• Title/Summary/Keyword: heat equation

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AN INVERSE PROBLEM OF THE THREE-DIMENSIONAL WAVE EQUATION FOR A GENERAL ANNULAR VIBRATING MEMBRANE WITH PIECEWISE SMOOTH BOUNDARY CONDITIONS

  • Zayed, E.M.E.
    • Journal of applied mathematics & informatics
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    • v.12 no.1_2
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    • pp.81-105
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    • 2003
  • This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small |t| and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small |t|.

Advanced One-zone Heat Release Analysis for IDI Diesel Engine (IDI 디젤기관의 개선된 단일영역 열발생량 계산)

  • Kim Gyu-Bo;Jeon Choung-Hwan;Chang Young-Jun;Lee Suk-Young
    • Journal of Advanced Marine Engineering and Technology
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    • v.28 no.7
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    • pp.1101-1110
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    • 2004
  • An one-zone heat release analysis was applied to a 4 cylinder indirect injection diesel engine. The objective of the study is to calculate heat release accurately considering the effect of specific heat ratio. heat transfer and crevice model and to find out combustion characteristics of an indirect diesel engine considering the effect of the pressures in main and swirl chambers. Especially specific heat ratio indicating combustion characteristics is adapted. instead of that indicating matter properties, which has been used in former studies Moreover by adaption of blowby model, cylinder gas mass became accurately calculated. Therefore, with ideal gas equation, calculating cylinder gas temperature, it was found to affect heat transfer loss and heat release. Determining heat transfer constants $C_1$. $C_2$ as 0.6 respectively. the integrated gross heat release values were predicted well for the measured value at various engine speed, full load operating conditions. The curve of heat release rate was similar to SI engine rather than DI engine. That is originated from that swirl chamber reduce an instant combustion which occurs in DI engine due to ignition delay on early stage of combustion.

Numerical Estimation of Heat flux on the Deck Exposed to the High Temperature Impinging Jet of VTOL Vehicle (수직 이착륙기의 고온 고속 배기열에 의한 함정 갑판의 열유속 계산을 위한 수치모델)

  • Jang, Hosang;Hwang, Seyun;Choi, Wonjun;Lee, Jang Hyun
    • Journal of the Korea Institute of Military Science and Technology
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    • v.21 no.1
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    • pp.74-85
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    • 2018
  • This study has analyzed the convective heat transfer on the deck exposed to the high-temperature impingement exhausting from a VTOL vehicle. The heat flow of the impingement on the deck is modeled by the convection heat transfer. The convective heat flux generated by the hot impinging jet is investigated by using both convective heat transfer formulation and conjugate heat transfer formulation. Computational fluid dynamics(CFD) code was used to compute the heat flux distribution. The RANS equation and the k-e turbulence model were used to analyze the thermal flow of the impinging jet. The heat flux distribution near the stagnation zone obtained by the conjugate heat transfer analysis shows more reasonable than the convective heat transfer analysis.

Analysis of Frosting Performance of a Fin-Tube Heat Exchanger (휜-관 열교환기의 착상 성능 해석)

  • Yang Dong-Keun;Lee Kwan-Soo
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.17 no.11
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    • pp.965-973
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    • 2005
  • This paper proposes a mathematical model for predicting the frosting performance on a fin-tube heat exchanger. The model consists of empirical correlations of average heat transfer coefficients for the plate and tube surfaces and a diffusion equation inside the frost layer. The numerical results are compared with experimental data for the frost thickness, the frosting rate and the heat transfer rate to validate the proposed model. The results are in good agreement with the experimental data, and show that this model can be applied to predict frosting performance of common fin-tube heat exchanger.

Thermal Transport Phenomena in the FET Typed MWCNT Gas Sensor with the 60 μm Electrode Distance (60 μm의 전극 간극을 갖는 FET식 MWCNT 가스센서에서 열 유동 현상)

  • Jang, Kyung-Uk
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.28 no.6
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    • pp.403-407
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    • 2015
  • Generally, MWCNT, with thermal, chemical and electrical superiority, is manufactured with CVD (chemical vapor deposition). Using MWCNT, it is comonly used as gas sensor of MOS-FET structure. In this study, in order to repeatedly detect gases, the author had to effectively eliminate gases absorbed in a MWCNT sensor. So as to eliminate gases absorbed in a MWCNT sensor, the sensor was applied heat of 423[K], and in order to observe how the applied heat was diffused within the sensor, the author interpreted the diffusion process of heat, using COMSOL interpretation program. In order to interpret the diffusion process of heat, the author progressed modeling with the structure of MWCNT gas sensor in 2-dimension, and defining heat transfer velocity($u={\Delta}T/{\Delta}x$), accorded to governing equation within the sensor, the author proposed heat transfer mechanism.

