• Title/Summary/Keyword: Heat Equation

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Analysis of Laminar Flow and Heat Transfer in Asymmetric, Sudden Expansion Channel (비대칭급확대채널의 층류유동 및 열전달 해석)

  • Won, Seung-Ho;Maeng, Joo-Sung;Son, Byung-Jin
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.13 no.1
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    • pp.5-13
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    • 1984
  • This analysis of numerical procedure is prediction of laminar flow and heat transfer at two dimension and steady flow in asymmetric sudden expansion channel. At former study, to analyse the flows with separation, the full Navier-Stokes equation is used, but there are many difficulties to analyse, and although significant progress has been made in the development of efficient computational methods for the Navier-Stokes equations, very large computation times are still required. In case of reward-facing flow, boundary-layer equation is used instead of full Navier-Stokes equation to analyse velocity fields, and result of this numerical analysis is good agreement with the given experimental study. In this case, since the computer time required for the boundary-layer calculation is an order of magnitude less than required for the solution of the full Navier-Stokes equation, this boundary-layer model provides a good approximate solution.

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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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New algorithm for simulating heat transfer in a complex CPFS (Cable Penetration Fire Stop)

  • Yun, Jong-Pil;Kwon, Seong-Pil;Cho, Jae-Kyu;Yoon, En-Sup
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.1798-1803
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    • 2003
  • In this work the dynamic heat transfer occurring in a cable penetration fire stop system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealants. The dynamic heat transfer can be described by a partial differential equation (PDE) and its initial and boundary conditions. For the shake of simplicity PDE is divided into two parts; one corresponding to the heat transfer in the axial direction and the other corresponding to the heat transfer on the vertical layers. Two numerical methods, SOR (Sequential Over-Relaxation) and FEM (Finite Element Method), are implemented to solve these equations respectively. The axial line is discretized, and SOR is applied. Similarly, all the layers are separated into finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The heat fluxes on the layers are calculated by FEM. It is shown that the penetration cable influences the temperature distribution of the fire stop system very significantly. The simulation results are shown in the three-dimensional graphics for the understanding of the transient temperature distribution in the fire stop system.

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Cooling Characteristics on the Forced Convection of an Array of Electronic Components in Channel Flow (II) - The Effect of the Reynolds Number (without the Heat Sink) - (채널 유동장 내에 배열된 전자부품의 강제대류 냉각특성에 관한 연구(II) -레이놀즈 수의 영향(히트싱크가 부착되지 않은 경우)-)

  • Kim, Kwang-Soo;Yang, Jang-Sik
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.18 no.6
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    • pp.509-517
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    • 2006
  • Present study is concerned with an experimental study on the cooling characteristics of heat-generating components arranged in channels which are made by printed circuit boards. To estimate the thermal performance of the heat-generating components arranged by $5\times11$ in channel flow, three variables are used: the inlet velocity, the height of channel, and row number of the component. The cooling characteristics of the heat-generating components such as the surface temperature rise, the adiabatic temperature rise, the adiabatic heat transfer coefficient, and the effect of thermal wake are compared with the result of the experiment and the numerical analysis. The experimental result is in a good agreement with the numerical analysis. The heat transfer coefficient increases as the Reynolds number increases, while the thermal wake function calculated for each row decreases as the Reynolds number increases. In addition, it is found that Nu-Re correlation equation is Identical to the previous studies, and the empirical correlation equation between the thermal wake function and Re is presented.

Analysis of forced convective laminar film boiling heat transfer on vertical surface (垂直平板에서의 强制對流 膜沸騰 流動의 熱傳達解析)

  • 이규식;최영돈
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.3
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    • pp.425-436
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    • 1987
  • Accurate predictions of heat transfer coefficient of vertical laminar film-boiling are very important in many engineering applications. There are many predictions, however they are not exact as yet, since they have used the assumption of constant thermodynamic properties in the analysis. In this paper, heat transfer of vertical film boiling was analysized by Runnge Kutta method using veriable thermodynamic properties. 1/4 interval method was exployed for the prediction of unknown wall boundary condition. Numerical computations were performed with varying the wall temperature and the free stream velocity of liquid. Results show that assumption of constant thermodynamic properties induced considerable error in predicting the heat transfer coefficient, friction factor, film thickness, and critical length for transition to turbulent flow. Comparision of the predicted heat transfer coefficient of present analysis with that from Bromley's correlation shows that the use of general latent heat in Bromely equation instead of modified latent heat is more desireable since it makes the coefficient of Bromley equation into constant.

