• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.4
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• pp.609-620
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• 1992

A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing (R.T.P) is obtained, and an analysis of onset and propagation of slip is performed and compared with experiment. In order to calculate temperature distribution of a wafer in R.T.P system, heat conduction equation that incorporated with radiative and convective heat transfer model is solved, and the solution of the equation is calculated numerically using alternating direction implicit (A.D.I) method. In dealing with radiative heat transfer, a partially transparent body that absorbs the radiation energy is assumed and this transparent body undergoes multiple internal reflections and absorptions. Two dimensional (assuming plane stress) thermoelastic constitutive equation is used to calculate thermal stress induced in a wafer and finite element method is employed to solve the equation numerically. The stress resolved in the slip directions on the slip planes of silicon is compared with the yield stress of silicon in order to predict the slip. The result of the analysis shows that the wafer temperature at which slip occurs is affected by the heating rate of the R.T.P system. It is observed that once slip occurs in the wafer, the slip grows.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.249-252
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• 2002

The change of critical current with a crack formation in a Bi-2223/Ag tape was studied by experimental and numerical analyses. Critical current of Bi-2223/Ag tape was measured with a continuous DC-power supply. The current-voltage relation of a Bi-2223/Ag tape is measured by the four point method. Numerical method is used to solve two dimensional heat conduction equation. By comparing the experimental and numerical results, the validity of numerical method is verified.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.245-248
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• 2002

One dimensional conduction equation is solved by finite difference method, to analyse the stability of Au/YBCO film deposited on a sapphire substrate. Jolue heat is included in the case of current sharing state. The analysis shows the quench and recovery of superconductor depending on the amount of thermal disturbance release on the center surface of superconductor. The critical disturbance energies for different filling factor and operating current are calculated.

• Progress in Superconductivity and Cryogenics
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• v.4 no.1
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• pp.73-77
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• 2002

The variation of critical current by the formation of crack in a high temperature super-conducting tape was studied by experimental and numerical analyses. The current-voltage relation of HTS tape is measured by the four-point measurement method. Numerical analyses are used to solve two dimensional heat conduction equation, considering the temperature distribution. By comparing current-voltage relation of experimental and numerical results, the validity of numerical method is verified.

• Progress in Superconductivity and Cryogenics
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• v.4 no.2
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• pp.27-30
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• 2002

One dimensional conduction equation is solved by finite difference method, to analyse the stability of Au/YBCO film deposited on a sapphire substrate. Joule heat is included in the case of current sharing state. The analysis shows the quench and recovery of superconductor depending on the amount of thermal disturbance release on the center surface of superconductor. The critical disturbance energies for different filling factor and operating current are calculated.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.341-349
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• 1997

The characteristics of defect correction method are discussed in a sample heat conduction problem showing the numerical solution of the error correction equation can predict the error of the numerical solution of the original governing equation. A way of using defect correction method combined with the existing algorithm for the incompressible fluid flow, is proposed and subsequently tested for the driven square cavity problem. The error correction equations for the continuity equation and the momentum equations are considered to estimate the errors of the numerical solutions of the original governing equations. With this new approach, better velocity and pressure fields can be obtained by correcting the original numerical solutions using the estimated errors. These calculated errors also can be used to estimate the orders of magnitude of the errors of the original numerical solutions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.10 s.253
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• pp.942-949
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• 2006

A lumped model is proposed to predict liquid ejection characteristics of a thermally driven inkjet print head. The model is based on a two-dimensional heat conduction equation, an empirical pressure-temperature equation and a nonlinear hydraulic flow-pressure equation. It has been simulated through the construction of an equivalent R-C circuit, and subsequently analyzed using SIMULINK and a circuit simulation tool, PLECS. Using the model, heating and cooling characteristics of the head are predicted to be in agreement with the IR temperature measurements. The effects of the head geometry on the drop ejection are also analyzed using the nonlinear hydraulic model. The present model can be used as a design tool for a better design of thermal inkjet print heads.

• Structural Engineering and Mechanics
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• v.56 no.1
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• pp.137-156
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• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2173-2187
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• 2022

A 3D thermo-elasto-hydrodynamic model is developed to analyze the sealing performance of a notched mechanical seal applied in the reactor coolant pump. In the model, the generalized Reynolds equation, the energy equation coupled with notch heat balance equation, the heat conduction equations, and the deformation equations of the sealing rings are iteratively solved by the finite element method. The film pressure and temperature distribution are obtained, and the deformation of the sealing rings is revealed to study the mechanism of the notched mechanical seals. A parameterized study is conducted to analyze the sealing performance under different operating conditions. As a comparison, the sealing performance of non-notched seals is also studied. The results show that the hydrostatic effect is dominant in the load-carrying capacity of the fluid film due to the radial mechanical and thermal deformations. The notch can cool the fluid film and influence the thermal deformation of seal rings. The sealing performance is sensitive to the pressure difference, ambient temperature, and rotational speed. It is suggested to set the notches on the softer sealing rings to acquire the greater hydrodynamic effect. Compared with the non-notched, the notched end face holds a better lubrication performance, especially under lower rotational speed.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.