• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.513-527
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• 2011

The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.3
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• pp.176-183
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• 1991

In this paper. boundary element method is applied to the analysis of nonlinear free surface wave. A particular concern is given to the treatment of the open boundaries at the in-flow boundary and out-flow boundary, which uses the mass-flux and energy-flux considering the continuity of fluid. By assuming the fluid to be inviscid and incompressible and the flow to be irrotational. the problem is formulated mathematically as a two-dimentional nonlinear problem in terms of a velocity potential. The equation(Laplace equation) and the boundary conditions are transformed into two boundary integral equations. Due to the nonlinearity of the problem. the incremental method is used for the numerical analysis. Numerical results obtained by the present boundary element method are compared with those obtained by the finite element method and also with experimental values.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.287-308
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• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

• International Journal of Naval Architecture and Ocean Engineering
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• v.9 no.6
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• pp.598-612
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• 2017

The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance the accuracy. Moreover, fixed mesh algorithm with free surface immersed is developed to improve the computational efficiency. Finally, a two dimensional (2D) multi-block strategy coupling boundary-fitted mesh and fixed mesh is proposed. It limits the computational costs and preserves the accuracy. A fully nonlinear 2D numerical wave tank is developed using the improved HPC method as a verification.

• 한국초전도학회:학술대회논문집
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• v.14
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• pp.33-33
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• 2004

• Advances in nano research
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• v.10 no.3
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• pp.221-234
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• 2021

During the previous few years, phenomenon of bioconvection along with the use of nanoparticles showed large number of applications in technological and industrial field. This paper analyzed the bioconvection phenomenon in magnetohydrodynamic boundary layer flow of a Powell-Eyring nanoliquid past a stretchable cylinder with Cattaneo-Christov heat flux. In addition, the impacts of chemical reaction and heat generation/absorption parameter are considered. By the use of appropriate transformation, the governing PDEs (nonlinear) have been transformed and formulated into nonlinear ODEs. The resulting nonlinear ODEs subjected to relevant boundary conditions are solved analytically through homotopy analysis method which is programmed in Mathematica software. Graphical and numerical results versus physical quantities like velocity, temperature, concentration and motile microorganism are investigated under the impact of physical parameters. It is noted that velocity profile enhances as the curvature parameter A and Eyring-Powell fluid parameter M increases but a decline manner for large values of buoyancy ratio parameter Nr and bio-convection Rayleigh number Rb. In the presence of Prandtl number Pr, Eyring-Powell fluid parameter M and heat absorption parameter ��, temperature profile decreases. Nano particle concentration profile increases for increasing values of magnetic parameter Ha and thermophoresis parameter Nt. The motile density profile has revealed a decrement pattern for higher values of bio-convection Lewis number Lb and bio-convection peclet number Pe. This study may find uses in bio-nano coolant systems, advance nanomechanical bio-convection energy conversion equipment's, etc.

• Steel and Composite Structures
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• v.38 no.5
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• pp.523-531
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• 2021

The generalized thermoelastic analysis problem of a two-dimension porous medium with and without energy dissipation are obtained in the context of Green-Naghdi's (GNIII) model. The exact solutions are presented to obtain the studying fields due to the pulse heat flux that decay exponentially in the surface of porous media. By using Laplace and Fourier transform with the eigenvalues scheme, the physical quantities are analytically presented. The surface is shocked by thermal (pulse heat flux problems) and applying the traction free on its outer surfaces (mechanical boundary) through transport (diffusion) process of temperature to observe the analytical complete expression of the main physical fields. The change in volume fraction field, the variations of the displacement components, temperature and the components of stress are graphically presented. Suitable discussion and conclusions are presented.

• Steel and Composite Structures
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• v.10 no.2
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• pp.129-149
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• 2010

The objective of this study is to formulate a general 3D material-structural analysis framework for the thermomechanical behavior of steel-concrete structures in a fire environment. The proposed analysis framework consists of three sequential modeling parts: fire dynamics simulation, heat transfer analysis, and a thermomechanical stress analysis of the structure. The first modeling part consists of applying the NIST (National Institute of Standards and Technology) Fire Dynamics Simulator (FDS) where coupled CFD (Computational Fluid Dynamics) with thermodynamics are combined to realistically model the fire progression within the steel-concrete structure. The goal is to generate the spatial-temporal (ST) solution variables (temperature, heat flux) on the surfaces of the structure. The FDS-ST solutions are generated in a discrete form. Continuous FDS-ST approximations are then developed to represent the temperature or heat-flux at any given time or point within the structure. An extensive numerical study is carried out to examine the best ST approximation functions that strike a balance between accuracy and simplicity. The second modeling part consists of a finite-element (FE) transient heat analysis of the structure using the continuous FDS-ST surface variables as prescribed thermal boundary conditions. The third modeling part is a thermomechanical FE structural analysis using both nonlinear material and geometry. The temperature history from the second modeling part is used at all nodal points. The ABAQUS (2003) FE code is used with external user subroutines for the second and third simulation parts in order to describe the specific heat temperature nonlinear dependency that drastically affects the transient thermal solution especially for concrete materials. User subroutines are also developed to apply the continuous FDS-ST surface nodal boundary conditions in the transient heat FE analysis. The proposed modeling framework is applied to predict the temperature and deflection of the well-documented third Cardington fire test.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.39-61
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• 2017

In this present article, we analyzed the heat and mass transfer characteristics of the nonlinear unsteady radiative MHD flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate under the influence of Soret and chemical reaction effects. The effect of physical parameters are accounted for two distinct types of thermal boundary conditions namely prescribed uniform wall temperature thermal boundary condition and prescribed heat flux thermal boundary condition. Based on the flow nature, the dimensionless flow governing equations are resolved to harmonic and non harmonic parts. In particular skin friction coefficient, Nusselt number and Sherwood number are found to evolve into their steady state case in the large time limit. Parametric study of the solutions are conducted and discussed.

• 전기의세계
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• v.30 no.4
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• pp.219-226
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• 1981

The magnetic field distribution in saturable iron part of electromagnetic energy conversion divices is defined by the nonlinear quasi-Poisson enquation that is described the electromagnetic field characteristics and satisfied the natural boundary condition. The solution of this equation is obtained by minimizing an energy functional by means of trial function that defined in triangular subregion of two-dimensional field region. As a result, the accuracy of the machine design is increased by use of its solution. In this respect, this study is developed the basic theory to analyze the magnetic flux distribution in saturable iron part and air gap of induction motor that its secondary part is short circuit by the variational principle, the minimized theory of energy functional, the application of F.E.M., and treatment of computer. As theoritical data compared with the practics, the validity of the theory in this study is supported by experimental findings.