• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.299-318
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• 2023

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.10
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• pp.3371-3380
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• 1996

Low resolution spectral modeling of water vapor is carried out by applying the weighted-sum-of-gray-gases model (WSGGM) to a narrow band. For a given narrow band, focus is placed on proper modeling of gray gas absorption coefficients vs. temeprature relation used for any solution methods for the Radiative Transfer Equation(RTE). Comparison between the modeled emissivity and the "true" emissivity obtained from a high temperatue statistical narrow band parameters is made ofr the total spectrum as well as for a few typical narrow bands. Application of the model to nonuniform gas layers is also made. Low resolution spectral intensities at the boundary are obtained for uniform, parabolic and boundary layer type temeprature profiles using the obtained for uniform, parabolic and boundary layer type temperature profiles using the obtained WSGGM's with 9 gray gases. The results are compared with the narrow band spectral intensities as obtained by a narrow band model-based code with the Curtis-Godson approximation. Good agreement is found between them. Local heat source strength and total wall heat flux are also compared for the cases of Kim et al, which again gives promising agreement.

• Journal of the Korean institute of surface engineering
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• v.40 no.1
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• pp.23-31
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• 2007

The objective of this study is to investigate the effect of Al addition on the reaction behavior of cobalt with molten zinc. Pure cobalt specimen was immersion tested in the three kinds of molten zinc (pure, 0.12%Al added and 0.24%Al added) baths at $460^{\circ}C,\;490^{\circ}C\;and\;520^{\circ}C$. For the understanding of degradation processes, specimens were analyzed with scanning electron microscope (SEM) and energy dispersive spectrum (EDS), and electrochemical stripping method. When 0.12% and 0.24% Al was added in molten zinc baths, three intermetallic compounds layers of ${\gamma},\;{\gamma}_1,\;and\;{\gamma}_2$ were formed on the Co matrix and ${\beta}_1$ layer was not formed between the Co matrix and the ${\gamma}$ layer. Particles of CoAl intermetallic compound were formed at the interface between the ${\gamma}_2$ layer and zinc melt and they did not adhere to the Co-Zn intermetallic layer. Weight loss of the Co specimen increased as Al content in the molten zinc increased and the relationship of weight loss vs. immersion time followed parabolic rate law. Rate controlling process for the reaction rate of Co with Al added molten zinc was analyzed as the diffusion process of Al atom through a boundary layer between the ${\gamma}_2$ layer and the Al added zinc melt.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.253-271
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• 2012

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of $w_{,n}$, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.247-269
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• 2020

A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

• Corrosion Science and Technology
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• v.12 no.2
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• pp.102-112
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• 2013

A very high-temperature gas reactor (VHTR) is one of the next generation nuclear reactors owing to its safety, high energy efficiency, and proliferation-resistance. Heat is transferred from the primary helium loop to the secondary helium loop through an intermediate heat exchanger (IHX). Under VHTR environment Alloy 617 is being considered a candidate Ni-based superalloy for the IHX of a VHTR, owing to its good creep resistance, phase stability and corrosion resistance at high temperature. In this study, high-temperature corrosion tests were carried out at 850 - $950^{\circ}C$ in air and impure helium environments. Alloy 617 specimens showed a parabolic oxidation behavior for all temperatures and environments. The activation energy for oxidation was 154 kJ/mol in helium environment, and 261 kJ/mol in an air environment. The scanning electron microscope (SEM) and energy-dispersive x-ray spectroscopy (EDS) results revealed that there were a Cr-rich surface oxide layer, Al-rich internal oxides and depletion of grain boundary carbide after corrosion test. The thickness and depths of degraded layers also showed a parabolic relationship with the time. A corrosion rate of $950^{\circ}C$ in impure helium was higher than that in an air environment, caused by difference in the outer oxide morphology.

• Korean Journal of Metals and Materials
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• v.50 no.9
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• pp.659-667
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• 2012

Alloy 617 is a Ni-base superalloy and a candidate material for the intermediate heat exchanger (IHX) of a very high temperature gas reactor (VHTR) which is one of the next generation nuclear reactors under development. The high operating temperature of VHTR enables various applications such as mass production of hydrogen with high energy efficiency. Alloy 617 has good creep resistance and phase stability at high temperatures in an air environment. However, it was reported that the mechanical properties decreased at a high temperature in an impure helium environment. In this study, high-temperature corrosion tests were carried out at $850^{\circ}C-950^{\circ}C$ in a helium environment containing the impurity gases $H_2$, CO, and $CH_4$, in order to examine the corrosion behavior of Alloy 617. Until 250 h, Alloy 617 specimens showed a parabolic oxidation behavior at all temperatures. The activation energy for oxidation in helium environment was 154 kJ/mol. The SEM and EDS results elucidated a Cr-rich surface oxide layer, Al-rich internal oxides and depletion of grain boundary carbides. The thickness and depths of degraded layers also showed a parabolic relationship with time. A normal grain growth was observed in the Cr-rich surface oxide layer. When corrosion tests were conducted in a pure helium environment, the oxidation was suppressed drastically. It was elucidated that minor impurity gases in the helium would have detrimental effects on the high-temperature corrosion behavior of Alloy 617 for the VHTR application.

• Journal of Powder Materials
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• v.28 no.2
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• pp.110-119
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• 2021

In this study, the high-temperature oxidation properties of austenitic 316L stainless steel manufactured by laser powder bed fusion (LPBF) is investigated and compared with conventional 316L manufactured by hot rolling (HR). The initial microstructure of LPBF-SS316L exhibits a molten pool ~100 ㎛ in size and grains grown along the building direction. Isotropic grains (~35 ㎛) are detected in the HR-SS316L. In high-temperature oxidation tests performed at 700℃ and 900℃, LPBF-SS316L demonstrates slightly superior high-temperature oxidation resistance compared to HR-SS316L. After the initial oxidation at 700℃, shown as an increase in weight, almost no further oxidation is observed for both materials. At 900℃, the oxidation weight displays a parabolic trend and both materials exhibit similar behavior. However, at 1100℃, LPBF-SS316L oxidizes in a parabolic manner, but HR-SS316L shows a breakaway oxidation behavior. The oxide layers of LPBF-SS316L and HR-SS316L are mainly composed of Cr₂O₃, Fe-based oxides, and spinel phases. In LPBF-SS316L, a uniform Cr depletion region is observed, whereas a Cr depletion region appears at the grain boundary in HR-SS316L. It is evident from the results that the microstructure and the high-temperature oxidation characteristics and behavior are related.