• Title/Summary/Keyword: heat equation

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A Study on Heat Transfer Enhancement for a Shear-Thinning Fluid in Triangular Ducts (삼각형 단면 덕트 내의 Shear-Thinning 유체에 대한 열전달 촉진에 관한 연구)

  • Lee, Dong-Ryul
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.12 no.9
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    • pp.3808-3814
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    • 2011
  • The prediction of heat transfer and pressure drops in the exchanger passages is a clue to the problem of heat exchanger design. In order to make such predictions for non-Newtonian fluids, it is necessary to know the relation between the viscous properties of the fluid and the wall shear rate in the duct. This study deals with the limits of validity of the power law equation. The useful methodology of the present research involves a consideration of a more general equation which has power law and Newtonian behavior as asymptotes. It isconcluded that use of the power law equation outside of its applicability range can lead to serious errors inpredicting the heat transfer and pressure drops. The present computational results of the friction factors times Reynolds number for shear-thinning fluid flows in a triangular duct are compared with previous published results, showing agreement with 0.13 % in Newtonian region and 2.85 % in power law region. These shear-thinning fluid results also showed the 12% increase of convective heat transfer enhancement compared with Newtonian heat transfer.

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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Thermal Deformation Induced Preload Changein the Tilting Pad Journal Bearing (열변형으로 인한 틸팅패드 저널베어링의 예압 변화)

  • Suh, Junho;Hwang, Cheolho
    • Tribology and Lubricants
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    • v.32 no.1
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    • pp.1-8
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    • 2016
  • This paper focuses on the thermal deformation induced preload change in the tilting pad journal bearing, using a three-dimensional (3D) thermo-hydro-dynamic (THD) approach. Preload is considered as a critical factor in designing the tilting pad journal bearing. The initial preload measured under nil external load and nil thermal gradient is influenced by two factors, namely, the thermal deformation and elastic deformation. Thermal deformation is due to a temperature distribution in the bearing pads, whereas the elastic deformation is due to fluid forces acting on the pads. This study focuses on the changes induced in preload and film clearance due to thermal deformation. The generalized Reynolds equation is used to evaluate the force of the fluid and the 3D energy equation is used to calculate the temperature of the lubricant. The abovementioned equations are combined by establishing a relationship between viscosity and temperature. The heat transfer within the bearing pads, the lubricant, and the spinning journal is calculated using the heat flux boundary condition. The 3D Finite Element Method (FEM) is used in modeling the (1) heat conduction in the spinning journal and bearing pads, (2) thermal gradient induced thermal distortion of the spinning journal and pads, and (3) viscous shearing, and heat conduction and convection in a thin film. This evaluation method has an increased fidelity, and it can prove to be a cost-effective tool that can be used by designers to predict the dynamic behavior of a bearing.

Analysis of Temperature Distribution and slip in Rapid Thermal Processing (급속 열처리시 실리콘 웨이퍼의 온도분포와 슬립 현상의 해석)

  • Lee, Hyouk;Yoo, Young-Don;Earmme, Youn-Young;Shin, Hyun-Dong;Kim, Choong-Ki
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.4
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    • pp.609-620
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    • 1992
  • A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing (R.T.P) is obtained, and an analysis of onset and propagation of slip is performed and compared with experiment. In order to calculate temperature distribution of a wafer in R.T.P system, heat conduction equation that incorporated with radiative and convective heat transfer model is solved, and the solution of the equation is calculated numerically using alternating direction implicit (A.D.I) method. In dealing with radiative heat transfer, a partially transparent body that absorbs the radiation energy is assumed and this transparent body undergoes multiple internal reflections and absorptions. Two dimensional (assuming plane stress) thermoelastic constitutive equation is used to calculate thermal stress induced in a wafer and finite element method is employed to solve the equation numerically. The stress resolved in the slip directions on the slip planes of silicon is compared with the yield stress of silicon in order to predict the slip. The result of the analysis shows that the wafer temperature at which slip occurs is affected by the heating rate of the R.T.P system. It is observed that once slip occurs in the wafer, the slip grows.

