• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.31-40
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• 2009

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

• Earthquakes and Structures
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• 제10권1호
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• pp.91-104
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• 2016

In this paper we investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

• 대한기계학회논문집B
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• 제23권2호
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• 대한토목학회논문집
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• 제5권1호
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• pp.65-74
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• 1985

본(本) 연구(硏究)는 교각주변(橋脚周邊) 하상(河床)의 국부세굴(局部洗掘)에 관한 실험적(實驗的) 해석(解析)으로서 세굴(洗掘)에 관계되는 여러 요소를 차원해석(次元解析)에 의해 무차원화(無次元化)하여, 교각(橋脚) Reynolds 수(數)와 무차원(無次元) 난류강도(亂流强度)로 나타내는 관계식을 유도하였으며 자료 검정(檢定)을 통하여 다중회귀분석(多重回歸分析)으로 관계식의 계수(係數)를 구하였다. 영각(迎角)이 $20^{\circ}$를 전후(前後)한 구간(區間)에서는, 교각(橋脚) Reynolds 수(數)와 세굴량(洗掘量)은 정비례(正比例)에서 반비례(反比例)로 무차원(無次元) 난류강도(亂流强度)와 세굴량(洗掘量)은 반비례(反比例)에서 정비례(正比例)로 바뀌는 천이구역(遷移區域)이 존재(存在)하였다. 본(本) 연구(硏究)에서 제안(提案)한 교각주변(橋脚周邊)의 세굴폭(洗掘幅)과 세굴심(洗掘深)에 대(對)한 관계식을 국립건설연구소(國立建設硏究所) 자료(資料)로 검정(檢定)을 실시(實施)한 결과(結果) 잘 일치하고 있음을 알 수 있다.

• 한국전산유체공학회지
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• 제6권1호
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• pp.21-30
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• 2001

A numerical study on the similarity of the developing laminar flows between in a straight duct rotating about an axis perpendicular to that of the duct and in a stationary curved duct was carried out. In order to clarify the analogy of two flows, dimensionless parameters K/sub LR/ = Re/(equation omitted) and Rossby number, Ro, in a rotating straight duct were used as a set corresponding to Dean number K/sub LC/ = Re/(equation omitted), and curvature ratio, λ, in a stationary curved duct. For the large values of Ro and λ, it is shown that the flow field satisfies the 'asymptotic invariance property', that is, there are strong quantitative similarities between the two flows such as flow patterns, friction factors, and maximum axial velocity magnitudes for the same values of K/sub LR/ and K/sub LC/ if they are correlated with dimensionless axial distances Z/sub R/ = z/(equation omitted) for a rotating duct flow and Z/sub C/ = z/(equation omitted) for a stationary curved duct flow.

• Structural Engineering and Mechanics
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• 제55권2호
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• 한국산학기술학회논문지
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• 제9권4호
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• pp.859-864
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• 2008

티모센포 회전축을 따라 이동하는 이동질량과의 동적상호작용에 관한 연구가 수행되었다. 이동질량의 속력이 티모센코축의 회전속도와 연계된 구속조건식을 도출하였다. 티모센코의 보 이론를 활용하여 시스템의 무차원방정식이 유도되었다. 이동질량의 속력을 포함하는 티모센코 축의 회전속도, 레일리히 계수, 축방향 압축력 등 다양한 무차원 변수들의 영향에 따른 회전축의 처짐과 주파수응답에 대한 해석이 수행되어졌다.

• 폴리머
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• 제29권6호
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• pp.549-556
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• 2005

단축압출기의 압출공정에서 고체수송부의 열전달 현상에 미치는 무차원수의 효과를 수치 해석적인 방법으로 연구하였다. 스크루의 기하학적 구조 및 특성에 따른 압출기 내에서의 고체 흐름 상태에 대한 이해를 바탕으로 고체 수송부에 대하여 열 수지 방정식을 세우고 무차원화하였다. 이에 유한체적법과 멱법칙 도식을 적용하여 이산화 방정식을 유도한 다음 반복 대입법과 완화법으로 해를 구하였다. 고체수송부의 열전달 특성을 규정하는 무차원수인 Biot 수와 Peclet 수가 수지 공급부의 온도와 고체수송부의 길이에 끼치는 영향을 조사하였다. Biot 수가 증가하면 냉각에 의한 열 손실이 지배하여 배럴의 온도는 급격히 감소하지만 고체층의 온도와 고체수송부의 길이에 미치는 영향은 적으며, Peclet 수가 증가하면 대류 항이 지배하여 고체층의 온도가 감소하고 고체수송부의 길이가 증가한다.

• Steel and Composite Structures
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• 제49권3호
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• pp.325-335
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• 2023

The missile is affected by both spinning and axial motion during its movement, which will have a very adverse impact on the stability and reliability of the missile. This paper regards missiles as cylindrical shell structures with spinning and axial motion. In this article, the forced vibration of carbon nanotube-reinforced composites (CNTRCs) cylindrical shells with spinning motion and axial motion is investigated, in which the clamped-clamped and simply-simply supported boundary conditions are considered. The displacement field is described by the first-order shear theory, and the vibration equation is deduced by using the Euler-Lagrange equation, after dimensionless processing, the dimensionless equation of motion is obtained. The correctness of this paper is verified by comparing with the results of the existing literature, in which the simply-simply supported ends are taken into account. In the end, the effects of different parameters such as spinning velocity, axial velocity, carbon nanotube volume fraction, length thickness ratio and load position on the resonance behavior of cylindrical shells are given. It can be found that these parameters can significantly change the resonance of axially moving and rotating moving CNTRCs cylindrical shells.

• 한국식품과학회지
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• 제35권4호
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• pp.738-742
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• 2003

로즈마리의 주요 항기 성분인 pinene, myrcene, cineol이 에탄올 용액에 흡수되는 물질전달 현상을 이해하기 위해 에탄올 농도에 따른 가스상 향기성분의 농도와 70% 에탄올 농도에서의 무차원 헨리상수를 구하였다. 에탄올 농도에 따른 가스상의 농도를 측정한 결과 3가지 화합물 모두 에탄올 농도가 증가함에 따라 headspace 농도가 감소하는 경향을 나타내었으나 화합물의 종류에 따라 다른 유형을 나타내었다. Cineol의 에탄올 농도(x)에 따른 무차원 헨리상수식은 $Hi=(-5.75+x)/(-7017.6+257.3{\times}x)$이며 1 atm, $25^{\circ}C$, 70% 에탄올 용액에서 무차원 헨리상수는 cineol은 0.0058, myrcene은 0.0182, pinene은 0.0365 이었다.