An experimental study on heat transfer characteristics of variable conductance heat pipe (가변전열 히이트 파이프의 특성에 관한 연구)

  • 김주년;이영호;김용모
    • Journal of Advanced Marine Engineering and Technology
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    • v.8 no.1
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    • pp.4-16
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    • 1984
  • The heat-pipe is characterised by the highly effective thermal conductance. In order to change the thermal conductance, the heat-pipe is connected to a reservior having a space which is filled with non-condensable gas. In normal operation, the vapour of working fluid will tend to pump the non- condensable gas into the reservoir and the gas-vapour interface situates at some point along the condenser section. The thermal conductance is affected by non- condensable gas. It is concluded that the suitable position of interface can be used to control the temperature of condenser section. In this experiment, the evaporating part is connected to the lowest position of heat-pipe. The copper heat-pipe which is filled with Freon-113 or distilled water as working fluid utilized. As results of experimental study, thermal conductance can be increased by the operating pressure which is infulenced by non-condensable gas. A correlative equation between the thermal conductance and the mass of non- condensable gas is also obtained.

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Laminar Convective Heat Transfer from a Horizontal Flat Plate of Phase Change Material Slurry Flow

  • Kim Myoung-Jun
    • Journal of Advanced Marine Engineering and Technology
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    • v.29 no.7
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    • pp.779-784
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    • 2005
  • This paper presents the theory of similarity transformations applied to the momentum and energy equations for laminar, forced, external boundary layer flow over a horizontal flat plate which leads to a set of non-linear, ordinary differential equations of phase change material slurry(PCM Slurry). The momentum and energy equation set numerically to obtain the non-dimensional velocity and temperature profiles in a laminar boundary layer are solved. The heat transfer characteristics of PCM slurry was numerically investigated with similar method. It is clarified that the similar solution method of Newtonian fluid can be used reasonably this type of PCM slurry which has low concentration. The data of local wall heat flux and convective heat transfer coefficient of PCM slurry are higher than those of water more than 150$\~$200$\%$, approximately.

Modeling of Turbulent Heat Transfer in an Axially Rotating Pipe Flow (축을 중심으로 회전하는 관유동에서 난류열전달의 모형화)

  • Shin, Jong-Keun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.31 no.9
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    • pp.741-753
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    • 2007
  • The elliptic conceptual second moment model for turbulent heat fluxes, which was proposed on the basis of elliptic-relaxation equation, was applied to calculate the turbulent heat transfer in an axially rotating pipe flow. The model was closely linked to the elliptic blending model which was used for the prediction of Reynolds stress. The effects of rotation on the turbulent characteristics including the mean velocity, the Reynolds stress tensor, the mean temperature and the turbulent heat flux vector were examined by the model. The numerical results by the present model were directly compared to the DNS as well as the experimental results to assess the performance of the model predictions and showed that the behaviors of the turbulent heat transfer in the axially rotating pipe flow were satisfactorily captured by the present models.

Study on the Thermal Storage Characteristics of a Multi-capsule type LTES System -Analysis for Heat Charging and Discharging Process for Water Flow- (다관형 잠열축열장치의 축열특성연구 -물을 매체로 한 축열 및 방열과정 분석-)

  • Kim, Y.B.
    • Journal of Biosystems Engineering
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    • v.19 no.1
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    • pp.62-69
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    • 1994
  • This study was designed to seek information on the heat charging and discharging characteristics of a multi-capsule type LTES(Latent Heat of Fusion Thermal Energy Storage) system, and especially prediction equation of outlet water temperature from the system. During heat charging process, the water temperature in the LTES tank increased very slowly in comparison with a predicted one and was kept near the melting point of the PCM for about 25 minutes. During heat discharging process, the latent heat discharging period of the outlet water temperature became longer as the inlet water temperature became higher and/or mass flow rate became lower. The dimensionless temperature of the outlet water was predicted by linking three equations of ${\theta}=1.1Exp(-{\tau}/0.82)$, ${\theta}=-0.06{\tau}+0.3$, ${\theta}=0.8Exp(-{\tau}/1.4)$ ($r^2{\leq}0.88$) depending on discharging period regardless of mass flow rates on the case of the inlet water temperature at $21.5^{\circ}C$.

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Analysis of a gas-particle direct-contact heat exchanger with two-phase radiation effect (복사효과를 고려한 기체-입자 직접접촉식 열교환기 해석)

  • Park, Jae-Hyeon;Baek, Seung-Uk;Gwan, Se-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.22 no.4
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    • pp.542-550
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    • 1998
  • A direct contact heat exchanger using particle-suspended gas as a heat transfer medium is analyzed with an extended emphasis on the radiation, i. e., considering the radiation by both gas and particles. While the Runge-Kutta method is used for a numerical analysis of the momentum and energy equations, the finite volume method is utilized to solve the radiative transfer equation. Present study shows a notable effect by the gas radiation in addition to the particle radiation, especially when changing the chamber length as well as the gas and particle mass flow rate. When the gas and particle mass flow rate is raised, the gas temperature in the particle heater still increases as the gas absorption coefficient increases, which is different from the results for the small scale heat exchanger.