• Journal of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.781-791
• /
• 2001

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

• Steel and Composite Structures
• /
• v.48 no.6
• /
• pp.641-648
• /
• 2023

In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.651-661
• /
• 2010

We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.7
• /
• pp.1684-1690
• /
• 1995

A large time asymptotic solution for an unsteady heat conduction problem of a coated hot wire thermal conductivity measurement process was theoretically found. The solution revealed that the slope of wire temperature versus logarthmic time, which is used to evaluate the thermal conductivity, remains unchanged for large values of time even if a layer of coating is present on the hot wire. The significance of this result is that the thermal conductivity of an electrically conductive fluid can be measured with a coated hot wire using the same conversion relation as for a bare wire.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.28 no.2
• /
• pp.189-198
• /
• 2004

We consider the problem of whether the three-dimensional checkerboard has the connectivity. For this purpose, we first consider the problem of determining the effective conductivity of a checkerboard-shaped composite material by the Brownian motion simulation method. Specifically, we use the efficient first-passage-time technique. Simulation results show that the effective conductivity of the three-dimensional checkerboard increases faster than the two-dimensional counterpart as the contrast between the phase conductivities increases. This implies that the three-dimensional checkerboard's connectivity is stronger than the two-dimensional checkerboard's and thus each phase material of the three-dimensional checkerboard is more likely to be connected than not to be connected.

• Communications of the Korean Mathematical Society
• /
• v.16 no.3
• /
• pp.415-425
• /
• 2001

We consider the problem of determining conductivity of the medium from the measurements of the electric potential on the boundary and the corresponding current flux across the boundary. We give a formula for reconstructing the conductivity and its normal derivative at the point of the boundary simultaneously from the localized Diichlet to Neumann map around that point.

• Design & Manufacturing
• /
• v.18 no.3
• /
• pp.37-43
• /
• 2024

With the development of technology in the electrical and electronic field, research on heat dissipation materials that can efficiently emit and control heat to solve the heat generation problem is being actively conducted. Since heat dissipation materials require electrical insulation and thermal conductivity, the polymer composite material was manufactured by mixing chemically stable silicone resins and ceramic fillers, and thermal conductivity and mechanical properties were observed. At the same filling amount, the larger the particle size and the higher the high thermal conductivity filler was added, the higher the thermal conductivity was, mechanical properties were confirmed to have higher tensile strength and elongation as the particles were smaller and the tissue was denser. After selecting materials in consideration of thermal conductivity and mechanical properties, an appropriate mixing ratio is considered important.

• Communications of the Korean Mathematical Society
• /
• v.16 no.3
• /
• pp.459-485
• /
• 2001

The aim of EIT (electrical impedance tomography) system is to image cross-section conductivity distribution of a human body by means of both generating and sensing electrodes attached on to the surface of the body, where currents are injected and voltages are measured. EIT has been suffered from the severe ill-posedness which is caused by the inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. With a limited set of current-to-voltage data, figuring out full structure of the conductivity distribution could be extremely difficult at present time, so it could be worthwhile to extract some necessary partial information of the internal conductivity. We try to extract some key patterns of current-to-voltage data that furnish some core information on the conductivity distribution such s location and size. This overview provides our recent observation on the location search and the size estimation.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.16 no.4
• /
• pp.99-106
• /
• 2012

This study presents estimation method of temperature-dependent thermal conductivity by using solution of inverse heat conduction problem. Time and depth temperature distribution data from full-scale fire test were used for estimating temperature-dependent thermal conductivity on hybrid-fiber reinforced shield tunnel lining. At short heating time, estimated thermal conductivity sharply decreased within $100^{\circ}C$. On the other hand, it reflected thermal properties of concrete and effect of steel fiber at heating time of measured maximum heating temperature. Thus arbitrary time should be determined to estimate temperature-dependent thermal conductivity in time zone of measured maximum heating temperature. Estimated temperature-dependent thermal conductivity is similar to results of other study.

• Bulletin of the Korean Chemical Society
• /
• v.24 no.2
• /
• pp.178-182
• /
• 2003

The stress and the heat-flux auto-correlation functions in the Green-Kubo formulas for shear viscosity and thermal conductivity have non-decaying long-time tails. This problem can be overcome by improving the statistical accuracy by N (number of particles) times, considering the stress and the heat-flux of the system as properties of each particle. The mean square stress and the heat-flux displacements in the Einstein formulas for shear viscosity and thermal conductivity are non linear functions of time since the quantities in the mean square stress and the heat-flux displacements are not continuous under periodic boundary conditions. An alternative to these quantities is to integrate the stress and the heat-flux with respect to time, but the resulting mean square stress and heat-flux displacements are still not linear versus time. This problem can be also overcome by improving the statistical accuracy. The results for transport coefficients of liquid argon obtained are discussed.