• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.79-86
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• 2011

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by $-K{\leq}0$ and (N, $\bar{g}$) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : $M{\times}[0,{\infty}){\rightarrow}N$ be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

• East Asian mathematical journal
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• 제35권1호
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• pp.99-108
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• 2019

In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

• 대한수학회보
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• 제56권3호
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• pp.631-648
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• 2019

In this paper, we consider a semilinear stochastic heat equation driven by an additive fractional white noise. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application to the convergence of the Picard successive approximation.

• 오토저널
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• 제4권2호
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• pp.58-68
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• 1982

It is well known to diesel engineers that the heat release pattern is one of the most important factors affecting engine performance. Thorough research in heat release pattern has materially helped the progress in high-speed diesel engine development . This paper is based on the research conducted at KAIST and Daewoo Heavy Industry last year. The purpose of this paper is to determine the heat release pattern in combustion chamber of MAN M type, the famous low-noise engine. Thermodynamic cycle simulation was performed using Whitehous-Way's heat release pattern with modified coefficients and Annand's heat transfer model. Instantaneous temperature and pressure of gas in cylinder could be determined by the numerical solution of simultaneous equation of mass conservation, equation of energy conservation, and state equation of ideal gas. Calculated results were compared with measured values in some details emphasizing upon the factors affecting rate of heat release. The agreement was fairly good and revealed why M type should have lower burning velocity at the early part of combustion in spite of high injection rate. Additional results by parametric studies were given in relation to fuel injection conditions for further application to engine development.

• 대한기계학회논문집B
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• 제22권1호
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• pp.1-11
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• 1998

For the analysis of phonon heat transfer within short time and spatial scales, conventional macroscopic heat conduction equations with jump boundary conditions are tried and the results are compared to those of equation of phonon radiative transport(EPRT), which is one of microscopic transport equation. In transient state the macroscopic temperatures show far different behavior from EPRT. In steady state the hyperbolic temperatures with temperature jump at the wall from time relaxation model agrees well with EPRT temperatures. Since EPRT is also an approximate form of microscopic transport equation and there are no experimental results to verify the proposed model in this study, we can not conclude whether the approaching method from this study is valid or not. To the authors' knowledge, there are no experimental results available which can be used to test the validity of these models. Such an experiment, while difficult to conduct, would be invaluable.

• 한국건축시공학회:학술대회논문집
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• 한국건축시공학회 2022년도 봄 학술논문 발표대회
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• pp.13-14
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• 2022

This study investigated the effect of fly ash content on the isothermal hydration heat of cement pastes. Two different pastes with fly ash content were studied to cure at 35℃. The hydration heat flow deceleration stage of slurry was simulated and compared by Jander Equation and Ginstling-Brounshtein Equation. The results show that Jander Equation and Ginstling-Brounshtein Equation have certain defects in the modeling of the deceleration stage of the heat flow of cement fly ash paste, and the fitted curve can not describe the deceleration stage well.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제3권1호
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Journal of Biosystems Engineering
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• 제36권4호
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• pp.267-272
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• 2011

The latent heat of vaporization in rough rice, brown rice, white rice and rice hull was calculated by Clausius-Clapeyron equation, which does not require complex constraints as in Othmer method. Equilibrium relative humidity and ratio of the latent heat of vaporization with ln$P_{\upsilon}$ and ln$P_S$ were estimated with moisture contents ranging from 10% (d.b.) to 36% (d.b.) with 2% (d.b.) increment and temperatures ranging from $10^{\circ}C$ to $50^{\circ}C$ with $2.5^{\circ}C$ increment. An empirical equation for calculating the latent heat of vaporization in rice was developed as a function of moisture content and temperature. The equation agreed well with the calculated results. The ratio for latent heat of vaporization were the greatest for white rice while they were similar among rough rice, brown rice and rice hull.

• 대한수학회논문집
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• 제23권3호
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• pp.401-411
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• 2008

In this paper, we characterize Sobolev spaces $H^s(\mathbb{R}^n),\;s{\in}\mathbb{R}$ by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.

• 대한기계학회논문집
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• 제6권3호
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• pp.211-221
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• 1982

Numerical analysis has been made on the heat transfer of two dimensional turbulent channel with a slat type blockage. Especially the effects of the height of slat and Reynolds number on the heat transfer characteristics of channel wall have been investigated. The methods of accelerating the convergence of the numerical solution of governing differential equation have been also examined. Line-by-line iterative method shows higher convergence rate than point-by-point iterative method for solution of both momentum equation and energy equation. The results show that the ratio of heat transfer coefficient of the wall near the blockage to that of the fully developed flow increase with increasing the ratio of blockage to channel height and decreasing the Reynolds number. These trends of variation of heat transfer coefficient with respect to the height of slat and Reynolds number agree with those of Sparrow's experiment on the pipe flow with slat type blockage.