• Journal of Advanced Marine Engineering and Technology
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• v.31 no.3
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• pp.272-281
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• 2007

A numerical simulation on nitrogen gas flow in a long parallel plate microchannel was performed to obtain the effect of compressibility and rarefaction on gaseous flow in microchannels. The simulation was based on steady. two dimensional compressible Navier-Stokes and energy equations with noslip and first order slip boundary conditions. The channel was $1.2{\mu}m$ deep and $3000{\mu}m$ long. The Reynolds numbers were in the range of order from $10^{-2}$ to $10^{-1}$. So the flow was assumed to be laminar. The computations were performed on various pressure ratios. The outlet pressure was fixed to atmospheric pressure. The outlet Knudsen number was 0.0585, consequently the flow was in the slip flow regime. The computations were performed with the assumption of isothermal channel walls. The results were compared with the experimental data. The agreement was good.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.103-119
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• 2020

In this work, the hydromagnetic and thermal characteristics of natural convection flow in a vertical parallel plate micro-porous-channel with suction/injection is analytically studied in the presence of Hall current by taking the temperature jump and the velocity slip at the wall into account. The governing equations, exhibiting the physics of the flow formation are displayed and the exact analytical solutions have been obtained for momentum and energy equations under relevant boundary conditions. The impact of distinct admissible parameters such as Hartmann number, Hall current parameter, permeability parameter, suction/injection parameter, fluid wall interaction parameter, Knudsen number and wall-ambient temperature ratio on the flow formation is discussed with the aid of line graphs. In particular, as rarefaction parameter on the micro-porous-channel surfaces increases, the fluid velocity increases and the volume flow rate decreases for injection/suction.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.228-233
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• 2005

Two-dimensional Stokes flows through a micro channel with a couple of symmetric vertical fins are investigated. At far up- and down-stream from the fins, the plane Poiseuille flow exists in the channel. The slip boundary conditions are applied to take account of the Knudsen number effects. For the analysis, the method of eigen function expansion and collocation method are employed. By the results, the streamline patterns and pressure distributions are shown and the force exerted on the fin and the excess pressure drop due to the fins are determined as functions of the length of the fin and Knudsen number. It may be conjectured that the force and the excess pressure drop are almost independent of the Knudsen number.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.323-351
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• 2021

The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes' [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy's law. In this study, matching conditions were used at the fluid-fluid interface, whereas the B-J slip boundary condition was employed at the fluid-porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.

• Steel and Composite Structures
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• v.20 no.5
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• pp.1023-1042
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• 2016

Based on Hamilton's principle, the flexural vibration differential equations and boundary conditions of the steel-concrete composite beam (SCCB) with comprehensive consideration of the influences of the shear deformation, interface slip and longitudinal inertia of motion were derived. The analytical natural frequencies of flexural vibration were compared with available results previously observed by the experiments, the results calculated by the FE model and the other similar beam theories available in the open literatures. The comparison results showed that, the calculation results of the analytical and Timoshenko models had a good agreement with the results of the experimental test and FE model. Finally, the influences of shear deformation and interface slip on the flexural natural frequencies of the SCCB were discussed. The shear deformation effect increases with the increase of the mode orders of flexural natural vibration, and the flexural natural frequencies of the higher mode orders ignoring the influence of shear deformations effect would be overestimated. The interface slip effect decrease with the increase of the mode orders of flexural natural vibration, and the influence of the interface slip effect on flexural natural frequencies of the low mode orders is significant. The influence of the degree of shear connection on shear deformation effect is insignificant, and the low order modes of flexural natural vibration are mainly composed of the rotational displacement of cross sections.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.625-630
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• 2000

Numerical and experimental investigations are peformed for the rarefied gas flows in pumping channels of a helical-type drag pump. Modern turbomolecular pumps include a drag stage in the discharge side, operating roughly in $10^{-2}{\sim}10Torr$. The flow occurring in the pumping channel develops from the molecular transition to slip flow traveling downstream. Two different numerical methods are used in this analysis: the first one is a continuum approach in solving the Navier-Stokes equations with slip boundary conditions, and the second one is a stochastic particle approach through the use of the direct simulation Monte Carlo(DSMC) method. The flow in a pumping channel is three-dimensional(3D), and the main difficulty in modeling a 3D case comes from the rotating frame of reference. Thus, trajectories of particles are no longer straight lines. In the Present DSMC method, trajectories of particles are calculated by integrating a system of differential equations including the Coriolis and centrifugal forces. Our study is the first instance to analyze the rarefied gas flows in rotating frame in the presence of noninertial effects.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.4
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• pp.333-354
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• 2016

