperature data. The modified Bass-Gura method is used to design a state observer to estimate the intensity of heat source and the whole temperature field of a 1-dimensional body. To verify the reliability of this estimator, analytic solutions obtained from the proposed method are compared.

• 수산해양기술연구
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• 제27권4호
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• pp.321-327
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• 1991

Experiments of quenching were made with cylindrical specimens of carbon steel S45C of diameters from 12 to 30mm were performed. The specimens were heated by electric furnace and quenched by immersion method. In order to analyze the temperature profile(cooling curves) of carbon steel including the latent heat of phase transformation, nonlinear heat conduction problem was calculated by the numerical method of inverse heat conduction problem using the apparent heat capacity method. The difference between the calculated and the experimented cooling curves was caused by the latent heat of phase transformation, and the effects of the latent heat were especially manifest at the cooling curves of center of specimens. The temperature and the quantity of the latent heat of phase transformation depend on the cooling speed at A sub(1) transformation point, and the region for cooling speed to become zero was caused by the latent heat of phase transformation.

• 대한기계학회논문집A
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• 제28권5호
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• pp.632-639
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• 2004

In this paper, an inverse problem of glass forming process is studied to determine a number of unknown heat transfer coefficients which are imposed as boundary conditions. An analysis program for transient heat conduction of axi-symmetric dimension is developed to simulate the forming and cooling process. The analysis is repeated until it attains periodic state, which requires at least 30 cycles of iteration. Measurements are made for the temperatures at several available time and positions of glass and moulds in operation. Heat removal by the cooling water from the plunger is also recorded. An optimization problem is formulated to determine heat transfer coefficients which minimize the difference between the measured data and analysis results. Significant time savings are achieved in finite difference based sensitivity computation during the optimization by employing distributed computing technique. The analysis results by the optimum heat transfer coefficients are found to agree well with the measured data.

• 대한수학회지
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• 제44권6호
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• pp.1397-1415
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• 2007

We consider an inverse heat conduction problem(IHCP) in a quarter plane which appears in some applied subjects. We want to determine the heat flux on the surface of a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that arbitrarily "small" differences in the input temperature data may lead to arbitrarily "large" differences in the surface flux. A semi-discrete central difference scheme in time is employed to deal with the ill posed problem. We obtain some error estimates which also give the information about how to choose the step length in time. Some numerical examples illustrate the effects of the proposed method.

• Journal of Advanced Marine Engineering and Technology
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• 제15권3호
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• pp.57-65
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• 1991

The quenching of steels by water is one of the important problems in engineering for the applications of heat treatment or continuous casting process, but the fundamental researches by the theoretical approaches have not been satisfactorily improved yet. The very rapid cooling problems by the thermal conduction including the latent heat of phase transformation in steel and the transient boiling heat transfer of water on the surface of the steel covering from $850^{\circ}C$ to $20^{\circ}C$ are the key problems of heat treatment. The present quenching experiments are performed for the cylindrical specimens of carbon steel, S45C of diameters (12-30). Nonlinear transient heat conduction and transient boiling heat transfer problem of water on the surface of specimens is analyzed by the numerical method of inverse heat conduction problem. The conditions for the calculation are that the initial temperature of specimens is $820^{\circ}C$ and the cooling water in bath are $20^{\circ}C$,$40^{\circ}C$,$60^{\circ}C$,$80^{\circ}C$,$95^{\circ}C$ with no agitation.

• 대한기계학회논문집
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• 제17권6호
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• pp.1529-1540
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• 1993

본 연구에서는 금속 열처리를 위한 고온면의 막비등 급냉각에 관한 1차적 연구로서 과냉과도 비등곡선의 정확한 형상과 냉각제의 냉각조건이 강재의 과냉과도 비등열전달에 미치는 영향, $A_1$변태점 부근의 $A_1$냉각속도와 상변태열량광의 관계, 그리고 상변태열이 냉각곡선에 미치는 영향 등을 규명하고자 한다.

• 비파괴검사학회지
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• 제17권4호
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• pp.237-247
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• 1997

경계요소법에 최소 에너지기법을 적용하여 적외선 스캐닝을 이용한 물체 내부 미지의 공동(cavity)을 탐지하는 기하학적 역 열전도 문제의 해를 구하였다. 이 문제에서 경계요소식은 에너지 최소화 과정을 적용한, quadratic programming 문제로 전환되었으며, 가상적인 내부 경계가 실제 공동의 영역 내부에 위치하도록 정의되었다. 적외선 스캐닝 표면 온도가 측정 오차의 구속 조건을 만족하도록 가상 내부 경계에서의 온도 분포를 결정한 후, 이를 내부 경계 조건으로 하는 경계요소 해석을 수행하여 미지 경계의 위치를 결정하였다. 공동 탐지 알고리듬이 제시되었고 수치해석을 통하여 역 해법에 대한 최소에너지 기법의 효과를 분석하였다.

• 비파괴검사학회지
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• 제15권1호
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• pp.299-309
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• 1995

IR CAT Scan 개발을 위한 기하학적 역 열전도 문제의 해를 경계요소법 및 정규화 과정을 사용하여 구하였다. 이 문제에서는 잉여기술된 온도조건이 적외선 스캐닝에 의해 표면에 주어지며, 이 조건은 다른 조건과 함께 미지경계의 위치를 계산하는데 사용되었다. 문제의 해를 구하기 위해 보조문제가 도입되었고, 이 보조문제의 영역에 대한 가상적인 내부경계를 정의함으로써 공동(cavity)이 영역 내부에 위치하게 되며, 포텐셜 문제의 해를 구하여 그 위치를 결정하였다 이 문제의 해를 구하기 위해 경계요소법이 정규화과정과 함께 사용되었으며, 수치해석을 통하여 역 해법에 대한 정규화 효과를 분석하였다.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

• 대한수학회논문집
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• 제33권3호
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• pp.1025-1037
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• 2018

We consider an ill-posed problem for the heat equation $u_{xx}=u_t$ in the quarter plane {x > 0, t > 0}. We propose a new method to compute the heat flux $h(t)=u_x(1,t)$ from the boundary temperature g(t) = u(1, t). The operator $g{\mapsto}h=Hg$ is unbounded in $L^2({\mathbb{R}})$, so we approximate h(t) by $h_{\delta}(t)=u_x(1+{\delta},\;t)$, ${\delta}{\rightarrow}0$. When noise is present, the data is $g_{\epsilon}$ leading to a corresponding heat $h_{{\delta},{\epsilon}}$. We obtain an estimate of the error ${\parallel}h-h_{{\delta},{\epsilon}}{\parallel}$, as well as the error when $h_{{\delta},{\epsilon}}$ is approximated by the trapezoidal rule. With an a priori choice rule ${\delta}={\delta}({\epsilon})$ and ${\tau}={\tau}({\epsilon})$, the step size of the trapezoidal rule, the main theorem gives the error of the heat flux as a function of noise level ${\epsilon}$. Numerical examples show that the proposed method is effective and stable.