• Journal of Power System Engineering
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• v.3 no.3
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• pp.14-21
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• 1999

The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(${\xi}<{\eta}_l$). It is shown that due to the thermal relaxation time, the hyperbolic heat conduction equation has thermal wave characteristics as the damped wave equation has wave nature.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1091-1101
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• 2018

We concern in this paper the graph Kazdan-Warner equation $${\Delta}f=g-he^f$$ on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h{\leq}0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.3
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• pp.349-356
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• 1986

For the extension of application in flash method measuring the thermophysical properties of materials, the heat diffusion equation with the heat transfer loss from front, rear, and circumferential surfaces of two layer cylinderical sample is mathematically analyzed by means of Green's function for axially symmetric pulse heating on the front of samples. The solutions are applied to determine the unknown thermal diffusivity of the two materials and analyzed the measurement error due to heat loss and finite pulse time effects.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.5
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• pp.376-385
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• 1991

The purpose of this paper is to propose basic data on convection heat-transfer coefficients in Ondol-heated room. Surface temperatures and several temperatures around each inside surface of wall, floor and ceiling composed of heating room are measured vertically in Ondol-heated model rooms, and the vertical temperature profiles could be expressed by nonlinear equation models. Also, the convection heat transfer phenomena are analysed from the nonlinear equation models. In the results, the convection heat-transfer coefficients of Ondol heated space are suggested by the term of temperature difference between each wall surface and room air temperature and by the relationship between Nusselt number and Rayleigh number of dimensionless numbers.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.26 no.5
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• pp.1-12
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• 2012

In order to reduce energy consumption and greenhouse gas emission in building domain, thermal insulation of building is being enhanced. In a well insulated and tightened environment, internal heat gain caused by solar radiation, luminaires, electronic appliances and metabolism can be more important to thermal condition of building. This paper presents mathematical/physical models of quasi-adiabtic room and lighting fixtures using heat balance equation and thermal-electric analogy to quantify and modelize the heat gain due to luminaires. Experimental results are used to identify thermal parameters of theoretical models. And simulation results of models using Matlab/Simulink are conducted to verify the models and to investigate the thermal effect of lighting fixtures into quasi-adiabatic room.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.505-513
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• 2015

The present paper deals with the determination of displacement and thermal stresses in a semi-infinite circular cylinder defined as $0{\leq}r{\leq}b$, $0{\leq}z<{\infty}$, due to internal heat generation within it. A circular cylinder is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary (r = b) whereas the zero temperature at the lower surface (z = 0) of the semi-infinite circular cylinder. The governing heat conduction equation has been solved by using integral transform method. The results are obtained in series form in terms of Bessel functions. The results for displacement and stresses have been computed numerically and illustrated graphically.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.441-453
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• 1998

We use the heat kernel method to prove newly the Paley-Wiener theorem for the distributions with compact support.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.567-573
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• 2016

We obtain solution formulas for some nonlocal heat equations. As a simple application, we prove finite time blow-up of the solution.