• 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.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.158-166
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• 2006

Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

• 대한기계학회논문집B
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• 제20권12호
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• pp.3991-4002
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• 1996

Thermally fully developed and thermally developing laminar flows of a Bingham plastic in a circular pipe have been studied analytically. For thermally fully developed flow, the Nusselt numbers and temperature profiles are presented in terms of the yield stress and Peclet number, proposing a correlation formula between the Nusselt number and the Peclet number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet and Brinkman numbers on the Nusselt number are discussed.

• 유변학
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• 제7권1호
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• pp.35-41
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• 1995

층류 열전달에서 작은 Reynolds number에서의 원통내의 흐름에대한 Power law 유 체의 해법이 사용될 수가 없는 것을 낮은 전단률(Shear Rate)에서 Power Law 법칙이 적용 되지 않기 때문이다. 본 연구에서는 이문제를 새로운 구성방정식을 이용하여 높은 전단률에 서는 Power Law 법칙이 낮은 전단률에서는 Newtonian 법칙이 그 중간에서는 천이과정을 모두 포함하는 전범위의 전단률에 대해 해결하였다. 이러한 구성방정식의 기본개졈은 실험 결과와도 잘 일치하였따. 이 구성방정식을 이용하여 Graetz 문제를 해결하였고 경계조건은 일정온도와 일정열속이다. 이용하기 쉬운 전단률변수는 적용범위가 Newtonian인지 Power law 인지 아니면 중간 천이과정인지를 나타내준다.

• Membrane and Water Treatment
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• 제8권1호
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• pp.35-50
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• 2017

The theoretical membrane gas absorption module treatments in a hollow fiber gas-liquid membrane contactor using Happel's free surface model were obtained under countercurrent-flow operations. The analytical solutions were obtained using the separated variable method with an orthogonal expansion technique extended in power series. The $CO_2$ concentration in the liquid absorbent, total absorption rate and absorption efficiency were calculated theoretically and experimentally with the liquid absorbent flow rate, gas feed flow rate and initial $CO_2$ concentration in the gas feed as parameters. The improvements in device performance under countercurrent-flow operations to increase the absorption efficiency in a carbon dioxide and nitrogen gas feed mixture using a pure water liquid absorbent were achieved and compared with those in the concurrent-flow operation. Both good qualitative and quantitative agreements were achieved between the experimental results and theoretical predictions for countercurrent flow in a hollow fiber gas-liquid membrane contactor with accuracy of $6.62{\times}10^{-2}{\leq}E{\leq}8.98{\times}10^{-2}$.

• 대한기계학회논문집B
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• 제20권12호
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• pp.4003-4012
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• 1996

Hydro dynamically developing and simultaneously (hydro dynamically and thermally) developing laminar flows of a Bingham plastic in a circular pipe have been investigated numerically. Solutions have been obtained by using a four-step fractional method combined with an equal order bilinear finite element method. For the hydro dynamically developing flow, shorter entrance length is required to reach fully developed velocity field for larger yield stress and non-monotonic pressure drop along the pipe centerline is observed when the yield stress exceeds a certain critical value. For the simultaneously developing flow, the heat transfer characteristics show the same trends as those predicted for the thermally developing flow (Graetz problem).