• Title/Summary/Keyword: Heat conduction

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A Study on the temperature Distributions at the Vicinity of a Very Fast Moving Heat Source (매우 빠르게 움직이는 열원 주위의 온도분포에 관한 연구)

  • Cho, Chang-Joo;Juhng, Woo-Nam;Lee , Yong-Ho
    • Journal of the Korean Society for Precision Engineering
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    • v.16 no.8
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    • pp.162-169
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    • 1999
  • Fourier heat conduction law becomes invalid for the situations involving extremely short time heating, very low temperatures and fast moving heat source(or crack), since the wave nature of heat propagation becomes dominant. For these conditions, the modified heat conduction equation with the finite propagation speed of heat in the medium could be applied to predict heat flux and temperature distributions. In this study, temperature distributions at the vicinity of a very fast moving heat source are investigated numerically. Thermal fields are characterized by thermal Mach numbers(M) defined as the ratio of moving heat source speed to heat propagation speed in the solid. In the transonic and supersonic ranges($M{\ge}1$), thermal shocks are shown, which separate the heat affected zone from the thermally undisturbed zone.

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Analysis of Inverse Heat Conduction Problem Using OpenFOAM and VisualDoc (OpenFOAM 과 VisualDoc 을 이용한 역열전도 문제의 해석)

  • Kim, Sung-Won;Kim, Sun Kyoung
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.37 no.6
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    • pp.539-544
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    • 2013
  • This study provides a solution method for the inverse heat conduction problem based on a combination of a public domain CAE (computer aided engineering) software and a commercial CAO (computer aided optimization) software. The solver system has been implemented without any in-house coding. The proposed method is simple to implement. Moreover, it can be easily reproduced.

Fuzzy finite element method for solving uncertain heat conduction problems

  • Chakraverty, S.;Nayak, S.
    • Coupled systems mechanics
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    • v.1 no.4
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    • pp.345-360
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    • 2012
  • In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

SIMPLIFIED TIKHONOV REGULARIZATION FOR TWO KINDS OF PARABOLIC EQUATIONS

  • Jing, Li;Fang, Wang
    • 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.

Transient Heat Conduction Through the Ondol Floor and Beat toss to the Ground (온돌의 구들장과 땅바닥의 비정상 열전도 해석)

  • Bae, Soon-Hoon;Kim, Doo-Chun
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.4 no.1
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    • pp.6-17
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    • 1975
  • For a periodic variation of the flue gas temperature the heat conduction through the Ondol floor was analysized. Also the heat loss to the ground was estimated. The floor thermal capacity, as a function of the floor thickness, has strong influence on the time lag of the temperature variation. It is an important design parameter for intermittent heating. Even for the steady periodic variation, there was significant heat loss to the ground below the Ondol floor.

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A framework for geometrically non-linear gradient extended crystal plasticity coupled to heat conduction and damage

  • Ekh, Magnus;Bargmann, Swantje
    • Multiscale and Multiphysics Mechanics
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    • v.1 no.2
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    • pp.171-188
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    • 2016
  • Gradient enhanced theories of crystal plasticity enjoy great research interest. The focus of this work is on thermodynamically consistent modeling of grain size dependent hardening effects. In this contribution, we develop a model framework for damage coupled to gradient enhanced crystal thermoplasticity. The damage initiation is directly linked to the accumulated plastic slip. The theoretical setting is that of finite strains. Numerical results on single-crystalline metal showing the development of damage conclude the paper.

Analysis of Thermal Loading of a Large LPG Engine Piston Using the Inverse Heat Conduction Method (열전도의 역문제 방법을 이용한 대형 LPG 엔진 피스톤의 열부하 해석)

  • Park Chul-Woo;Lee Boo-Youn
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2006.04a
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    • pp.820-827
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    • 2006
  • The convection heat transfer coefficients on the top surface of a large liquid petroleum liquid injection(LPLi) engine piston are analyzed by solving an inverse thermal conduction problem. The heat transfer coefficients are numerically found so that the difference between analyzed temperatures from the finite element method and measured temperatures is minimized. Using the resulting heat transfer coefficients as the boundary condition, temperature of a large LPLi engine piston is analyzed.

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INTEGRALS INVOLVING SPHEROIDAL WAVE FUNCTION AND THEIR APPLICATIONS IN HEAT CONDUCTION

  • Gupta, R.K.;Sharma, S.D.
    • Kyungpook Mathematical Journal
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    • v.18 no.2
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    • pp.311-319
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    • 1978
  • This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

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Transient heat conduction in rock mass around arch shape cold storage cavern and estimation of in-situ thermal properties (아치형 냉동저장공동 주위암반의 비정상상태 열전도 특성 및 열물성 평가)

  • Synn, Joong-Ho;Park, Yeon-Jun;Kim, Ho-Yeong;Park, Chan
    • Tunnel and Underground Space
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    • v.9 no.1
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    • pp.27-35
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    • 1999
  • The characteristics of heat conduction for the heat source boundary like an arch shape cavern are different from those for the semi-infinite or circular boundary which can be driven theoretically. A new form of transient heat conduction equation in rock mass around the arch shape cavern is evaluated with analyzing the pattern of the rock temperature distribution measured at the cold storage pilot plant. The new equation, which is driven by adopting a shape function, $SF=\sqrt{logx_0/log(x_0+x)}$ to the solution for a semi-infinite boundary, has the semi-radial form of temperature variation with distance. And, thermal properties of rock mass are estimated by comparing the rock temperature distributions by this equation with those by measurement. Thermal conductivity and specific heat of rock mass are estimated as giving the difference of 20~25% compared to those of laboratory scale. This difference seems to be caused by discontinuity like joint and water content in rock mass.

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Analysis of Hyperbolic Heat Conduction in a Thin Film (박막에서 쌍곡선형 열전도 방정식에 의한 열전도 해석)

  • 정우남;이용호;조창주
    • Journal of Energy Engineering
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    • v.8 no.4
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    • pp.540-545
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    • 1999
  • The classical Fourier heat conduction equation is invalid at temperatures near absolute zero or at very early times in highly transient heat transfer processes. In such situations, a hyperbolic equation model for heat conduction based on the modified Fourier law is introduced because the wave nature of heat propagation becomes dominant. The Fourier model and the hyperbolic model for heat conduction are analyzed by using the Green's function technique together with the integral transform. Analytical expressions for the heat flux and temperature distributions in a finite slab subjected to a periodic surface heating at one of its surfaces are presented and the results obtained from each model are compared with each other. The thermal wave implied b the hyperbolic model is shown to travel through a medium and to reflect back toward the origin at the other insulated surface. On the other hand, the heat by the Fourier model propagates at an infinite speed instantaneously after a thermal disturbance is felt throughout the medium.

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