• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.385-397
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• 2001

Consider an inverse problem of determining of the 2-D temperature distribution from known temperature given at some time T>0. Our aim is to find the temperature for 0

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.14 no.11
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• pp.923-930
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• 2002

Cooling characteristics of a parallel channel with protruding heat sources using convection and conduction heat transfer are studied numerically. A two-dimensional model has been developed for numerical prediction of transient, compressible, viscous, laminar flow, and conjugate heat transfer between parallel plates with uniform block heat sources. The finite volume method is used to solve the problem. The assembly consists of two channels formed by two covers and one printed circuit board which has three uniform heat source blocks. Six different cooling methods are considered to find out the most efficient cooling method in a given geometry and heat sources. The velocity and temperature fields of cooling medium, the temperature distribution along the block surface, and the maximum temperature in each block are obtained. The results are compared to examine the cooling characteristics of the different cooling methods.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1741-1752
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• 2006

A combined Streamline Upwind Petrov-Galerkin method (SUPG) and segregated finite element algorithm for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow is presented. The Streamline Upwind Petrov-Galerkin method is used for the analysis of viscous thermal flow in the fluid region, while the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the presented method is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the conjugate Couette flow problem in parallel plate channel, the counter-flow in heat exchanger, the conjugate natural convection in a square cavity with a conducting wall, and the conjugate natural convection and conduction from heated cylinder in square cavity, are selected to evaluate efficiency of the presented method.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1529-1540
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• 1993

The quenching of steels by water is one of the imprtant problems in the applications of heat treatment, but the fundamental researches by way of theoretical approaches have not been satisfactorily improbed yet. This study aimed at measuring the exact subcooled transient boiling curve for cylindrical specimens and at conducting the analytical researches into the prediction of cooling curves, including the latent heat of phase transformation of steel. Experiments of quenching were made with cylindrical specimens of carbon steel S45C of diameters from 12 to 30 mm and with Cu specimens of 12 mm diameter respectively. The internal temperature of specimens during the quenching process was measured by C-A sheathed thermocouple. The heat fluxes were numerically calculated by the numerical method of inverse heat conduction problem, using the measured inner temperature of specimen as a boundary condition. In case of ${\Delta}T_{sub}=80K$, $q_{s}$ is as follows $q_{s}=2.02{\times}10^{5}{\Delta}T_{set}^{0.05}:{\Delta}T_{set}\le500K.$ And the numerical analysis of unsteady heat conduction during the quenching process was made and the cooling curves were calculated by TDMA method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2995-3002
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• 1995

The cooling problem of the hot internal pipe flow has been investigated. Simultaneous conduction, convection, and radiation were considered with azimuthally varying convective heat loss at the pipe wall. A complex, nonlinear integro-differential radiative transfer equation was solved by the discrete ordinates method (or called S$_{N}$ method). The energy equation was solved by control volume based finite difference technique. A parametric study was performed by varying the conduction-to-radiation parameter, optical thickness, and scattering albedo. The results have shown that initially the radiatively active medium could be more efficiently cooled down compared with the cases otherwise. But even for the case with dominant radiation, as the medium temperature was lowered, the contribution of conduction became to exceed that of radiation.n.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.390-395
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• 2001

Cooling characteristics using convection and conduction heat transfer in a parallel channel with extruding heat sources are studied numerically. A two-dimensional model has been developed for numerical prediction of transient, compressible, viscous, laminar flow, and conjugate heat transfer between parallel plates with uniform block heat sources. The finite volume method is used to solve this problem. The considered assembly consists of two channels formed by two covers and one PCB which has three uniform heat source blocks. Five different cooling methods are considered to find efficient cooling method in a given geometry and heat source. The velocity and temperature fields, local temperature distribution along surface of blocks, and the maximum temperature in each block are obtained.

• Kyungpook Mathematical Journal
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• v.30 no.2
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• pp.205-214
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• 1990

• Kyungpook Mathematical Journal
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• v.21 no.2
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• pp.289-297
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• 1981

• 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.