• Journal of Magnetics
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• v.21 no.3
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• pp.468-475
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• 2016

In this article, entropy generation on MHD Williamson nanofluid over a porous shrinking sheet has been analyzed. Nonlinear thermal radiation and chemical reaction effects are also taken into account with the help of energy and concentration equation. The fluid is electrically conducting by an external applied magnetic field while the induced magnetic field is assumed to be negligible due to small magnetic Reynolds number. The governing equations are first converted into the dimensionless expression with the help of similarity transformation variables. The solution of the highly nonlinear coupled ordinary differential equation has been obtained with the combination of Successive linearization method (SLM) and Chebyshev spectral collocation method. Influence of all the emerging parameters on entropy profile, temperature profile and concentration profile are plotted and discussed. Nusselt number and Sherwood number are also computed and analyzed. It is observed that entropy profile increases for all the physical parameters. Moreover, it is found that when the fluid depicts non-Newtonian (Williamson fluid) behavior then it causes reduction in the velocity of fluid, however, non-Newtonian behavior enhances the temperature and nanoparticle concentration profile.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1152-1157
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• 2004

Temporal behavior of the laser induced incandescence (LII) signal is often used for soot particle sizing, which is possible because the cooling behavior of a laser heated particle is dependent on the particle size. In present study, LII signals of soot particles are modeled using two non-linear coupled differential equations deduced from the energy- and mass-balance of the process. The objective of this study is to see the effects of particle size, laser fluence on soot temperature characteristics and cooling behavior. Together with this, we focus on validating our simulation code by comparing with other previous results. Results of normalized LII signals obtained from various laser fluence conditions showed a good agreement with that of Dalzell and Sarofim's. It could be found that small particles cool faster at a constant laser fluence. And it also could be observed that vaporization is dominant process of heat loss during first 100ns after laser pulse, then heat conduction played most important role while thermal radiation had little influence all the time.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.256-263
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• 2008

The assumed modes method is developed to derive a set of linear differential equations describing the motion of a flexible wind turbine blade and to propose an approach to investigate the forced responses result from various wind excitations. In this work, we have adopted Euler beam theory and considered that the root of the blade is clamped at the rigid hub. And the aerodynamic parameters and forces are determined based on Blade Element Momentum (BEM) theory and quasi-steady airfoil aerodynamics. Numerical calculations show that this method gives good results and it can be used fur modeling and the forced vibration analysis including the coupling effect of wind-turbine blades, as well as turbo-machinery blades, aircraft propellers or helicopter rotor blades which may be considered as straight non-uniform beams with built-in pre-twist.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Macromolecular Research
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• v.14 no.2
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• pp.155-165
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• 2006

The present article describes the experimental and theoretical observations on the formation of holographic, polymer-dispersed, liquid crystals and electrically switchable, photonic crystals. A phase diagram of the starting mixture of nematic liquid crystal and photo-reactive triacrylate monomer was established by means of differential scanning calorimetry (DSC) and cloud point measurement. Photolithographic patterns were imprinted on the starting mixture of LC/triacrylate via multi-beam interference. A similar study was extended to a dendrimer/photocurative mixture as well as to a single component system (tetra-acrylate). Theoretical modeling and numerical simulation were carried out based on the combination of Flory-Huggins free energy of mixing and Maier-Saupe free energy of nematic ordering. The combined free energy densities were incorporated into the time-dependent Ginzburg-Landau (Model C) equations coupled with the photopolymerization rate equation to elucidate the spatio-temporal structure growth. The 2-D photonic structures thus simulated were consistent with the experimental observations. Furthermore, 3-D simulation was performed to guide the fabrication of assorted photonic crystals under various beam-geometries. Electro-optical performance such as diffraction efficiency was evaluated during the pattern photopolymerization process and also as a function of driving voltage.

• Computational Structural Engineering
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• v.10 no.3
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• pp.185-193
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• 1997

The order of the stress singularity that occurs at the termination of an interface between materials exhibiting bilinear stress-strain response under plane strain conditions has been calculated, The governing equation of elasticity together with traction-free boundary condition and interface continuity condition defines a two-point boundary value problem. The stress components near the free edge are assumed to be proportional to r/sup s-1/, with solutions existing only for certain values of s. Finding these values entails the solution of an eigenvalue problem. Because it has been impossible to integrate the differential equations analytically, the integration has been performed numerically with a shooting method coupled with a Newton improvement scheme.

• Journal of Mechanical Science and Technology
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• v.16 no.4
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• pp.512-521
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• 2002

The flap-lag-torsion coupled aeroelastic behavior of a hingeless rotor blade with composite flexures in hovering flight has been investigated by using the finite element method. The quasisteady strip theory with dynamic inflow effects is used to obtain the aerodynamic loads acting on the blade. The governing differential equations of motion undergoing moderately large displacements and rotations are derived using the Hamilton's principle. The flexures used in the present model are composed of two composite plates which are rigidly attached together. The lead-lag flexure is located inboard of the flap flexure. A mixed warping model that combines the St. Versant torsion and the Vlasov torsion is developed to describe the twist behavior of the composite flexure. Numerical simulations are carried out to correlate the present results with experimental test data and also to identify the effects of structural couplings of the composite flexures on the aeroelastic stability of the blade. The prediction results agree well with other experimental data. The effects of elastic couplings such as pitch-flap, pitch-lag, and flap-lag couplings on the stability behavior of the composite blades are also investigated.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.985-1000
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• 2010

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.7
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• pp.521-528
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• 2007

The desiccant rotor is the most essential component of desiccant cooling system, but its design relies on manufacturer's experience and principles are not yet clear in spite of a lot of theoretical/experimental work published. The mathematical modeling of desiccant rotor needs solution of coupled partial differential equations of heat and mass transfer. In this study, numerical program is developed and validated using a real desiccant rotor. The calculation results are in reasonable agreement with the experimental data and other available numerical results. Optimization of desiccant rotor on the condition of low regeneration temperature are investigated. The optimal rotor speed at which the process outlet humidity becomes minimized, shows same as that of the system optimization. Compared to high regeneration temperature, broad is the range of optimal speed of low regeneration temperature. Systematic analysis on the optimal area ratio of regeneration to dehumidification section has also been conducted.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.719-742
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• 2015

This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.