• Title/Summary/Keyword: Heat conduction

### Frost behavior of a fin surface with temperature variation along heat exchanger fins (열교환기 휜에 따라 온도 분포를 갖는 휜 표면에서의 서리층 거동)

• Kim, Jung-Soo;Kim, Min-Soo;Lee, Kwan-Soo;Kim, Ook-Joong
• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2091-2096
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• 2007
• This paper presents a mathematical model for predicting the frost behavior formed on heat exchanger fins, considering fin heat conduction under frosting condition. The model is composed of air-side, the frost layer, and fin region, and they are coupled to the frost layer. The frost behavior is more accurately predicted with fin heat conduction considered (Case A) than with a constant fin surface temperature assumed (Case B). The results indicate that the frost thickness and heat transfer rate for Case B are over-predicted in most regions of the fin, as compared to those for Case A. Also, for Case A, the maximum frost thickness varies little with the fin length variations, and the extension of the fin length over 30 mm contributes insignificantly to heat transfer.

### APPROXIMATE SOLUTIONS TO ONE-DIMENSIONAL BACKWARD HEAT CONDUCTION PROBLEM USING LEAST SQUARES SUPPORT VECTOR MACHINES

• Wu, Ziku;Li, Fule;Kwak, Do Young
• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.631-642
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• 2016
• This article deals with one-dimension backward heat conduction problem (BHCP). A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solution consists of two parts. The first part is a known function that satisfies initial and boundary conditions. The other is a product of two terms. One term is known function which has zero boundary and initial conditions, another term is unknown which is related to kernel functions. This method has been successfully tested on practical examples and has yielded higher accuracy and stable solutions.

### Two-dimensional Heat Conduction and Convective Heat Transfer a Circular Tube in Cross Flow (원관 주위의 2차원 전도열전달과 국소 대류열전달)

• Lee Euk-Soo
• Journal of Advanced Marine Engineering and Technology
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• v.29 no.1
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• pp.25-33
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• 2005
• When a circular tube with uniform heat generation within the wall was placed in a cross flow, heat flows by conduction in the circumferential direction due to the asymmetric nature of the fluid flow around the perimeter of the circular tube The circumferential heat flow affects the wall temperature distribution to such an extent that. in some cases, significantly different results may be obtained for geometrically similar surfaces. In the present investigation, the effect of circumferential wall heat conduction is investigated for forced convection around circular tube in cross flow of air and water Two-dimensional temperature distribution $T_w(r,{\theta})$ is calculated through the numerical analysis. The difference between one-dimensional and two-dimensional solutions is demonstrated on the graph of local heat transfer coefficients. It is observed that the effect of working fluid is very remarkable.

### Inverse Heat Conduction Problem in One-Dimensional Time-Dependent Medium with Modified Newton-Raphson Method

• Kim, Sin;Lee, Yoon-Joon;Lee, Jung-hoon;Kim, Min-Chan
• Journal of Energy Engineering
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• v.9 no.1
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• pp.37-40
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• 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.

### Inverse Estimation of Surface Temperature Using the RBF Network (RBF Network 를 이용한 표면온도 역추정에 관한 연구)

• Jung, Bup-Sung;Lee, Woo-Il
• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1183-1188
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• 2004
• The inverse heat conduction problem (IHCP) is a problem of estimating boundary condition from temperature measurement at one or more interior points. Neural networks are general information processing systems inspired by the connectionist theory of human brain. By properly training the network by the learning rule, the neural network method can handle many non-linear or other complex problems. In this work, neural network is applied to complicated inverse heat conduction problems. Efficiency of the procedure is enhanced by incorporating the radial basis functions (RBF). The RBF is trained faster than other neural network and can find smooth solution. In order to demonstrate the effectiveness of the current scheme, a typical one-dimensional IHCP is considered. At one surface, the temperature as well as the heat flux is known. The unknown temperature of interest is estimated on the other side of the slab. The results from the proposed method based on RBF neural network are compared with the conventional method.

