• International Journal of Aeronautical and Space Sciences
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• v.18 no.3
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• pp.395-402
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• 2017

The local heat transfer and total pressure drops of developed turbulent flows in the ribbed rectangular convergent/divergent channels with ${\Lambda}/V-shaped$ ribs have been investigated experimentally. The channels have the exit hydraulic diameter ($D_{ho}$) to inlet hydraulic diameter ($D_{hi}$) ratios of 0.67 for convergence and 1.49 for divergence, respectively. The ${\Lambda}/V-shaped$ ribs with three different flow attack angles of $30^{\circ}$, $45^{\circ}$, and $60^{\circ}$ are manufactured with a fixed rib height (e) of 10 mm and the ratio of rib spacing (S) to height (e) of 10 on the walls. Thermal performances of the ribbed rectangular convergent/divergent channels are compared with the smooth straight tube under identical pumping power. The results show that the flow attack angle of $45^{\circ}$ with ${\Lambda}-shaped$ rib has the greatest thermal performance at all the Reynolds numbers studied in the convergent channel; whereas, the flow attack angle of $60^{\circ}$ with V-shaped rib has the greatest thermal performance over Reynolds number of 30,000 in the divergent channel.

• Journal of Gifted/Talented Education
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• v.15 no.2
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• pp.59-76
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• 2005

We examined the relations between the score of the divergent thinking in mathematical (Mathematical Creative Problem Solving Ability Test; MCPSAT: Lee etc. 2003) and non-mathematical situations (Torrance Test of Creative Thinking Figural A; TTCT: adapted for Korea by Kim, 1999). Subjects in this study were 213 eighth grade students(129 males and 84 females). In the analysis of data, frequencies, percentiles, t-test and correlation analysis were used. The results of the study are summarized as follows; First, mathematically gifted students showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than regular students. Second, female showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than males. Third, there was statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for middle students was r=.41 (p<.05) and regular students was r=.27 (p<.05). A test of statistical significance was conducted to test hypothesis. Fourth, the correlation between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students was r=.11. There was no statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students. These results reveal little correlation between the scores of the divergent thinking in mathematical and non-mathematical situations in both mathematically gifted students. Also but for the group of students of relatively mathematically gifted students it was found that the correlations between divergent thinking in mathematical and non-mathematical situations was near zero. This suggests that divergent thinking ability in mathematical situations may be a specific ability and not just a combination of divergent thinking ability in non-mathematical situations. But the limitations of this study as following: The sample size in this study was too few to generalize that there was a relation between the divergent thinking of mathematically gifted students in mathematical situation and non-mathematical situation.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.103-112
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• 2005

This paper is designed to characterize the concept of flexibility of mind and analyze relationship between flexibility of mind and divergent thinking in view of mathematical problem solving. This study shows that flexibility of mind is characterized by two constructs, ability to overcome fixed mind in stage of problem understanding and ability to shift a viewpoint in stage of problem solving process, Through the analysis of writing test, we come to the conclusion that students who overcome fixed mind surpass others in divergent thinking and so do students who are able to shift a viewpoint.

• Research in Mathematical Education
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• v.15 no.1
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• pp.69-79
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• 2011

Based on the work of Haylock (cf [Haylock, D. W. (1987). A framework for assessing mathematical creativity in schoolchildren. Educ. Stud. Math. 18(1),59-74]) a mathematical creativity test containing items of two categories overcoming fixation and divergent thinking has been developed for Bengali medium school students with sample size 262. The items measuring divergent thinking are found highly internally consistent and there is a significant correlation between overcoming fixation and divergent thinking. Study of the factorial validity of the test by Thursstone's centroid method gives satisfactory result. Validity coefficient of the test with teachers' rating, alpha reliability and test-retest reliability of the test are also found satisfactory.

