• Education of Primary School Mathematics
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• v.19 no.4
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• pp.277-289
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• 2016

Fraction is one of the concepts which are difficult to elementary school students. So, many researches about fraction were performed in mathematics education research. In special, fraction has so many subordinative concepts-proper fraction, improper fraction, mixed number. We have to concentrate on the conceptual understanding in teaching of fraction. In this case, a mixed number and improper fraction are concepts which can convert respectively. And there are methods that a mixed number and improper fraction can be converted. So, it's needed to analyze the converting methods in textbooks for getting the implication of teaching in this areas. In this study, I analyzed the Korean and foreign's textbooks. I certified the methods-using addition expression, using part-whole model in the textbooks. For the conceptual understanding, I suggested to use the fusion of the various part-whole fraction models and addition expression more than the algorithm in converting between a mixed number and improper fraction. It's reason that the use of models in converting between a mixed number and improper fraction is important for the relational understanding.

• Journal of Power System Engineering
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• v.11 no.4
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• pp.56-64
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• 2007

A numerical simulation is carried out mixed convection in horizontal channel with a heat source from below of rectangular cavity. Finite volume method was employed for the discretization and PISO algorithm was used for calculating pressure term. The parameters governing the problem are the Reynolds number ($10^{-2}{\leq}Re{\leq}50$), the Rayleigh number ($10^3{\leq}Ra{\leq}2.06{\times}10^5$), the Prandtl number ($0.72{\leq}Pr{\leq}909$), the aspect ratio ($0.5{\leq}AR=W/H{\leq}2$) and the angle of inclination ($0^{\circ}{\theta}60^{\circ}$). Mean Nusselt number distributions were obtained and effect of Reynolds number, Rayleigh number and Prandtl number on mixed convection in the horizontal channel with rectangular cavity were investigated.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.11a
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• pp.29-30
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• 2005

A three-dimensional numerical calculation has been performed to investigate mixed convective vortex flow in rectangular channels(width/height=4) with the upper part cooled and the lower part heated uniformly. In this study, the Prandtl number was 909, the Reynolds number was varied from 0 to $9.6{\times}10^{-2}$ and the Rayleigh number from $10^3$ to $5{\times}10^4$. The governing equations were discretized using the finite volume method. From a parametric study, velocity and temperature distributions were obtained and discussed. It is found that vortex flow of mixed convection in rectangular channels can be classified into three flow patterns which depend on Reynolds and Rayleigh numbers, and the regular vortex structure disappears around Rayleigh number $5{\times}10^4$.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.06a
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• pp.210-215
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• 2005

A three-dimensional numerical simulation is performed to investigate on a low Reynolds number mixed convection in a horizontal rectangular channel with the upper part cooled and the lower part heated uniformly. The three-dimensional governing equations are solved using a finite volume method. For convective term, the central differencing scheme is used and for the pressure correction, the PISO algorithm is used. Solutions are obtained for A=4, Pr=0.72, 10, 909, the Reynolds number ranging from $2.1{\times}10^{-2}$ to $1.2{\times}10^{-1}$, the Rayleigh number is $3.5{\times}10^4$. It is found that vortex roll structures of mixed convection in horizontal rectangular channel can be classified into three roll structures which affected by Prandtl number and Reynolds number.

• Journal of Power System Engineering
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• v.19 no.4
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• pp.36-42
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• 2015

TMixed convective flow in a bottom heated and top cooled rectangular channel can be significantly affected by the channel aspect ratio, Prandtl number, Reynolds number, Rayleigh number and angle of inclination. In such a mixed convection, the flow pattern plays an important role in various technological processes. In this study, a numerical investigation is carried out to explore mixed convection in a three-dimensional rectangular channel with bottom heated and top cooled uniformly. The three-dimensional governing equations are discretized using the finite volume method. In the range of low Reynolds number($0{\leq}Re{\leq}9.6{\times}10^{-2}$), the effects of the aspect ratio($2{\leq}AR{\leq}12$) and Gr/Re are presented and discussed. The longitudinal roll number in the channel is increased with increasing aspect ratio, and the roll number induced, regardless of the aspect ratio number, is even in the range of aspect ratios between 2 and 12, New vortex flow structure containing inclined longitudinal rolls is found, which is affected by aspect ratio and Reynolds number. The ratio Gr/Re is used to check the relative magnitudes of forced and natural convection in the mixed convective flow of high viscous fluid.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.2
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• pp.345-353
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• 1987

