• 대한수학회지
• /
• 제48권2호
• /
• pp.311-327
• /
• 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.

• 대한기계학회논문집B
• /
• 제37권6호
• /
• pp.539-544
• /
• 2013

본 연구는 공개 해석프로그램과 상용 최적화 프로그램을 연계하여 역열전도 문제를 해결하는 방법론을 제시하고 구현하였다. 이 해석 방법은 구동이 간단하며, 내부 코딩 없이도 구동이 가능하기 때문에 다른 연구자들도 쉽게 역열전도 문제를 재현할 수 있다.

• 대한기계학회논문집B
• /
• 제22권12호
• /
• pp.1715-1725
• /
• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• 대한기계학회논문집B
• /
• 제33권1호
• /
• pp.17-27
• /
• 2009

Water jet impingement cooling is used to remove heat from high-temperature surfaces such as hot steel plates in the steel manufacturing process (thermo-mechanical cooling process; TMCP). In those processes, uniform cooling is the most critical factor to ensure high strength steel and good quality. In this study, experiments are performed to measure the heat transfer coefficient together with the inverse heat conduction problem (IHCP) analysis for a plate cooled by planar water jet. In the inverse heat transfer analysis, spatial and temporal variations of heat transfer coefficient, with no information regarding its functional form, are determined by employing the conjugate gradient method with an adjoint problem. To estimate the two dimensional distribution of heat transfer coefficient and heat flux for planar waterjet cooling, eight thermo-couple are installed inside the plate. The results show that heat transfer coefficient is approximately uniform in the span-wise direction in the early stage of cooling. In the later stage where the forced-convection effect is important, the heat transfer coefficient becomes larger in the edge region. The surface temperature vs. heat flux characteristics are also investigated for the entire boiling regimes. In addition, the heat transfer rate for the two different plate geometries are compared at the same Reynolds number.

• 대한수학회지
• /
• 제44권6호
• /
• pp.1281-1290
• /
• 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.651-661
• /
• 2010

We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제9권2호
• /
• pp.75-82
• /
• 2005

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as $0\;{\leq}\;r\;{\leq}\;a,\;0\;{\leq}\;z\;{\leq}\;h$. The results, obtained in the series form in terms of Bessel's functions, are illustrated numerically.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2012년도 제38회 춘계학술대회논문집
• /
• pp.397-402
• /
• 2012

본 논문에서는 미지의 두 열물성 값인 열전도율과 열확산율을 구하기 위하여 Levenberg-Marquardt 방법에 의한 역해석 기법을 도입하였다. 일차원 열전도 문제에 대하여 연산식을 유도하였으며, 시편에 대하여 두 지점의 온도 및 입력유동의 열유속 측정값을 적용하였다. 예측된 열전도율 및 열확산율은 알려진 그라파이트 시편에 대한 열물성 값과 비교하였으며 그 결과 본 논문에서 제시된 역해석 예측 기법 실험의 유효성이 파악되었다.

• 에너지공학
• /
• 제9권1호
• /
• pp.37-40
• /
• 2000

An inverse problem is solved to determine the space-dependent thermal conductivity in one-dimensinoal time-dependent heat conduction medium with the data imposed and measured at the two end-points. The thermal conductivity is approximated as a linear combination of known functions with unknown coefficients and the unknowns are obtained by the governing and sensitivity equations using modified Newton-Raphson method. The estimated results are compared with exact thermal conductivities and it shows good agreements. This approach is expected to be used to estimate spatial composition of heat conduction medium.

• 대한수학회논문집
• /
• 제16권3호
• /
• pp.385-397
• /
• 2001

Consider an inverse problem of determining of the 2-D temperature distribution from known temperature given at some time T>0. Our aim is to find the temperature for 0