The present investigation deals, heat and mass transfer characteristics with the effect of slip on the hydromagnetic pulsatile flow through a parallel plate channel filled with saturated porous medium. Based on the pulsatile flow nature, exact solution of the governing equations for the fluid velocity, temperature and concentration are obtained by using two term perturbation technique subject to physically appropriate boundary conditions. The expressions of skin friction, Nusselt number and Sherwood number are also derived. The numerical values of the fluid velocity, temperature and concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. By increasing the slip parameter at the cold wall the velocity increases whereas the effect is totally reversed in the case of shear stress at the cold wall.

• Tunnel and Underground Space
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• v.32 no.6
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• pp.598-610
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• 2022

Avoiding a fault zone would be a best practice for safety in underground construction, which is only sometimes possible because of many restrictions and other field conditions. For instance, there is an ongoing conception of Korea-Japan subsea tunnels that inevitably cross a massive fault system in the Korea Strait. Therefore it was deemed necessary to find an efficient way of predicting the likely behaviour of underground structures under fault slip. This paper presents the findings from simple numerical analysis for investigating the stress induced at a normal fault with a dip of 45 degrees. We used a boundary element software that assumed constant displacement discontinuity, which allowed the displacement to be estimated separately at both the fault's hangingwall and footwall sides. The results suggested that a principal stress rotation of 45 degrees occurred at the edges of the fault during the slip, which was in agreement with the phenomenon for fault plane suggested in the body of literature. A simple numerical procedure presented in this paper could be adopted to investigate other fault-related issues associated with underground structure construction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.3
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• pp.511-518
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• 1997

The technique of fretting fatigue test was developed and fretting fatigue tests of A12024-T4 were conducted under several conditions. The newly developed calibration methods for measuring surface contact tractions showed good linearity and repeatability. The plate type specimen to which tow bridge type pads were attached and vision system was used to observe the crack behaviour. The oblieque cracks appeared in the early stage of crack growth and they became mode I cracks as they grow about 1 mm. The mode I transition points were found to be longer when surface tractions are higher or bulk stress is lower. Before the crack becomes mode I crack, 'well point' where crack grow about rate is minimum, was detected under every experimental condition. The crack behaviour was found to be affected by surface tractions, contact area, bulk stress. It was also found that partial slip and stick condition is most detrimental and the crack starts from the boundary of stick and slip. For gross slip crack started at the outside edge of pad. After crack mode transition, fretting fatigue cracks showed almost same behaviour of plain mode I fatigue cracks. Equivalent stress intensity factor was used to analyze the behaviour of fretting fatigue cracks and it was found that stress intensity factors can be applied to fretting fatigue cracks.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.89-107
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• 2017

In this paper, we have proposed a modified Marker-And-Cell (MAC) method to investigate the problem of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers with no-slip and slip boundary conditions. We have used this method to solve the governing equations along with the boundary conditions and thereby to compute the flow variables, viz. u-velocity, v-velocity, P, T, and C. We have used the staggered grid approach of this method to discretize the governing equations of the problem. A modified MAC algorithm was proposed and used to compute the numerical solutions of the flow variables for Reynolds numbers Re = 10, 500, and 50000 in consonance with low, moderate, and high Reynolds numbers. We have also used appropriate Prandtl (Pr) and Schmidt (Sc) numbers in consistence with relevancy of the physical problem considered. We have executed this modified MAC algorithm with the aid of a computer program developed and run in C compiler. We have also computed numerical solutions of local Nusselt (Nu) and Sherwood (Sh) numbers along the horizontal line through the geometric center at low, moderate, and high Reynolds numbers for fixed Pr = 6.62 and Sc = 340 for two grid systems at time t = 0.0001s. Our numerical solutions for u and v velocities along the vertical and horizontal line through the geometric center of the square cavity for Re = 100 has been compared with benchmark solutions available in the literature and it has been found that they are in good agreement. The present numerical results indicate that, as we move along the horizontal line through the geometric center of the domain, we observed that, the heat and mass transfer decreases up to the geometric center. It, then, increases symmetrically.