• 열처리공학회지
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• 제8권1호
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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.

• 대한수학회지
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• 제33권4호
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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.

• 대한수학회논문집
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• 제34권3호
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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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• 제21권1호
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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.

• 한국구조물진단유지관리공학회 논문집
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• 제5권4호
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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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• 제2권1호
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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.

• 한국추진공학회지
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• 제16권2호
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• pp.42-50
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• 2012

열전달 연구의 목적은 온도와 열유속 분포를 보다 정확하게 예측하는 것이다. 이를 위해 상용 CFD 코드인 FLUENT를 사용하여 2종류의 노즐에 대해 질량유속비와 압력비를 계산하였으며, 실험결과와 잘 일치하였다. 또한 1종류의 노즐에 대해 FLUENT를 사용한 노즐 벽면에서의 열전달계수 계산결과는 노즐 축소부에서 실험결과 보다 약간 크게 예측되었으나 확대부에서는 잘 일치하고 있다. Bartz식을 이용한 열전달계수 계산결과는 전체적으로 실험결과 보다 크게 예측되었다. 계산결과가 실험결과와 차이를 보이는 원인은 노즐 내 급가속 유동에 의한 층류화, 난류모델 및 격자구성 등을 고려해 볼 수 있다.

• 대한기계학회논문집B
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• 제24권2호
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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.

• 한국항공운항학회지
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• 제23권3호
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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.

• 폴리머
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• 제29권6호
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• pp.549-556
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• 2005

단축압출기의 압출공정에서 고체수송부의 열전달 현상에 미치는 무차원수의 효과를 수치 해석적인 방법으로 연구하였다. 스크루의 기하학적 구조 및 특성에 따른 압출기 내에서의 고체 흐름 상태에 대한 이해를 바탕으로 고체 수송부에 대하여 열 수지 방정식을 세우고 무차원화하였다. 이에 유한체적법과 멱법칙 도식을 적용하여 이산화 방정식을 유도한 다음 반복 대입법과 완화법으로 해를 구하였다. 고체수송부의 열전달 특성을 규정하는 무차원수인 Biot 수와 Peclet 수가 수지 공급부의 온도와 고체수송부의 길이에 끼치는 영향을 조사하였다. Biot 수가 증가하면 냉각에 의한 열 손실이 지배하여 배럴의 온도는 급격히 감소하지만 고체층의 온도와 고체수송부의 길이에 미치는 영향은 적으며, Peclet 수가 증가하면 대류 항이 지배하여 고체층의 온도가 감소하고 고체수송부의 길이가 증가한다.