• Journal of the Korean Society for Heat Treatment
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• v.8 no.1
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• pp.24-31
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• 1995

Heat flow equation and FEM have been used to calculate the hardening section of material in laser transformation hardening. SCM440 used as the diesel engine piston of vessel has been hardened by a $CO_2$ laser with the wavelength of $10.6{\mu}m$. The specimens were inclined from 0 to 70 degree to investigate the characteristics of laser hardening. The geometrical factor of heat flow equation affects the size of hardening area. The case width decreased with increasing travel speed and the case width increased with increasing inclined angle. Maximum case depth was achieved about 1.0mm and maximum hardness of laser hardened area was of 2.8 times than that of base metal. Experimental data show good agreement with the theoretical calculations for given laser hardening conditions.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1039-1046
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• 1996

In the theory of partial differential equations with given initial values and boundary values one usually investigates to examine the well-posedness, that is, the unique existence of the solution as well as its continuous dependence on the data. This theory is strong enough for us to determine the situation anywhere and anytime provided that the initial data are actually given. However, in many cases the data are not completely known for us. Then in those situations arise the new problem to determine the unknown initial data by taking other conditions for the solutions.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.757-769
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• 2019

A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.1-16
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• 2017

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

• Journal of the Korea institute for structural maintenance and inspection
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• v.5 no.4
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• pp.121-129
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• 2001

The semi-adiabatic temperature rise and the losses of temperature of cement paste, mortar and concrete were measured by an apparatus of semi-adiabatic temperature. Heat of hydration was measured by a conduction calorimeter and adiabatic temperature rise of concrete was measured by an adiabatic calorimeter. The derived equation which can assume the adiabatic temperature was proposed by measuring the semi-adiabatic temperature of concrete. The maximum adiabatic temperature rise of concrete obtained by the derived equation of adiabatic temperature, $T_{ad}(t)=T_{sad}(t)+T_{dis}(t)$, showed $55^{\circ}C$ approximately and it had good relation with the other one obtained by the heat of hydration of cement paste and with maximum value which was measured by the adiabatic calorimeter. The adiabatic temperature rise obtained by derived equation was a different information in comparison with the value obtained by adiabatic temperature rise equations by Hell and et. al. in early age, but it showed similar tendencies with the other one according to elapsed time. Adiabatic temperature rise of lich mix concrete with highly cement content was predicted. The adiabatic temperature rise of cement paste and mortar obtained by derived equation from us showed comparatively matching results to compared with that of obtained by adiabatic temperature equation from concrete standard specification.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.2
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• pp.42-50
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• 2012

The goal of heat transfer studies is the accurate prediction of temperature and heat flux distribution on material boundaries. To this purpose, general-purpose computational fluid dynamics(CFD) code is used : FLUENT. Mass fluxes and pressure ratio are calculated for two types of nozzle. The comparative studies reveal that the computational results are in agreement with the experimental data. Also, heat transfer coefficients from FLUENT for one type of nozzle are very similar and agree well with the experimental data in the diverging part of the nozzle, but the calculated results are large in the converging part. The heat transfer coefficients from Bartz equation are over-predicted. We can consider various reasons for these differences, i.e., laminarization by the highly accelerated flow in the nozzle, turbulent flow model and grid generation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.2
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• pp.316-323
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• 2000

A nonlinear low-Reynolds-number heat transfer model is developed to predict turbulent flow and heat transfer in separated and reattaching flows. The $k-{\varepsilon}-f_{\mu}$ model of Park and Sung (1997) is extended to a nonlinear formulation, based on the nonlinear model of Gatski and Speziale (1993). The limiting near-wall behavior is resolved by solving the $f_{\mu}$ elliptic relaxation equation. An improved explicit algebraic heat transfer model is proposed, which is achieved by applying a matrix inversion. The scalar heat fluxes are not aligned with the mean temperature gradients in separated and reattaching flows; a full diffusivity tensor model is required. The near-wall asymptotic behavior is incorporated into the $f_{\lambda}$ function in conjunction with the $f_{\mu}$ elliptic relaxation equation. Predictions of the present model are cross-checked with existing measurements and DNS data. The model preformance is shown to be satisfactory.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.23 no.3
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• pp.8-17
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• 2015

In this research, low fidelity air/heat load analysis was conducted for the intake of high speed vehicle. For air/heat load calculations, aerodynamic properties at the surface and the boundary layer edge were estimated using Taylor-Maccoll equation for conical flow, shockwave relation and Prandtl-Meyer expansion equation for internal and external flow. Couette flow assumption and Reynolds analogy were used in order to calculate convective heat transfer coefficient. In order to calculate skin friction coefficient for heat transfer coefficient analysis, Van Driest method II and Reference Enthalpy method were considered. An axis symmetric SCRAMJET model was selected as a reference configuration for verifying the proper implementation of the present method. Comparison of the results using the present method and Computational Fluid Dynamic analysis showed that the present method is valuable for efficiently providing pressure and heat loads for air-intake structure design of the high speed air vehicle.

• Polymer(Korea)
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• v.29 no.6
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• pp.549-556
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• 2005

Effects of the dimensionless variables on the heat transport phenomena in the extrusion process of a single screw extruder have been studied numerically. Based on the understanding of the solids conveying related to the geometrical structure and characteristics of the screw, the heat balance equation for the solids conveying zone was established and normalized. The finite volume method and power-law scheme were applied to derive a discretized equation and the equation was solved using the alternating direction iterative method with relaxation. Effects of the dimensionless parameters, Biot and Peclet numbers, that define the heat transfer characteristics of the solids conveying zone have been investigated with respect to the temperature of the feeding zone and the length of the solids conveying zone. As the Biot number is increased, the heat loss by cooling dominates to decrease the temperature of the barrel but it has little effects on the temperature of the solids bed and the length of the solids conveying zone. On the other hand, if the Peclet number is increased, the convection term dominates to decrease the temperature of the solids bed and it results in an increase in the length of the solids conveying zone.