• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.1
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• pp.1-15
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• 2021

A Green's function approach is adopted to solve the two-dimensional thermoelastic problem of a thin hollow circular disk. Initially, the disk is kept at temperature T0(r, z). For times t > 0, the inner and outer circular edges are thermally insulated and the upper and lower surfaces of the disk are subjected to convection heat transfer with convection coefficient hc and fluid temperature T∞, while the disk is also subjected to the axisymmetric heat source. As a special case, different metallic disks have been considered. The results for temperature and thermal deflection has been computed numerically and illustrated graphically.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.2
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• pp.54-65
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• 2021

In this study, a two-dimensional thermoelastic problem under hyperbolic heat conduction theory with an internal heat source is considered. The general solution for the temperature field, stress components and displacement field are obtained using the reduced differential transform method. The stress and displacement components are obtained using the thermal stress function in the reduced differential transform domain. All the solutions are obtained in the form of power series. The special case with a time-dependent laser heat source has been considered. The problem is considered for homogeneous material with finite rectangular cross-section heated with a non-Gaussian temporal profile. The effect of the heat source on all the characteristics of a material is discussed numerically and graphically for magnesium material taking a pulse duration of 0.2 ps. This study provides a powerful tool for finding the solution to the thermoelastic problem with less computational work as compared to other methods. The result obtained in the study may be useful for the investigation of thermal characteristics in engineering and industrial applications.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.18 no.8
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• pp.664-671
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• 2006

We propose the correlation to predict the spreading thermal resistance on a plate with symmetrical four heat sources. The correlation transforms four heat sources to a single equivalent heat source and then the spreading thermal resistance can be obtained with the existing equation for a single heat source. When the four heat sources are mounted on a square base plate, the correlation is expressed as a function of the heat source size, the length of base plate, the plate thermal conductivity and the distance between heat sources. Compared to the results of three-dimensional numerical analysis, the spreading thermal resistance by the proposed correlation is in good agreement within 10 percent accuracy.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.6
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• pp.73-77
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• 2019

In this paper, the heat pump system was designed using heat absorption of the refrigerant or condensation heat. The cooperation system has been developed to pass a heat source of low temperature to a high temperature or to pass the heat source of high temperature to a low temperature. Heat pump for using the valve as a function of switching a condenser and an evaporator in a refrigerating cycle. As a result, heat pump system was developed by air source method. Therefore cooperating system for energy saving to solve at the same time as the cooling and heating by system of one was equipped.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.683-688
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• 2007

Surface heat treatment of SM45C round bar by diode laser was simulated to find it's condition by using commercial finite element code MARC. Due to axisymmetric geometry, a quarter of model for SM45C round bar was considered and user subroutines were applied to boundary condition for the heat transfer. Material properties such as conductivity, specific heat and mass density were given as a function of temperature. Rotation speed of round bar and feed rate of beam were considered to design heat source model. Shape parameter values of heat source were determined by beam profile. As results, Three dimensional heat source model for diode laser beam conditions of surface hardening has been designed by the comparison between the finite element analysis results and experimental data on SM45C round bar. Diode laser surface hardening for SM45C round bar was successfully simulated and it should be useful to determine optimal heat treatment condition.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• 한국신재생에너지학회:학술대회논문집
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• 2010.06a
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• pp.172.2-172.2
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• 2010

This study was carried out in order to reduce the installation expense of heating system for greenhouse comparing to geothermal heat pump and develope the coefficient of performance (COP) for a heat pump. For getting plenty of heat flux from geothermal energy. Surface water in river channel was used for getting a lots of geothermal heat by penetrating water through underground soil layer of the river bank that make heat transmission to passing water. The range of water temperature after the process of Ground filtration is 13~18 degrees celsius which is very similar to low heat source of geothermal heat pump system and the plenty amount of heat source from that make the number of geothermal heat exchanging hole and the expense for geothermal heat exchanger construction reduced. Drainage well is also used for returning filtration water to the aquifer that keep the water good recirculation from losing geothermal heat and water resource. For the COP improvement of Heat pump, thermal storage tank with separating insulation plate according to the temperature difference make the COP of Heat pump that is similar to thermal storage tank with diffuser. Developed thermal storage tank make construction expense cheaper than customarily used one's. and that sand filter and oxidation sand (FELOX) are going to be used for improving ground filtration water quality that make heat exchanger efficiency better. All above developed component skill are going to be set on the Ground filtration water source heat pump system and applied for medium, large scale for protected greenhouse in riverside area and on-site experiment is going to do for optimizing the heating system function and overcome the problem happening in the process of on-site application afterward.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.3377-3382
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• 2007

In proton exchange membrane fuel cell, the heat is generated at the catalyst layer as result of exothermic electrochemical reaction. This heat increases temperature of gas diffusion layer and membrane whose conductivity is very sensitive to humidity, function of temperature. So it is very important to analysis heat transfer through fuel cell to maintain temperature at specified range. In this paper numerical simulation was done including reversible, irreversible, ionic resistance, water formation loss to source term of energy equation. Results show that irreversible and water formation loss contributes mainly to energy source term and as current density increases, all of energy source terms become increased and Nusselt number is increased as results of more heat generation. Particularly irreversible loss is found to be predominant among the all energy source and water formation at cathode channel influences the temperature distribution of fuel cell greatly.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.2
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• pp.257-264
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• 1989

For the extension of the flash method the heat diffusion equation with heat loss and with an arbitrary heat pulse is mathematically analyzed. In the analysis the heat loss includes the axial and radial directions on the front, rear and peripheral surfaces. The heat pulse is irradiated from the source to the front surface of the sample and the heat receiving area on the front surface is controlled by the apertures of an optical system. From this analysis the thermal diffusivity of the samples can be determined more precisely than before by the data reduction method using various percent time. The data can be obtained by the extended radial flash technique adjusted correctly the heating area on the central part of the front surface with a proper aperture or the conventional axial flash technique heated uniformly all parts of the front surface.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.