• Title/Summary/Keyword: Biot Number

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Numerical Analysis in Heat Transfer of a Triangular Fin (삼각휜 열전달의 수치해석)

  • Chun, Sang-Myung;Kwon, Young-Pil
    • The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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    • v.11 no.3
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    • pp.52-57
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    • 1982
  • One-dimensional approximation for fin problems is widely used in current texts and industrial practice. The errors caused by this approximation is analysed for a longitudinal triangular fin by the numerical solution of two-dimensional fin equation. Two-dimensional solution is obtained by the finite element method and com pared with the one-dimensional esact solution. The results show that total heat transfer and fin efficiency are overestimated by the one-dimensional approximation. The factors which cause these errors are the Biot number (Bi) and the ratio of fin length to half the thickness (L/a). When Bi is smaller than 1.0 these errors are smaller than $10\%$, but when Bi is larger than 5.0 they are a few ten percents. Fin efficiency obtaned by one-dimensional and long fin assumption is valid only then Bi is small and L/a is large.

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Analysis of Two-Dimensional Transient Heat Conduction Problems in a Finite Strip by the Heat Balance Integral Method (熱平衡積分法에 의한 有限 Strip에서의 2次元 過渡熱傳導 問題의 解析)

  • 서정일;조진호;조종철
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.7 no.4
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    • pp.417-424
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    • 1983
  • This paper presents two methods of obtaining approximate analytic solutions for the temperature distributions and heat flow to two-dimensional transient heat conduction problems in a finite strip with constant thermal properties using the Heat Balance Integral. The methods introduced in this study are as follows; one using the Heat Balance Integral only, and the other successively using the Heat Balance Integral and an exact analytic method. Both methods are applicable to a large number of the two-dimensional unsteady conduction problems in finite regions such as extended surfaces with uniform thickness, but in this paper only solutions for the unsteady problems in a finite strip with boundary condition at the base expressed in terms of step function are provided as an illustration. Results obtained by both methods are compared with those by the exact two-dimensional transient analysis. It is found that both approximate methods generate small time solutions, which can not be obtained easily by any exact analytic method for small values of Fourier numbers. In the case of applying the successive use of the Heat Balance Integral and Laplace transforms, the analysis shows good agreement with the exact solutions for any Fourier number in the range of Biot numbers less than 0.5.

NUMERICAL ANALYSIS ON THE NATURAL CONVECTION IN A LONG HORIZONTAL PIPE WITH THERMAL STRATIFICATION

  • Ahn, Jang-Sun;Park, Byeong-Ho;Kim, Seoug-Beom;Kim, Eun-Kee;Park, Man-Heung
    • Proceedings of the Korean Nuclear Society Conference
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    • 1996.05b
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    • pp.95-101
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    • 1996
  • In this paper, the steady 2-dimensional model for a long horizontal line with different end temperatures undergoing natural convection at very high Rayleigh number is proposed to numerically investigate the heat transfer and flow characteristics. The dimensionless governing equations are solved by using SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which is developed using control volumes and staggered grids. The numerical results are verified by comparison with the operating PWR test data. The analysis focuses on the effects of variation of the heat transfer rates at the pipe surface, the thermal conductivities of the pipe material and the thickness of the pipe wall on the thermal stratification. The results show that the heat transfer rate at the pipe surface is the controlling parameter. A significant reduction and disappearance of thermal stratification phenomenon is observed at the Biot number of 5.0$\times$10$^{-2}$. The results also show that the increment of the thermal conductivity and thickness of the wall weakens the thermal stratification and somewhat reduces azimuthal temperature gradient in the pipe wall. Those effects are however minor, when compared with those due to the variation of the heat transfer rates at the surface of the pipe wall.

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Evaluation of Thermal Stratification Effect in a Long Horizontal Pipeline with Turbulent Natural Convection

