• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.690-694
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• 2008

In this presentation, we study numerically an optimization problem of a fire fighting robot cooling system. The governing equation for the system is the unsteady heat equation with source term. We use a multigrid method for numerical solutions in three-dimensional space. We investigated the effects of various parameters and the results will be presented.

• Journal of Advanced Marine Engineering and Technology
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• v.12 no.1
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• pp.37-45
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• 1988

A calculating method of transient temperature distribution due to spot welding of thin plates is studied in this paper. Considering the contact stress between upper and lower plate and temperature-dependence of specific resistance and elastic limit of base metal, the model of calorific density of heat source was decided. Using 2-dimensional polar coordinates system, the governing equation of heat transfer was developed. The thermal cycles of various points were recorded using C-A thermocouples during spot welding procedure for mild steel plates of 1mm thickness, and those results were compared with the results of calculations presented in this paper.

• Journal of the korean Society of Automotive Engineers
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• v.14 no.2
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• pp.54-64
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• 1992

During combustion process in a diesel engine radiation heat transfer is the same order of magnitude as the convection heat transfer. An approximation of heat and momentum source distributions is applied at a level consistent with those used in modelling the soot distribution and the turbulence instead of modelling the fuel spray and the chemical kinetics. This paper illustrates a use of the third order spherical harmonics approximation to the radiative transfer equation and delta-Eddington approximation to the scattering phase function for droplets in the flow. Results are obtained numerically by a time marching finite difference scheme. This study aims to compare heat transfer with convection heat transfer and to investigate the importance of scattering by fuel droplets and of accounting for spatial variations in the extinction coefficient on the radiative heat flux distributions at the walls of a disc shaped diesel engine.

• Tunnel and Underground Space
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• v.9 no.1
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• pp.27-35
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• 1999

The characteristics of heat conduction for the heat source boundary like an arch shape cavern are different from those for the semi-infinite or circular boundary which can be driven theoretically. A new form of transient heat conduction equation in rock mass around the arch shape cavern is evaluated with analyzing the pattern of the rock temperature distribution measured at the cold storage pilot plant. The new equation, which is driven by adopting a shape function, $SF=\sqrt{logx_0/log(x_0+x)}$ to the solution for a semi-infinite boundary, has the semi-radial form of temperature variation with distance. And, thermal properties of rock mass are estimated by comparing the rock temperature distributions by this equation with those by measurement. Thermal conductivity and specific heat of rock mass are estimated as giving the difference of 20~25% compared to those of laboratory scale. This difference seems to be caused by discontinuity like joint and water content in rock mass.

• Fire Science and Engineering
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• v.16 no.2
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• pp.8-13
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• 2002

Induction heating is widely used in today's industry, in operations such as metal hardening, pre-heating for forging operations, melting or cooking. In this paper, the magneto-thermal analysis of an induction heating jar(IH-JAR) was presented as an efficient design. The magnetic field intensity inside the axisymmetric shaped cooker was analyzed using three-dimensional axisymmetric finite element method(FLUX2D) and the effectual heat source was obtained by ohmic losses from eddy currents induced in the jar. The heat was calculated using the heat source and heating equation. Also, it was presented the temperature characteristics of the IH-JAR according to time and relative permeability in stainless parts and in aluminum parts.

• Fire Science and Engineering
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• v.10 no.2
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• pp.28-39
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• 1996

A recently developed electro-thermal simulation methodology is used to analyze the behavior of a PWM(Pulse-Width-Modulated) voltage source inverter which uses IGBT(Insulated Gate Bipolar Transistor) as the switching devices. In the electro-thermal network simulation methdology, the simulator solves for the temperature distribution within the power semiconductor devices(IGBT electro-thermal model), control logic circuitry, the IGBT gate drivers, the thermal network component models for the power silicon chips, package, and heat sinks as well as the current and voltage within the electrical network. The thermal network describes the flow of heat form the chip surface through the package and heat sink and thus determines the evolution of the chip surface temperature used by the power semiconductor device models. The thermal component model for the device silicon chip, packages, and heat sink are developed by discretizing the nonlinear heat diffusion equation and are represented in component from so that the thermal component models for various package and heat sink can be readily connected to on another to form the thermal network.

• East Asian mathematical journal
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• v.34 no.3
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• Proceedings of the KWS Conference
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• 2002.10a
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• pp.763-768
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• 2002

This paper presents a mathematical model predicting the temperature distribution in rotating GMA welding. The bead width increases with rotation frequency at the same rotation diameter because the molten droplets are deflected by centrifugal force. The numerical solution is obtained by solving the transient three-dimensional heat conduction equation considering the heat input from the welding arc, cathode heating and molten droplets. Generally in GMA welding the heat input may be assumed as a normally distributed source, but the droplet deflection causes some changes in the heat input distribution. To estimate the heat flux distribution due to the molten droplet, the contact point where the droplet is transferred on the weld pool surface is calculated from the flight trajectory of the droplets under the arc plasma velocity field obtained from the arc plasma analysis. The numerical analysis shows a tendency of broadened bead width and shallow penetration depth with the increase of rotating frequency. The simulation results are in good agreement with those obtained by the experiments under various welding conditions.

• Journal of computational fluids engineering
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• v.18 no.2
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• pp.9-16
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• 2013

The heat transfer enhancement of heat sink with mist flow is studied numerically by solving the conservation equations for mass, momentum and energy in the continuous and dispersed phases. A Lagrangian method is used for tracing dispersed water droplets in the heat sink and an Eulerian species transport model for air and steam mixture. The continuous and dispersed phases are interacted with the drag and evaporation source terms. The computed results show that addition of evaporating mist droplets enhances the cooling performance of heat sink significantly.