Transient Heat Transfer in Porous Media under Oscillating Flow Condition (왕복유동조건에서 다공성 물질의 비정상 열전달)

  • Byeon, Su-Yeong;Lee, Dae-Yeong;No, Seung-Tak
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.25 no.3
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    • pp.422-432
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    • 2001
  • An analytical characterization is presented on the transient heat transfer by an oscillating flow through a porous slab. Based on a two-equation model, analytic solutions are obtained for both the fluid and solid temperature variations. Two parameters are identified as the Stanton number for the internal heat exchange and the ratio of the thermal capacities between the solid and fluid phases. The heat transfer characteristics are shown to be classified into four regimes according to the two parameters and physical interpretation is presented on the particular heat transfer processes within each regime. In addition, the condition for the local thermal equilibrium between the phases is examined and the relevant criterion is suggested.

A study on the forced convection heat transfer in the vertical copper tube at uniform wall heat flux (균일한 열유속에서의 수직동관내의 강제대류 열전달에 관한 연구)

  • Baek, Go-Gil;Cha, Ji-Yeong;Seo, Jeong-Yun
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.8 no.4
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    • pp.213-220
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    • 1979
  • A number of methods has been developed for calculation of heat transfer in the vertical round tube under conditions of forced convection with uniform heat flux at wall. I would like to express hereby one of applications of this study in the design of heat exchanger instruments for water flow at $15.8^{\circ}C(p_r=8)$ used frequently in our daily life. Also all the results are investigated for forced convective heat transfer in the case of heated water-flow at uniform wall heat flux in the vortical round copper tube, where the ratio of length to diameter will be 44. They are well in agreement with Gratz and Kraussold equation respectively in laminar and transition flow range. In turbulent flow in the range from Re=10,000 to 65,000, the experimental formula Is show as follows ; Nu=0.023 $R_e^{0.814}\;P_r^{0.4}$. And this is agreed with Dittus - Boelter equation when Reynolds number exponent increases from 0.80 to 0.814.

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Flow Visualization and Numerical Calculation in a Channel Perturbed by Curvilinear Blockages (장애물을 갖는 덕트내의 유동가시화 및 수치해석에 관한 해석)

  • Moon, C.;Park, J.C.;Kim, C.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.6 no.3
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    • pp.218-226
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    • 1994
  • Laminar flow and heat transfer in a channel with blockages are obtained numerically in a Reynolds-number range of $100{\leq}Re{\leq}400$. A boundary-fitted curvilinear coordinate system is generated for irregular boundary of the physical region, and solutions of Navier-Stokes equation and energy equation are obtained by finite analytic method in the transformed computational domain. The flow separates in downstream of the blockage and the length of separated-flow region increases with Reynolds number. The heat flux is high on the top of the blockages and increase in the heat transfer occurs where the fluid reattaches the wall. Comparison between computed streamlines and experimental flow-visualization is also presented and discussed.

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Modeling of Heat Transfer Equations for Estimation of Temperature Variations Inside the Oil Transport Pipe Line (원유 수송관 내부의 온도 변화 예측 을 위한 열전달 방정식의 모델링)

  • Jin, J.J.;Chung, H.T.;Bae, J.S.;Lee, S.O.
    • 한국전산유체공학회:학술대회논문집
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    • 2008.03b
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    • pp.300-303
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    • 2008
  • In the present study, the simple form of the heat transfer equation were suggested to estimate the temperature variation inside the oil pipe in order to determine the thickness of the insulating materials to retain the working oils below the critical temperature. The conservation of the thermal energy at arbitrary time were modeled to one dimensional unsteady equation with the empirical formula or data. The calculating results for non-insulation case showed that the temperature were very sensitive to the thermal convection by the velocity of the external wind. For insulation case, the insulation material which has higher density and specific heat, lower thermal conductivity should be chosen with more brighter coloring outside the pipe in order to retain the working oils below the critical temperature.

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A boundary element method based on time-stepping approximation for transient heat conduction in anisotropic solids

  • Tanaka, Masa;Matsumoto, T.;Yang, Q.F.
    • Structural Engineering and Mechanics
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    • v.4 no.1
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    • pp.61-72
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    • 1996
  • The time-stepping boundary element method has been so far applied by the authors to transient heat conduction in isotropic solids as well as in orthotropic solids. In this paper, attempt is made to extend the method to 2-D transient heat conduction in arbitrarily anisotropic solids. The resulting boundary integral equation is discretized by means of the boundary element with quadratic interpolation. The final system of equations thus obtained is solved by advancing the time step from the given initial state to the final state. Through numerical compuation of a few examples the potential usefulness of the proposed method is demonstrated.