• Journal of the Korean Society of Industry Convergence
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• v.5 no.4
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• pp.303-307
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• 2002

We consider the problem y"=a(x,y)(y-b), (0$$y(0)=0,\;y^{\prime}(1)=g(y({\xi}),\;y^{\prime}({\xi})),\;{\xi}$$ fixed in (0,1). This is a model of steady-state heat conduction in a rod when the heat flux at the end x=1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness, and positivity of solutions.

• Journal of the korean Society of Automotive Engineers
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• v.2 no.1
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• pp.39-50
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• 1980

This paper presents the variations obtained in heat flow rate and engine performance of a four-stroke cycle Diesel engine when there were changes in the temperature of cooling water, compression ratio, injection timing of fuel, and other factors. Heat dissipation of engine cylinder was calculated by the heat transfer coefficient of Nusselt's empirical equation and the analysis of distribution of temperature in cylinder barrel was obtained by the finite element method of two-dimensional steady state heat conduction. In this experiment, the out side temperature of cylinder liner was measured by the data logger, and the temperature distribution of liner was computed by the analysis of triangular finite element model under the assumption due to surface heat flux of cylinder inner surface. The results obtained by this study are as follows. Under the given operating condition, the temperature distribution of cylinder liner by using finite element method shows that the mean temperature of barrel is in accordance with the experimental results of Eichelberg and temperature difference is lower than 4.23.deg. C. The heat dissipation of engine decrease in accordance with the decrease of piston mean velocity, compression ratio, and the increase of coolant temperature. Influence on the delay of injection timing of fuel brings about the decrease of heat rejection over the cylinder at constant test conditions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1621-1628
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• 1990

Numerical solutions are presented for the heat transfer from radiating and convecting fins. Consideration is given to thin, annular fins attached to a tube surface for which the temperature is constant. Fin to fin, fin to base, and fin to environment radiative interactions are considered. It is assumed that the radiating surface is diffuse-gray, the environment is black, and the surrounding fluid is transparent. The radiation terms are formulated by using Poljak's net-radiation methoad. The mathematical description of the simultaneously heat transport by conduction, convection, and radiation leads to a nonlinear integro-differential equation. This has been solved for a wide range of the pertinent physical parameters by using finite difference method and iteration method based on the Newton-Raphson technique. The temperature distributions, heat transfer rates, fin efficiencies, and fin effectivenesses are presented in dimensionless form. The results definitely indicate that the use of fins leads to a significant increase in heat transfer compared with the unfinned tube.

• Fire Science and Engineering
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• v.28 no.1
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• pp.52-57
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• 2014

In this paper, the unsteady incompressible Navier-Stokes equations coupled with energy equation were solved to find out the optimal location of electrical heat trace for anti-freeze of water inside the pipe for fire protection. Since the conduction equation of pipe was coupled with the natural convection of water, the analysis of conjugate heat transfer was conducted. A commercial code (ANSYS-FLUENT) based on SIMPLE-type algorithm was used for investigating the unsteady flows and temperature distributions in water region. From the numerical experiments, the isotherms and the vector fields in water region were obtained. Furthermore, it was found that the lowest part of the pipe cross-section was an optimal position of electrical heat trace assuming the constant thermal expansion coefficient of water since the minimum temperature of the water with the position is higher than those with the other positions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.215-222
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• 2019

The heat conduction problem with discontinuous material coefficients generally consists of the conservative equation, boundary condition, and interface condition, which should be additionally satisfied in the solution procedure. This feature often makes the development of new numerical schemes difficult as it induces a layered singularity in the solution fields; thus, a special approximation is required to capture the singular behavior. In addition to the approximation, the construction of a total system of equations is challenging. In this study, a wedge function is devised for enriching the approximation, and the interface condition itself is embedded in the moving least squares(MLS) derivative approximation to consistently satisfy the interface condition. The heat conduction problem is then discretized in a strong form using the developed derivative approximation, which is named as the interface immersed MLS difference method. This method is able to efficiently provide a numerical solution for such interface problems avoiding both numerical quadrature as well as extra difference equations related to the interface condition enforcement. Numerical experiments proved that the developed numerical method was highly accurate and computationally efficient at solving the heat conduction problem with interfacial jump as well as the problem with a geometrically induced interfacial singularity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.69-81
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• 2015

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1025-1037
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• 2018

We consider an ill-posed problem for the heat equation $u_{xx}=u_t$ in the quarter plane {x > 0, t > 0}. We propose a new method to compute the heat flux $h(t)=u_x(1,t)$ from the boundary temperature g(t) = u(1, t). The operator $g{\mapsto}h=Hg$ is unbounded in $L^2({\mathbb{R}})$, so we approximate h(t) by $h_{\delta}(t)=u_x(1+{\delta},\;t)$, ${\delta}{\rightarrow}0$. When noise is present, the data is $g_{\epsilon}$ leading to a corresponding heat $h_{{\delta},{\epsilon}}$. We obtain an estimate of the error ${\parallel}h-h_{{\delta},{\epsilon}}{\parallel}$, as well as the error when $h_{{\delta},{\epsilon}}$ is approximated by the trapezoidal rule. With an a priori choice rule ${\delta}={\delta}({\epsilon})$ and ${\tau}={\tau}({\epsilon})$, the step size of the trapezoidal rule, the main theorem gives the error of the heat flux as a function of noise level ${\epsilon}$. Numerical examples show that the proposed method is effective and stable.

• Fire Science and Engineering
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• v.29 no.6
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• pp.33-39
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• 2015

In this paper, a numerical experiment was conducted to find out the optimal location of electrical heat trace for anti-freeze of water inside the CPVC pipe for fire protection. The unsteady incompressible Navier-Stokes equations coupled with energy equation were solved. Since the conduction equation of pipe was coupled with the natural convection of water, the analysis of conjugate heat transfer was conducted. A commercial code (ANSYS-FLUENT) based on SIMPLE-type algorithm was used for investigating the unsteady flows and temperature distributions in water region. From the present numerical experiment, it has been found that the vector field of water inside the PVC pipe is opposite to the case of steel because of the huge difference of material properties of the two pipes. Furthermore, it was found that the lowest part of the pipe was an optimal position for electrical heat trace since the minimum water temperature of the case was higher than those of the other cases.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.823-835
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• 2016

Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1997.10a
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• pp.298-303
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• 1997

Over the last few year, there has been a growing interest in quantitative representation of heat transfer phenomena in weld pools in order to relate the processing conditions to the quality of the weldment produced and to use this information for the optimisation and robotization of the welding process. Normally, a theoretical model offers a powerful alternative to check out the physical concepts of the welding process and to calculate the effects of varying any of parameters. To solve this problem, a transient 2D(two-dimensional) heat conduction were developed for determining bead geometry and temperature distribution for the GMA welding process. The equation was solved using a general thermofluid-mechanics computer program, PHOENICS code, which is based on the SIMPLE algorithm. The simulation results showed that the calculated bead geometry from the developed models reasonablely agree with the experiment results.