Fuel Consumption Rate Calculation Equation and its Application at fewer Boiler (화력발전소 보일러 연료소비량 계산 및 정확성 검증)

  • Jang, Seok-Won;Kim, Jae-Hoo
    • Journal of Energy Engineering
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    • v.14 no.2 s.42
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    • pp.147-152
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    • 2005
  • Calculation equations of fired fuel comsumption rating at boiler can lead from combustion anal-ysis and boiler heat balance using mass & energy conservations. By comparing calculation equation results with those of measurement, we can confirm the deviation of fuel consumption rate, and correction rate, and correction degree, and can also establish the proven technology to apply the equation at the site. We applied fuel rate equation to the operating power plant and recorded $2.4\%\;&\;1.5\%$ of deviation at each coal and oil fired boilers. This range of deviation is regarded as trustable to apply the fuel consumption equation to the actual site.

ON A STABILITY OF PEXIDERIZED EXPONENTIAL EQUATION

  • Chung, Jae-Young
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.295-301
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    • 2009
  • We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

Comparative Study on the Performance of Correlations of the Enthalpy of Vaporization for Pure Substance Refrigerants

  • Park Kyoung Kuhn
    • International Journal of Air-Conditioning and Refrigeration
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    • v.12 no.4
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    • pp.214-219
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    • 2004
  • A few commonly used correlation equations of the enthalpy of vaporization are reviewed and a new three-parameter correlation equation is proposed. Performance of the pro­posed equation is examined using the data listed in the ASHRAE table for 22 pure substance refrigerants. The new equation yields an average absolute deviation of $0.14\%$ for 22 refrig­erants, which is better than those of other equations, such as Xiang $(0.18\%),$ Majer-Svoboda­Pick $(0.18\%),$ and Somayajulu equation $(0.23\%)$.

Comparative Study on the Performance of Correlations of the Enthalpy of Vaporization for Pure Substance Refrigerants (순수물질 냉매에 대한 증발 엔탈피 상관식의 성능비교 연구)

  • 박경근
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.15 no.8
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    • pp.704-709
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    • 2003
  • A few commonly used correlation equations of the enthalpy of vaporization are reviewed and a new three-parameter correlation equation is proposed. Performance of the proposed equation is examined using the data listed in the ASHRAE table for 22 pure substance refrigerants. The new equation yields an average absolute deviation of 0.14% for 22 refrigerants, which is better than those of other equations, such as Xiang (0.18%), Major-Svoboda-Pick (0.18%), and Somayajulu equation (0.23%).

A Finite Element Analysis of Conjugate Heat Transfer Inside a Cavity with a Heat Generating Conducting Body (고체 열원이 존재하는 공동 내의 복합열전달 문제의 유한요소해석)

  • Ahn, Young-Kyoo;Choi, Hyoung-Gwon;Yong, Ho-Taek
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.33 no.3
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    • pp.170-177
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    • 2009
  • In the present study, a finite element analysis of conjugate heat transfer problem inside a cavity with a heat-generating conducting body, where constant heat flux is generated, is conducted. A conduction heat transfer problem inside the solid body is automatically coupled with natural convection inside the cavity by using a finite element formulation. A finite element formulation based on SIMPLE type algorithm is adopted for the solution of the incompressible Navier-Stokes equations coupled with energy equation. The proposed algorithm is verified by solving the benchmark problem of conjugate heat transfer inside a cavity having a centered body. Then a conjugate natural heat transfer problem inside a cavity having a heat-generating conducting body with constant heat flux is solved and the effect of the Rayleigh number on the heat transfer characteristics inside a cavity is investigated.

Conjugated heat transfer on convection heat transfer from a circular tube in cross flow (원관 주위의 대류 열전달에 대한 복합 열전달)

  • 이승홍;이억수;정은행
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.10 no.5
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    • pp.523-534
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    • 1998
  • The convection heat transfer on horizontal circular tube is studied as a conjugated heat transfer problem. With uniform heat generation in a cylindrical heater placed in a cross flow boundary condition, heat flow that is conducted along the wall of the heater creates a non-isothermal surface temperature and non-uniform heat flux distribution. In the present investigation, the effects of circumferential wall heat conduction on convection heat transfer are investigated for the case of forced convection around horizontal circular tube in cross flow of air and water. Non-dimensional conjugation parameter $ K^*$ which can be deduced from the governing energy differential equation should be used to express the effect of circumferential wall heat conduction. Two-dimensional temperature distribution$ T({\gamma,\theta})$ is presented. The influence of circumferential wall heat conduction is demonstrated on graph of local Nusselt number.

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