• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.3 no.2
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• pp.97-102
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• 1991

Finite element method has been developed recently for the solution of the convection-diffusion problems. Finite element method has several advantages over finite difference method, but its requirement of the larger memory size of the computer has prevented from wide application. In the present study, line-by-line technique has been implemented to finite element method to overcome this disadvantage. Two dimensional laminar natural convection in square cavity was chosen as an example in this study. The numerical result shows good agreement with bench mark solution and the size of the coefficient marix has been reduced drastically.

• 대한공업교육학회지
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• v.30 no.2
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• pp.123-129
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• 2005

A Rayleigh-Benard problem with non-uniform wall temperatures of the form, $T_L=T_1+{\delta}{\Delta}T{\sin}kx$ and $T_U=T_2-{\delta}{\Delta}{\sin (kx)$, is numerically investigated. In the conduction-dominated regime with small a Rayleigh number, a two-tier structure appears with two counter-rotating rolls stacked on the top of each other. The flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximetely square-shape cells. Four multiple flows and dual flows classified by the number of cells are found at k=0.5 and k=1, respectively.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.644-653
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• 1991

A wave instability problem is formulated for natural convection flows adjacent to a inclined isothermal surface in pure water near the density extremum. It accounts for the nonparallelism of the basic flow and temperature fields. Numerical solutions of the hydrodynamic stability equations constitute a two-point boundary value problem which are accurately solved using a computer code COLSYS. Neutral stability results for Prandtl number of 11.6 are obtained for various angles of inclination of a surface in the range from-10 to 30 deg. The neutral stability curves are systematically shifted toward modified Grashof number G=0 as one proceeds from downward-facing inclined plate(.gamma.<0.deg.) to upward-facing inclined plate (.gamma.>0.deg.). Namely, an increase in the positive angle of inclination always cause the flows to be significantly more unstable. The present results are compared with the results for the parallel flow model. The nonparallel flow model has, in general, a higher critical Grashof number than does the parallel flow model. But the neutral stability curves retain their characteristic shapes.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.683-695
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• 2002

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.

• Journal of the Korean Society of Propulsion Engineers
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• v.13 no.1
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• pp.51-57
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• 2009

In this study, a new topology optimization method is developed to design heat-dissipating structure with forced convection. To cool down electrical devices or mechanical machines, two types of convection models have been widely used: the natural convection model with a large Archimedes number and the forced convection with a small Archimedes number. In these days, lots of engineering application areas such as electrochemical conversion devices (Fuel cell) or rocket propulsion engines adopt the forced convection to dissipate the generated heat. Therefore, to our knowledge, it becomes an important issue to design flow channels inside which the generated heat dissipate. Thus, this paper studies optimal topological designs considering fluid-heat interactions. To consider the effect of the advection in the heat transfer problem, the incompressible Navier-stokes equation is solved. This paper numerically studies the coupling phenomena and presents optimal channel design considering forced convection.

• Fire Science and Engineering
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• v.11 no.1
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• pp.21-35
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• 1997

The natural convection and combined heat transfer induced by fire in a rectangular enclosure is numerically studied. The model for this numerical analysis is partially opened right wall. The solution procedure includes the standard k-$\varepsilon$ model for turbulent flow and the discrete ordinates method (DOM) is used for the calculation of radiative heat transfer equation. In numerical study, SIMPLE algorithm is applied for fluid flow analysis, and the investigations of combustion gas induced by fire is performed by FAST model of HAZARD I program. In this study, numerical simulation on the combined naturnal convection and radiation is carried out in a partial enclosure filled with absorbed-emitted gray media, but is not considered scattering problem. The streamlines, isothermal lines, average radiation intensity and kinetic energy are compared the results of pure convection with those of the combined convection-radiation, the combined heat transfer. Comparing the results of pure convection with those of the combined convection-radiation, the combined heat transfer analysis shows the stronger circulation than those of the pure convection. Three different locations of heat source are considered to observe the effect of heat source location on the heat transfer phenomena. As the results, the circulation and the heat transfer in the left region from heating block are much more influenced than those in the right region. It is also founded that the radiation effect cannot be neglected in analyzing the building in fire. And as the results of combustion gas analysis from FAST model, it is found that O2 concentration is decreased according to time. While CO and CO2 concentration are rapidly increased in the beginning(about 100sec), but slowly decreased from that time on.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2353-2364
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• 1995

The ignition phenomena of a solid fuel plate of polymethyl-methacrylate(PMMA), which is vertically positioned and exposed to a thermal radiation source, is numerically studied here. A two-dimensional transient model includes such various aspects as thermal decomposition of PMMA, gas phase radiation absorption, gas phase chemical reaction and air entrainment by natural convection. Whereas the previous studies considers the problem approximately in a one-dimensional form by neglecting the natural convection, the present model takes account of the two-dimensional effect of radiation and air entrainment. The inert heating of the solid fuel is also taken into consideration. Radiative heat transfer is incorporated by th Discrete Ordinates Method(DOM) with the absorption coefficient evaluated using gas species concentration. The thermal history of the solid fuel plate shows a good agreement compared with experimental results. Despite of induced natural convective flow that induces heat loss from the fuel surface, the locally absorbed radiant energy, which is converted to the internal energy, is found to play an important role in the onset of gas phase ignition. The ignition is considered to occur when the rate of variation of gas phase reaction rate reaches its maximum value. Once the ignition takes place, the flame propagates downward.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.266-271
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• 2003

The numerical study was carried out to effectively cool Induction motor applied to a washing machine. The outer rotor made of steel periodically spins up and down. The stator consists of the thin layered iron plates and copper coil. The effective cooling system is necessary to solve the reliability problem caused by the electric losses at the coil and the iron plate. Because the heat transfer rate of the natural convection in partially open space is generally low, thus it is necessary to enhance the heat transfer using rotating perforated plate. The flow phenomena around the motor are very complex due to the motor geometry and the outer rotor motion. The mixed convection takes place due to the slow rotation speed. The three dimensional flow simulation was performed using rotating reference frame technique and Boussinesq approximation but the radiation effect was neglected. It was found that the angle and direction of the cooling blades play an important role in the stator temperature.