• Title/Summary/Keyword: Heat source equation

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Ground Air Heat Exchanger Design and Analysis for Air Source Heat Pump (공기열원 히트펌프를 위한 공기식 지중 열교환기(GAHX) 설계 및 분석 연구)

  • Lee, Kwang-Seob;Lyu, Nam-Jin;Kang, Eun-Chul;Lee, Euy-Joon
    • Journal of the Korean Society for Geothermal and Hydrothermal Energy
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    • v.12 no.2
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    • pp.1-6
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    • 2016
  • A ground air heat exchanger (GAHX), also called earth air heat exchanger is a useful technology to be integrated with other renewable energy technologies. In this study, ground-air heat exchanger system for the air source heat pump is introduced. The purpose of this study is to design the volumetric flow rate and the length of GAHX system. A GAHX length model equation has been developed and used for calculation. GAHX thermal efficiency are recommended as 75% and 85% in order to optimize pipe length. $2,750m^3/h$, $2,420m^3/h$ of volumetric flow rate on 88.3m, 111.7m length are suggested for providing 7.5kW thermal capacity. And the number of path is recommended more than two to minimize pressure drop. For future study, advanced model equation study with ground thermal behavior and a more efficient GAHX design will be considered.

MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A NONLINEAR PARABOLIC EQUATION UNDER DIRICHLET BOUNDARY CONDITION

  • Choi, Q-Heung;Jin, Zheng-Guo
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.697-710
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    • 2000
  • We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

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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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Conjugate Heat Transfer in a Vertical Channel with Protrunding Heat Source (돌출된 열원이 부착된 수직 채널내 복합열전달)

  • Kim, Ui-Gwang;Baek, Byeong-Jun;Jo, Byeong-Su
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.2
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    • pp.741-751
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    • 1996
  • The coupled conduction and convection heat transfer from the protruding heat source in a vertical channel is numerically investigated. Conjugate solution of the two-dimensional energy equation is obtained for the incompressible air flow over the rectangular block with local heat source. It was found that several recirculation zones and separation bubble near the block were related to Re and Gr. And the results show that fractions of the heat transfer through each of the block face, maximum temperature of the block and the relative effect of each parameter on the maximum temperature and heat transfer.

STRONG CONTROLLABILITY AND OPTIMAL CONTROL OF THE HEAT EQUATION WITH A THERMAL SOURCE

  • Kamyad, A.V.;Borzabadi, A.H.
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.787-800
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    • 2000
  • In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

a Study on Heat Source Equations for the Prediction of Weld Shape in Laser Micro-welding (미세 레이저 용접에서 용융부 형상예측을 위한 열원의 방정식에 관한 연구)

  • 장원석;나석주
    • Journal of Welding and Joining
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    • v.18 no.4
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    • pp.76-81
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    • 2000
  • In this research, various heat source equations that have been proposed in previous study were calculated and compared with new model in various laser parameters. This is to treat the problem of predicting, by numerical analysis, the thermo-mechanical behaviors of laser spot welding for thin stainless steel plates. A finite element code, ABAQUS is used for the heat transfer analysis with a three-dimensional plane assumption. Experimental studies if the laser spot welding have also bee conducted to validate the numerical models presented. The results suggest that temperature profiles and weld dimensions are varied according to the heat source of the laser beam. For this reason, it is essential to incorporate an accurate description of the heat source.

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A Study on the heat analysis of Induction Heating Jar (IH-Jar의 열해석에 관한 연구)

  • Lee, Jae-Bok
    • Journal of the Korean Society of Industry Convergence
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    • v.5 no.2
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    • pp.133-139
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    • 2002
  • In this paper, the magneto-thermal analysis of an induction heating jar is presented as an efficient design. The magnetic field inside the axisymmetric shaped cooker is analyzed using an axisymmetric FEM(Finite Element Method) and the effectual heat source is obtained by calculation of the induction current in the Jar. The temperature distribution can be calculated using the heat source and heat equation.

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Analysis of Heat Source Distribution in Low Voltage Condenser (저압 콘덴서의 열원 분포 해석)

  • Kim, Jong-Gyeum;Lee, Dong-Ju;Kim, Il-Jung;Park, Young-Jeen
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.7
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    • pp.1242-1247
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    • 2010
  • In this study, the heat source distributions at the end side and the center of the electrode are analyzed to estimate the electrical stress due to the harmonics from the nonlinear loads. The governing equation at the analysis area of low voltage condenser are numerically solved using the finite element software package to analyze the effects of heat source distribution due to the 5th and 7th harmonics, which can exist normally in the distribution network and can be applied to the low voltage condenser. Finally, the heat source distribution from the harmonics is compared and analyzed with the heat source distribution from the fundamental component of the applied voltage.

A Study on the Heat Source Equation for the Thermal Effect Analysis of Guss Asphalt Pavement (구스 아스팔트의 열 영향 해석을 위한 열원방정식에 관한 연구)

  • Park, Hyun-Woong;Lee, Wan-Hoon
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.23 no.3
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    • pp.96-102
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    • 2019
  • The study of thermal effect on the structure is carried out in the case of Guss asphalt which is paved at the temperature of $240^{\circ}C$ or higher in the bridge pavement of the steel deck bridges. However, studies on the heat source data applicable to numerical analysis are insufficient, the temperature load is used as a joint load. In this study, the heat source equations that can be directly loaded on the plate elements, although limited, are presented using the measured temperature data in the Guss asphalt pavement and its validity is confirmed by a brief numerical analysis.

Evaluation of Spreading Thermal Resistance in Symmetrical Four-Heat Generating Electronic Components (4개 대칭배열 발열 전자소자에서의 확산 열저항 산정)

  • Kim Yun-Ho;Kim Seo-Young;Rhee Gwang-Hoon
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.18 no.8
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    • pp.664-671
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    • 2006
  • We propose the correlation to predict the spreading thermal resistance on a plate with symmetrical four heat sources. The correlation transforms four heat sources to a single equivalent heat source and then the spreading thermal resistance can be obtained with the existing equation for a single heat source. When the four heat sources are mounted on a square base plate, the correlation is expressed as a function of the heat source size, the length of base plate, the plate thermal conductivity and the distance between heat sources. Compared to the results of three-dimensional numerical analysis, the spreading thermal resistance by the proposed correlation is in good agreement within 10 percent accuracy.