• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.13 no.1
• /
• pp.37-49
• /
• 2000

This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.2
• /
• pp.193-203
• /
• 1983

The mixed convective heat transfer problems are characterized by the relatively significant contribution of buoyancy force to the transport processes of momentum and heat. Past analytical studies on this kind of problems have been carried out by employing either the conventional R-.epsilon. turbulence model which includes constant turbulent Prandtl number .sigma.$_{+}$ 1 or an extended R-.epsilon. turbulence model which takes account of the buoyancy effect in appropriate length scale equations. But in the latter case, the temperature variance .the+a.$^{2}$ over bar is approximated by a model under local equilibrium condition and the time scale ratio between velocity and temperature is assumed to be constant. These approximation is known to break down when the buoyancy effect is dominant. The present study is aimed at development of new computational turbulence closure level which can be applied to this rather complex turbulent process. The temperature variance is obtained directly by solving its dynamic transport equation and the time scale ratio which is variable in space is computed by a solution of a dynamic equation for the rate of scalar dissipation .epsilon.$_{\thetod}$ It was found that the computational results are in good agreement with available experimental data of wide range of unstable conditions.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.20 no.8
• /
• pp.2681-2692
• /
• 1996

The finite-volume method for radiation in a three-dimensional non-orthogonal gas turbine combustion chamber with absorbing, emitting and anisotropically scattering medium is presented. The governing radiative transfer equation and its discretization equation using the step scheme are examined, while geometric relations which transform the Cartesian coordinate to a general body-fitted coordinate are provided to close the finite-volume formulation. The scattering phase function is modeled by a Legendre polynomial series. After a benchmark solution for three-dimensional rectangular combustor is obtained to validate the present formulation, a problem in three-dimensional non-orthogonal gas turbine combustor is investigated by changing such parameters as scattering albedo, scattering phase function and optical thickness. Heat flux in case of isotropic scattering is the same as that of non-scattering with specified heat generation in the medium. Forward scattering is found to produce higher radiative heat flux at hot and cold wall than backward scattering and optical thickness is also shown to play an important role in the problem. Results show that finite-volume method for radiation works well in orthogonal and non-orthogonal systems.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.19 no.8
• /
• pp.555-562
• /
• 2007

In this study, condensation heat transfer coefficients (HTCs) of R22, R134a, R245fa and R123 are measured on a horizontal plain tube. All data are taken at the vapor temperature of $39^{\circ}C$ with a wall subcooling temperature $3-8^{\circ}C$. Test results show the HTCs of newly developed alternative low vapor pressure refrigerant, R245fa, on a plain tube are 9.5% higher than those of R123 while they are 3.3% and 5.6% lower than those of R134a and R22 respectively. Nusselt's prediction equation for a plain tube underpredicts the data by 13.7% for all refrigerants while a modified equation yielded 5.9% deviation against all data. From the view point of environmental safety and condensation heat transfer, R245fa is a long term good candidate to replace R123 used in centrifugal chillers.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.24 no.1
• /
• pp.53-58
• /
• 2016

Modeling of engine coolant temperature was conducted for a series hybrid powertrain system. The purpose of this modeling was a simplification of complex heat transfer process inside a engine cooling system in order to apply it to the vehicle powertrain simulation software. A basic modeling concept is based on the energy conservation equation within engine coolant circuit and are composed of heat rejection from engine to coolant, convection heat transfer from an engine surface and a radiator to ambient air. At the final stage, the coolant temperature was summarized as a simple differential equation. Unknown heat transfer coefficients and heat rejection term were defined by theoretical and experimental methods. The calculation result from this modeling showed a reasonable prediction by comparison with the experimental data.

• Honam Mathematical Journal
• /
• v.33 no.4
• /
• pp.467-485
• /
• 2011

We consider the Hyers-Ulam-Rassias stability problem $${\parallel}u{\circ}A-{\upsilon}{\circ}P_1-w{\circ}P_2{\parallel}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)$$ for the Schwartz distributions u, ${\upsilon}$, w, which is a distributional version of the Pexider generalization of the Hyers-Ulam-Rassias stability problem ${\mid}(x+y)-g(x)-h(y){\mid}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)$, x, $y{\in}\mathbb{R}^n$, for the functions f, g, h : $\mathbb{R}^n{\rightarrow}\mathbb{C}$.

• Bulletin of the Korean Chemical Society
• /
• v.30 no.9
• /
• pp.2001-2006
• /
• 2009

Temperature dependence of the critical micelle concentration (CMC), $x_{CMC}$, in micellization can be described by ln $x_{CMC}$ = A + BT + C lnT + D/T, which has been derived statistical-mechanically. Here A, B, C, and D are fitting parameters. The equation fits the CMC data better than conventionally used polynomial equations of temperature. Moreover, it yields the unique(exponent) value of 2 when the CMC is expressed in a power-law form. This finding is quite significant, because it may point to the universality of the thermal behavior of CMC. Hence, in this article, the nature of the equation ln $x_{CMC}$ = A + BT + C lnT + D/T is examined from a lattice-theory point of view through the Flory-Huggins model. It is found that a linear behavior of heat capacity change of micellization is responsible for the CMC equation of temperature.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.14 no.3
• /
• pp.261-267
• /
• 2002

The integral boundary layer equation for the air side and the diffusion equation for the frost layer are numerically analyzed in order to predict the behavior of frost layer growth. The thickness and density of the frost layer obtained from the present study agree well with those of previous numerical results and experimental data with a maximum error of 13%. The characteristics of heat and mass transfer within the frost layer and the frost layer growth along the flow direction are investigated by performing numerical analysis. The effects of operating conditions on the frost layer growth are also examined.

• Journal of Ship and Ocean Technology
• /
• v.8 no.3
• /
• pp.50-60
• /
• 2004

In this paper, a continuum-based design sensitivity analysis (DSA) method is developed for the weakly coupled thermo-elasticity problems. The temperature and displacement fields are described in a common domain. Boundary value problems such as an equilibrium equation and a heat conduction equation in steady state are considered. The direct differentiation method of continuum-based DSA is employed to enhance the efficiency and accuracy of sensitivity computation. We derive design sensitivity expressions with respect to thermal conductivity in heat conduction problem and Young's modulus in equilibrium equation. The sensitivities are evaluated using the finite element method. The obtained analytical sensitivities are compared with the finite differencing to yield very accurate results. Extensive developments of this method are useful and applicable for the optimal design problems incorporating welding and thermal deformation problems.

• Journal of the Korean Society for Precision Engineering
• /
• v.16 no.8
• /
• pp.162-169
• /
• 1999

Fourier heat conduction law becomes invalid for the situations involving extremely short time heating, very low temperatures and fast moving heat source(or crack), since the wave nature of heat propagation becomes dominant. For these conditions, the modified heat conduction equation with the finite propagation speed of heat in the medium could be applied to predict heat flux and temperature distributions. In this study, temperature distributions at the vicinity of a very fast moving heat source are investigated numerically. Thermal fields are characterized by thermal Mach numbers(M) defined as the ratio of moving heat source speed to heat propagation speed in the solid. In the transonic and supersonic ranges($M{\ge}1$), thermal shocks are shown, which separate the heat affected zone from the thermally undisturbed zone.