An analysis is performed to study flow and heat transfer characteristics of mixed free and forced convection about a sphere. Nonsimilar boundary layer equations which are valid over the entire regime of mixed convection are derived in terms of the mixed convection parameter, Gr/Re$^{2}$, through a dimensional analysis. The transformed conservation equations are solved by a finite difference method for the whole range of mixed convection regime. Numerical results for fluids having the Prandtl number 0.7 and 7 are presented. As the mixed convection parameter increases, the local friction coefficient and local heat transfer coefficient increases as well. For small Prandtl number, the friction coefficient is larger, while for large Prandtl number, the heat transfer coefficient is larger. Natural convection effect on the forced flow is more sensitive for small Prandtl number fluid. Flow separation migrates rearward as an increase in the mixed convection parameter. For small Prandtl number, the buoyancy effect is relatively small so that the flow separation occurs earlier.

• Asian-Australasian Journal of Animal Sciences
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• v.14 no.7
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• pp.910-914
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• 2001

The teat number of a sow plays an important role for weaning pigs and has been utilized in selection of swine breeding stock. Various linear models have been employed for genetic analyses of teat number although the teat number can be considered as a count trait. Theoretically, Poisson error mixed models are more appropriate for count traits than Normal error mixed models. In this study, the two models were compared by analyzing data simulated with Poisson error. Considering the mean square errors and correlation coefficients between observed and fitted values, the Poisson generalized linear mixed model (PGLMM) fit the data better than the Normal error mixed model. Also these two models were applied to analyzing teat numbers in four breeds of swine (Landrace, Yorkshire, crossbred of Landrace and Yorkshire, crossbred of Landrace, Yorkshire, and Chinese indigenous Min pig) collected in China. However, when analyzed with the field data, the Normal error mixed model, on the contrary, fit better for all the breeds than the PGLMM. The results from both simulated and field data indicate that teat numbers of swine might not have variance equal to mean and thus not have a Poisson distribution.

• Proceedings of the Safety Management and Science Conference
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• 2002.05a
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• pp.91-97
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• 2002

In this thesis presents line balancing problems of two-sided and mixed model assembly line widely used in practical fields using genetic algorithm for reducing throughput time, cost of tools and fixtures and improving flexibility of assembly lines. Two-sided and mixed model assembly line is a special type of production line where variety of product similar in product characteristics are assembled in both sides. This thesis proposes the genetic algorithm adequate to each step in tow-sided and mixed model assembly line with suitable presentation, individual, evaluation function, selection and genetic parameter. To confirm proposed genetic algorithm, we apply to increase the number of tasks in case study. And for evaluation the performance of proposed genetic algorithm, we compare to existing algorithm of one-sided and mixed model assembly line. The results show that the algorithm is outstanding in the problems with a larger number of stations or larger number of tasks.

• Journal of the Korea Safety Management & Science
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• v.4 no.2
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• pp.83-101
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• 2002

In this thesis presents line balancing problems of two-sided and mixed model assembly line widely used in practical fields using genetic algorithm for reducing throughput time, cost of tools and fixtures and improving flexibility of assembly lines. Two-sided and mixed model assembly line is a special type of production line where variety of product similar in product characteristics are assembled in both sides. This thesis proposes the genetic algorithm adequate to each step in tow-sided and mixed model assembly line with suitable presentation, individual, evaluation function, selection and genetic parameter. To confirm proposed genetic algorithm, we apply to increase the number of tasks in case study. And for evaluation the performance of proposed genetic algorithm, we compare to existing algorithm of one-sided and mixed model assembly line. The results show that the algorithm is outstanding in the problems with a larger number of stations or larger number of tasks.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1731-1740
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• 1995

Experimental investigations have been made to study the double-diffusive nature of convection of an initially stratified salt-water solution due to heating from below in a rotating cylindrical cavity. The objective is to examine the flow phenomena and the heat transfer characteristics according to the changes in temperature gradient, concentration gradient and rotating velocity of cavity. Thermal and solutal boundary conditions at side wall are adiabatic and impermeable, respectively. The top and bottom plate are maintained each at constant temperature and concentration. The cavity is put into a state of solid body rotation. Like the stationary case, the types of initially-formed flow pattern are classified into three regimes depending on the effective Rayleigh number and Taylor number; stagnant flow regime, single mixed-layer flow regime and successively formed multi-mixed layer flow regime. At the same effective Rayleigh number, the number of initially-formed mixed layer and its growth rate decrease as the effect of rotation increases. The temperature and concentration profiles are both uniform in each layer due to convective mixing in the layered-flow regime, but look both liner in stagnant flow regime and single mixed-layer flow regime. At the interface between adjacent layers, the temperature changes smoothly but the concentration changes rapidly.