  • Park, Man-Heung;Ahn, Jang-Sun;Nam, Seung-Deog
    • Nuclear Engineering and Technology
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    • v.30 no.6
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    • pp.581-591
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    • 1998
  • Numerical analysis was peformed for the two-dimensional turbulent natural convection for a long horizontal line with different end temperatures. The turbulent model has been applied a standard k-$\varepsilon$ two equation model of turbulence similar to that the proposed by the Launder and Spalding. The dimensionless governing equations are solved by using SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which is developed using control volumes and staggered grids. The numerical results are verified by comparison with the operating PWR test data. The analysis focuses on the effects of variation of the heat transfer rates at the pipe surface, the thermal conductivities of the pipe material and the thickness of the pipe wall on the thermal stratification. The results show that the heat transfer rate at the pipe surface is the controlling parameter for mitigating of thermal stratification in the long horizontal pipe. A significant reduction and disappearance of the thermal stratification phenomenon is observed at the Biot number of 4.82$\times$10$^{-1}$ . The results also show that the increment of the thermal conductivity and thickness of the wall weakens a little the thermal stratification and somewhat reduces temperature gradient of y-direction in the pipe wall. These effects are however minor, when compared with those due to the variation of the heat transfer rates at the surface of the pipe wall.

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Seabed Sediment Feature Extraction Algorithm using Attenuation Coefficient Variation According to Frequency (주파수에 따른 감쇠계수 변화량을 이용한 해저 퇴적물 특징 추출 알고리즘)

  • Lee, Kibae;Kim, Juho;Lee, Chong Hyun;Bae, Jinho;Lee, Jaeil;Cho, Jung Hong
    • Journal of the Institute of Electronics and Information Engineers
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    • v.54 no.1
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    • pp.111-120
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    • 2017
  • In this paper, we propose novel feature extraction algorithm for classification of seabed sediment. In previous researches, acoustic reflection coefficient has been used to classify seabed sediments, which is constant in terms of frequency. However, attenuation of seabed sediment is a function of frequency and is highly influenced by sediment types in general. Hence, we developed a feature vector by using attenuation variation with respect to frequency. The attenuation variation is obtained by using reflected signal from the second sediment layer, which is generated by broadband chirp. The proposed feature vector has advantage in number of dimensions to classify the seabed sediment over the classical scalar feature (reflection coefficient). To compare the proposed feature with the classical scalar feature, dimension of proposed feature vector is reduced by using linear discriminant analysis (LDA). Synthesised acoustic amplitudes reflected by seabed sediments are generated by using Biot model and the performance of proposed feature is evaluated by using Fisher scoring and classification accuracy computed by maximum likelihood decision (MLD). As a result, the proposed feature shows higher discrimination performance and more robustness against measurement errors than that of classical feature.

Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
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    • v.10 no.1
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    • pp.66-74
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    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

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Adsorption Characteristics of Methyl Orange on Ginkgo Shell-Based Activated Carbon (은행 껍질 기반 활성탄의 메틸오렌지 흡착 특성)

  • Lee, Jeong Moon;Lee, Eun Ji;Shim, Wang Geun
    • Applied Chemistry for Engineering
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    • v.33 no.6
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    • pp.636-645
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    • 2022
  • In this study, we investigated the adsorption characteristics of methyl orange (MO), an anionic dye, on ginkgo shell-based activated carbon (AC). For this purpose, ACs (GS-1, GS-2, and GS-4) with different textural properties were prepared using ginkgo shells and potassium hydroxide (KOH), a representative chemical activating agent. The correlation between the textural characteristics of AC prepared and the mixing ratio of KOH was investigated using nitrogen adsorption/desorption isotherms. The MO adsorption equilibrium experiment on the prepared ACs was conducted under different pH (pH 3~11) and temperature (298~318 K) conditions, and the results were investigated by Langmuir, Freundlich, Sips and temperature-dependent Sips equations. The feasibility of the MO adsorption treatment process of the prepared AC was also investigated using the dimensionless Langmuir separation factor. The heterogeneous adsorption properties of MO for the prepared AC examined using the adsorption energy distribution function (AED) were closely related to the system temperature and textural characteristics of AC. The kinetic results of the batch adsorption performed at different temperatures can be satisfactorily explained by the homogeneous surface diffusion model (HSDM), which takes into account the external mass transfer, intraparticle diffusion, and active site adsorption. The relationship between the activation energy value obtained by the Arrhenius plot and the adsorption energy distribution function value was also investigated. In addition, the adsorption process mechanism of MO on the prepared AC was evaluated using Biot number.

