• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.17 no.4
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• pp.303-311
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• 2005

The problem of conjugate laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A simple and efficient numerical method is proposed for its solution. The interfacial temperature is obtained as a root of 3rd order polynomial for laminar film condensation, and it is presented as a function of the conjugate parameter. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Jacob number, $Ja^{\ast}$, defined by an overall temperature difference, a property ratio R and the conjugate parameter ${\zeta}$. The approximate solutions thus obtained reveal the effects of the conjugate parameter.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.3 s.246
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• pp.238-245
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• 2006

This paper proposes appropriate conjugate parameters and dimensionless temperatures to analysis the conjugate problem of heat conduction in solid wall coupled with laminar film condensation flow adjacent to horizontal flat plate. An efficient methods for some fluids are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, $Ja^*/Pr$, defined by an overall temperature difference, a property ratio $\sqrt{\rho_l{\mu}_l/{\rho_v{\mu}_v}$ and the conjugate parameter $\zeta$. The obtained similarity solution reveals the effect of the conjugate parameter, and the results are compared with the simplified solution. The variations of the heat transfer rates as well as the interface temperature and frictions along the plate are shown explicitly.

• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.5
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• pp.577-582
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• 2015

This paper is the fundamental study for the application of cold storage system to the transportation equipment by sea and land. This numerical study presents the solid-liquid phase change phenomenon of calcium chloride solution of 30wt %. The governing equations are 1-dimensional unsteady state heat transfer equations of $1^{st}$ order partial differential equations. This type of latent heat storage material is often usable in fishery vessel for controlling the temperature of container with constant condition. The governing equation was discretized with finite difference method and the program was composed with Mathcad program. The main parameters of this solution were the initial temperature of heat storage material, ambient temperature of cold air and the velocity of cold air. The data of boundary layer thickness becomes thin with the increasing of cold air flowing velocity and also the heat storage completion time become shorten.

• Korea-Australia Rheology Journal
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• v.21 no.1
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• pp.47-58
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• 2009

We have investigated the transient behavior of 1D fully developed Poiseuille viscoelastic flow under finite pressure gradient described by the Oldroyd-B and Leonov constitutive equations. For analysis we employ a simple $2^{nd}$ order discretization scheme such as central difference for space and the Crank-Nicolson for time approximation. For the analysis of the Oldroyd-B model, we also apply the analytical solution, which is obtained again in this work in terms of elementary solution procedure simpler than the previous one (Waters and King, 1970). Both models demonstrate qualitatively similar solutions, but their eventual steady flowrate exhibits noticeable difference due to the absence or presence of shear thinning behavior. In the inertialess flow, the flowrate instantaneously attains a large value corresponding to the Newtonian creeping flow and then decreases to its steady value when the applied pressure gradient is low. However with finite liquid density the flow field shows severe fluctuation even accompanying reversals of flow directions. As the assigned pressure gradient increases, the flowrate achieves its steady value significantly higher than its value during oscillations after quite long period of time. We have also illustrated comparison between 1D and 2D results and possible mechanism of complex 2D flow rearrangement employing a previous solution of [mite element computation. In addition, we discuss some mathematical points regarding missing boundary conditions in 2D modeling due to the change of the type of differential equations when varying from inertialess to inertial flow.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1303-1309
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• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.61-71
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• 1993

The stress waves generated by the mechanical energies by impact or the chemical energies by the explosions are transmitted through medium. The wave propagation process through medium is a very complicated procedure due to the reflections and refractions of the waves at the free surfaces and interfaces. In this study the pressure independent Von-Mises model is employed for the wave propagation analysis in the layered systems. Governing equations of this study are conservation equations of momentum and mass in Lagrangian coordinate system which is fixed to the material. Due to the shock-front which violates the continuity assumptions inherent in the differential equations numerical artificial viscosity is used to spread the shock front over several computational zones. These equations are solved by Finite Difference Method with discretized time and space coordinates. The associate normality flow rule as a plastic theory is implemented to find the plastic strains.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.21-33
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• 1992

Under the intense-impulsive loading, structures are subjected to the wide range of pressures at an instantaneous time. The constitutive laws capable to describe the material behavior under the extreme pressure as well as the low pressure are necessary for the analysis of the structural behavior under the intense -impulsive loadings. In this study, two plastic models, the pressure independent Von-Mises model and the pressure dependent Drucker-Prager model, are employed for the wave propagation analysis. Governing equations of this study are conservation equations of momentum and mass in Lagrangian coordinate system which is fixed to the material. Due to the shock-front which violates the continuity assumptions inherent in the differential equations numerical artificial viscosity is used to spread the shock front over several computational zones. These equations are solved by Finite Difference Method with discretized time and space coordinates. The associate normality flow rule as a plastic theory is implemented to find the plastic strains.

• Advances in nano research
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• v.16 no.5
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• pp.473-487
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• 2024

The current study employs the nonlocal Timoshenko beam (NTB) theory and von-Kármán's geometric nonlinearity to develop a non-classic beam model for evaluating the nonlinear free vibration of bi-directional functionally-graded (BFG) nanobeams. In order to avoid the stretching-bending coupling in the equations of motion, the problem is formulated based on the physical middle surface. The governing equations of motion and the relevant boundary conditions have been determined using Hamilton's principle, followed by discretization using the differential quadrature method (DQM). To determine the frequencies of nonlinear vibrations in the BFG nanobeams, a direct iterative algorithm is used for solving the discretized underlying equations. The model verification is conducted by making a comparison between the obtained results and benchmark results reported in prior studies. In the present work, the effects of amplitude ratio, nanobeam length, material distribution, nonlocality, and boundary conditions are examined on the nonlinear frequency of BFG nanobeams through a parametric study. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies for the same amplitude of the nonlinear oscillator. The study finds that the difference between the dimensionless linear frequency and the nonlinear frequency is smaller for CC nanobeams compared to SS nanobeams, particularly within the α range of 0 to 1.5, where the impact of geometric nonlinearity on CC nanobeams can be disregarded. Furthermore, the nonlinear frequency ratio exhibits an increasing trend as the parameter µ is incremented, with a diminishing dependency on nanobeam length (L). Additionally, it is established that as the nanobeam length increases, a critical point is reached at which a sharp rise in the nonlinear frequency ratio occurs, particularly within the nanobeam length range of 10 nm to 30 nm. These findings collectively contribute to a comprehensive understanding of the nonlinear vibration behavior of BFG nanobeams in relation to various parameters.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.274-281
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• 2002

Numerical analysis for the Bragg reflection due to a sinusoidally and a doubly-sinusoidally varying seabeds was performed by using a couple of ordinary differential equations derived from the Boussinesq equations. Incident waves are a train of cnoidal waves. The effects of the dispersion and shape of seabed were investigated. It is shown that the reflection of a sinusoidally varying seabed is enhanced by increasing the dispersion and the amplitude of a seabed. The reflection of waves over a doubly-sinusoidally varying seabed can also be enhanced by increasing the amplitude of seabed decreasing the difference of wave numbers of seabed components.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.