• Research in Mathematical Education
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• v.13 no.3
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• pp.181-195
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• 2009

Students' approaches to mathematical problem solving vary greatly with each other. The main objective of the current study was to compare students' performance with different thinking styles (divergent vs. convergent) and working memory capacity upon mathematical problem solving. A sample of 150 high school girls, ages 15 to 16, was studied based on Hudson's test and Digit Span Backwards test as well as a math exam. The results indicated that the effect of thinking styles and working memory on students' performance in problem solving was significant. Moreover, students with divergent thinking style and high working memory capacity showed higher performance than ones with convergent thinking style. The implications of these results on math teaching and problem solving emphasizes that cognitive predictor variable (Convergent/Divergent) and working memory, in particular could be challenging and a rather distinctive factor for students.

• The Mathematical Education
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• v.46 no.3
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• pp.293-302
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• 2007

In this paper, we review definition and concept of mathematical creativity. A couple of criteria have established for perspectives in mathematical creativity, The first is specific domain(mathematics) vs general domain(creativity) and the second is process(thinking process) vs outcome(divergent production). By these criteria, four perspectives have constructed : mathematics-thinking process approach(McTd), mathematics-divergent production approach(MctD), creativity-thinking process approach(mCTd), creativity-divergent production approach(mCtD). When mathematical creativity is researched by the specific reason and particular focus, an appropriate approach can be chosen in four perspectives.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.10
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• pp.773-778
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• 2015

The local heat transfer and pressure drop of developed turbulent flows in convergent/divergent channels with square axial cross-sectional areas were experimentally investigated to improve the channel design, such as a gas turbine cooling system. Square convergent/divergent channels with one ribbed wall were manufactured with a fixed rib height e of 10 mm and a ratio of rib spacing p to height e of 10. The measurement was conducted for Reynolds numbers from 15,000 to 89,000. Convergent, divergent, and straight channels with ratios $D_{ho}/D_{hi}$ of 0.75, 1.33, and 1.0, respectively, are considered. Of the three channel types, the ribbed divergent channel was found to produce the best thermal performance under identical flow rate, pumping power, and pressure loss conditions.

• Bulletin of the Korean Chemical Society
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• v.31 no.7
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• pp.1835-1836
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• 2010

• Bulletin of the Korean Chemical Society
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• v.18 no.11
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• pp.1192-1195
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• 1997

A divergent approach to 2-(hydroxymethyl)pyrrolidine-3,4-diols has been studied with 1,4-dideoxy-1,4-imino-D-arabinitol (D-AB1), a potent glycosidase inhibitor. D-AB1 was efficiently synthesized from 2,3-epoxyalcohol 6a in overall 11% yield.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.2
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• pp.187-205
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• 2014

The global price of oil, which is both finite and limited in quantity, has been rising steadily because of the increasing requirements for energy in both developing and developed countries. Furthermore, regulations have been strengthened across all industries to address global warming. Many studies of hull resistance, propulsion and operation of ships have been performed to reduce fuel consumption and emissions. This study examined the design parameters of the propeller boss cap fin (PBCF) and hub cap for 6,000TEU container ships to improve the propulsion efficiency. The design parameters of PBCF have been selected based on the geometrical shape. Computational fluid dynamics (CFD) analysis with a propeller open water (POW) test was performed to check the validity of CFD analysis. The design of experiment (DOE) case was selected as a full factorial design, and the experiment was analyzed by POW and CFD analysis. Analysis of variance (ANOVA) was performed to determine the correlation among design parameters. Four design alternatives of PBCF were selected from the DOE. The shape of a propeller hub cap was selected as a divergent shape, and the divergent angle was determined by the DOE. Four design alternatives of PBCF were attached to the divergent hub cap, and the POW was estimated by CFD. As a result, the divergent hub cap with PBCF has a negative effect on the POW, which is induced by an increase in torque coefficient. A POW test and cavitation test were performed with a divergent hub cap with PBCF to verify the CFD result. The POW test result showed that the open water efficiency was increased approximately 2% with a divergent hub cap compared to a normal cap. The POW test result was similar to the CFD result, and the divergent hub cap with the PBCF models showed lower open water efficiency. This was attributed to an increase in the torque coefficient just like the CFD results. A cavitation test was performed using the 2 models selected. The test result showed that the hub vortex is increased downstream of the propeller.