### Behavior of frost formed on heat exchanger fins (열교환기 휜에서의 착상 거동)

• Kim, Jung-Soo;Lee, Kwan-Soo
• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2334-2339
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• 2008
• This paper proposes an improved mathematical model for predicting the frosting behavior on a two-dimensional fin considering the heat conduction of heat exchanger fins under frosting conditions. The model consists of laminar flow equation in airflow, diffusion equation of water vapor for frost layer, and heat conduction equation in fin, and these are coupled together. In this model, the change in three-dimensional airside airflow caused by frost growth is accounted for. The fin surface temperature increased toward the fin tip due to the fin heat conduction. On the contrary, the temperature gradient in the airflow direction(x-dir.) is small throughout the entire fin. The frost thickness in the direction perpendicular to airflow, i.e. z-dir., decreases exponentially toward the fin tip due to non-uniform temperature distribution. The rate of decrease of heat transfer in the airflow direction is high compared to that in the z-direction due to more decrease in the sensible and latent heat rate in x-direction.

### Topology Design Optimization of Heat Conduction Problems using Adjoint Sensitivity Analysis Method

• Kim, Min-Geun;Kim, Jae-Hyun;Cho, Seon-Ho
• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.683-691
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• 2010
• In this paper, using an adjoint variable method, we develop a design sensitivity analysis(DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.25% of CPU time for the finite differencing. Also, the topology optimization yields physical meaningful results.

### A MONTE CARLO METHOD FOR SOLVING HEAT CONDUCTION PROBLEMS WITH COMPLICATED GEOMETRY

• Shentu, Jun;Yun, Sung-Hwan;Cho, Nam-Zin
• Nuclear Engineering and Technology
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• v.39 no.3
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• pp.207-214
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• 2007
• A new Monte Carlo method for solving heat conduction problems is developed in this study. Differing from other Monte Carlo methods, it is a transport approximation to the heat diffusion process. The method is meshless and thus can treat problems with complicated geometry easily. To minimize the boundary effect, a scaling factor is introduced and its effect is analyzed. A set of problems, particularly the heat transfer in the fuel sphere of PBMR, is calculated by this method and the solutions are compared with those of an analytical approach.

### Analysis on the three-dimensional unstationary heat conduciton on the welding of thick plate by F. E. M. (有限要素法에 依한 厚板熔接時의 3次元 非定常熱傳導解析)

• 방한서;김유철
• Journal of Welding and Joining
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• v.9 no.2
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• pp.37-43
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• 1991
• In order to analyze the mechanical phenomena of three dimensional elato-plastic behavior caused by welding of thick plate, it is necessary to solve exactly the three dimensional unstationary heat conduction problem considering the moving effect of heat source and the temperature-dependence of material properties. In this paper, the three-dimensional unstationary heat conduction problem is formulated by using an isoparametric finite element method. Thereafter, the transient temperature distributions, according to time, of thick plate during welding are defined from the results calculated by the developed computer program.

### Analysis of an Inverse Heat Conduction Problem Using Maximum Entropy Method (최대엔트로피법을 이용한 역열전도문제의 해석)

• Kim, Sun-Kyoung;Lee, Woo-Il
• Proceedings of the KSME Conference
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• 2000.04b
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• pp.144-147
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• 2000
• A numerical method for the solution of one-dimensional inverse heat conduction problem is established and its performance is demonstrated with computational results. The present work introduces the maximum entropy method in order to build a robust formulation of the inverse problem. The maximum entropy method finds the solution that maximizes the entropy functional under given temperature measurement. The philosophy of the method is to seek the most likely inverse solution. The maximum entropy method converts the inverse problem to a non-linear constrained optimization problem of which constraint is the statistical consistency between the measured temperature and the estimated temperature. The successive quadratic programming facilitates the maximum entropy estimation. The gradient required fur the optimization procedure is provided by solving the adjoint problem. The characteristic feature of the maximum entropy method is discussed with the illustrated results. The presented results show considerable resolution enhancement and bias reduction in comparison with the conventional methods.