Subsidence estimation of breakwater built on loosely deposited sandy seabed foundation: Elastic model or elasto-plastic model

  • Shen, Jianhua;Wu, Huaicheng;Zhang, Yuting
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.9 no.4
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    • pp.418-428
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    • 2017
  • In offshore area, newly deposited Quaternary loose seabed soils are widely distributed. There are a great number of offshore structures has been built on them in the past, or will be built on them in the future due to the fact that there would be no very dense seabed soil foundation could be chosen at planed sites sometimes. However, loosely deposited seabed foundation would bring great risk to the service ability of offshore structures after construction. Currently, the understanding on wave-induced liquefaction mechanism in loose seabed foundation has been greatly improved; however, the recognition on the consolidation characteristics and settlement estimation of loose seabed foundation under offshore structures is still limited. In this study, taking a semi-coupled numerical model FSSI-CAS 2D as the tool, the consolidation and settlement of loosely deposited sandy seabed foundation under an offshore breakwater is investigated. The advanced soil constitutive model Pastor-Zienkiewics Mark III (PZIII) is used to describe the quasi-static behavior of loose sandy seabed soil. The computational results show that PZIII model is capable of being used for settlement estimation problem of loosely deposited sandy seabed foundation. For loose sandy seabed foundation, elastic deformation is the dominant component in consolidation process. It is suggested that general elastic model is acceptable for subsidence estimation of offshore structures on loose seabed foundation; however, Young's modulus E must be dependent on the confining effective stress, rather than a constant in computation.

Characteristics of Microwave-Assisted Drying of Plant Cells of Taxus chinensis for Moisture Removal (수분 제거를 위한 식물세포 Taxus chinensis의 마이크로웨이브를 이용한 건조 특성)

  • Nam, Hyeon-Woo;Kim, Jin-Hyun
    • Applied Chemistry for Engineering
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    • v.31 no.2
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    • pp.208-214
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    • 2020
  • In this study, the characteristics and mechanism of microwave-assisted drying were investigated to improve the efficiency of the storage and extraction of biomass through the removal of moisture from plant cell Taxus chinensis. The efficiency of microwave-assisted drying increased with increasing microwave power. When the experimental data were fitted to typical drying kinetic models, the page and modified Page models were the most appropriate. The microwave-assisted drying was determined to be a spontaneous endothermic process, and randomness increased during the drying process. The effective diffusion coefficient (3.445 × 10-9~7.163 × 10-7 ㎡/s) and mass transfer coefficient (3.1529 × 10-5~1.2895 × 10-2 m/s) increased with increasing microwave power. The small Biot number (0.3890~0.7198) indicated that the mass transfer process was externally controlled.

Effects of macroporosity and double porosity on noise control of acoustic cavity

  • Sujatha, C.;Kore, Shantanu S.
    • Advances in aircraft and spacecraft science
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    • v.3 no.3
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    • pp.351-366
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    • 2016
  • Macroperforations improve the sound absorption performance of porous materials in acoustic cavities and in waveguides. In an acoustic cavity, enhanced noise reduction is achieved using porous materials having macroperforations. Double porosity materials are obtained by filling these macroperforations with different poroelastic materials having distinct physical properties. The locations of macroperforations in porous layers can be chosen based on cavity mode shapes. In this paper, the effect of variation of macroporosity and double porosity in porous materials on noise reduction in an acoustic cavity is presented. This analysis is done keeping each perforation size constant. Macroporosity of a porous material is the fraction of area covered by macro holes over the entire porous layer. The number of macroperforations decides macroporosity value. The system under investigation is an acoustic cavity having a layer of poroelastic material rigidly attached on one side and excited by an internal point source. The overall sound pressure level (SPL) inside the cavity coupled with porous layer is calculated using mixed displacement-pressure finite element formulation based on Biot-Allard theory. A 32 node, cubic polynomial brick element is used for discretization of both the cavity and the porous layer. The overall SPL in the cavity lined with porous layer is calculated for various macroporosities ranging from 0.05 to 0.4. The results show that variation in macroporosity of the porous layer affects the overall SPL inside the cavity. This variation in macroporosity is based on the cavity mode shapes. The optimum range of macroporosities in poroelastic layer is determined from this analysis. Next, SPL is calculated considering periodic and nodal line based optimum macroporosity. The corresponding results show that locations of macroperforations based on mode shapes of the acoustic cavity yield better noise reduction compared to those based on nodal lines or periodic macroperforations in poroelastic material layer. Finally, the effectiveness of double porosity materials in terms of overall sound pressure level, compared to equivolume double layer poroelastic materials is investigated; for this the double porosity material is obtained by filling the macroperforations based on mode shapes of the acoustic cavity.