• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.3
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• pp.294-300
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• 1983

The purpose of this study is to investigate the radiant emission characteristics of diffuse equi-lateral trapezoid groove cavity for the case of uniform surface temperature. The theoretically developed results for the apparent emissivity are presented and the values of apparent emissivity for the trapezoid groove cavity were compared with those of the V-groove cavity. In the experimental part of this study, the test models were manufactured from 100x 100x 15mm copper plates on which the equi-lateral trapezoid cavities were grooved. The inclined angles of the groove were 30,45 and 60 degrees and the ratio of groove depth to base surface width varied from 1 to 5 for each inclined angle. As a result of this work, it was found that the trapezoid groove cavity was more general form of V-groove and the apparent emissivity of trapezoid groove cavity was greater than that of V-groove cavity. The resulting equation for the apparent emissivity in the trapezoid groove cavity was valid for the angles greater than 40 degrees.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.565-571
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• 2001

The objective of this study was to investigate the characteristics of air flow and heat transfer caused by trapezoid rods array in impinging air jet system. In this study, trapezoid rods have been set up on front of flat plate to act as a turbulence promoter. Local Nusselt numbers were determined as a function of three parameters: (a) the space from rods to heating surface(C=1, 2, 4mm), (b) the pitch between each rods(P=30, 40, 50mm), (c) the distance from nozzle exit to flat plate(H/B=2, 6, 10). And this research compared the above with the experiment without trapezoid rods. As a result, heat transfer performance was best under the condition of C=1mm and as the pitch is 30mm. In this case, maximum rate of heat transfer augmentation is about 1.9 times greater compared to that without trapezoid rods.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.260-267
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• 2001

The objective of this study was to investigate the characteristics of jet flow and heat transfer caused by trapezoid rods array in impinging jet system. In this study, trapezoid rods have been set up in front of flat plate to serve as a turbulence promoter. The bottom width of trapezoid rod was W=4, 8mm and oblique angle were $80^{\circ}$. The space from rods to the heating surface was C=1, 2, 4mm, the pitch between each rods was P=30, 40, 50mm, and the distance from nozzle exit to flat plate was H=100, 500mm. This results were compared with the case without trapezoid rods. As a result, when rods are installed in front of the impinging plate, the acceleration of the jet flow and the eddies due to the rods seem to contribute to the heat transfer enhancement. Among test conditions, the heat transfer performance was best for the condition of W=8mm, C=1mm, P=30mm and H/B=10. The maximum heat transfer rate is about 1.9 times larger than that without trapezoid rods.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.9
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• pp.904-913
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• 2001

The objective of this study was to investigate the characteristics of jet flow and heat transfer caused by trapezoid rods array in impinging jet system. In this study, trapezoid rods have been set up in front of flat plate to serve as a turbulence promoter. The bottom width of trapezoid rod was W=4, 8 mm and oblique angle were 80$^{\circ}$. The space from rods to the heating surface was C=1, 2, 4 mm, the pitch between each rods was P=30, 40, 50 mm, and the distance from nozzle exit to flat plate was H=100, 500 mm. This results were compared with the case without trapezoid rods. As a result, when rods are installed in front of the impinging plate, the acceleration of the jet flow and the eddies due to the rods seem to contribute to the heat transfer enhancement. Among test conditions, the heat transfer performance was best for the condition of W=8 mm, C=1 mm, P=30 mm and H/B=10. The maximum heat transfer rate is about 1.9 times larger than that without trapezoid rods.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.633-639
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• 2004

In this paper using integral representations for n-time differentiable mappings, we establish new generalizations of certain Ostrowski and Trapezoid type inequalities by using fairly elementary analysis.

• Journal of Ocean Engineering and Technology
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• v.15 no.1
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• pp.7-11
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• 2001

In this paper, trapezoid sections and prominence sections were examined to improve the performance of floating breakwater in long waves. The linear potential theory is used and the boundary element method with a matching boundary is employed for numerical computation. The effects of the side slope of the trapezoid section and the geometry ratio of the prominence section on the floating breakwater were examined. It was found that trapezoid sections show lower transmission coefficients than the rectangular sections in the long wave range. In prominence sections the size of the sides are more important than the size of the top. Proper choices of the pontoon type geometry may move the local minimum point of the wave transmission coefficient toward the longer wave ranges and improve the performance of the floating breakwater in the long wave range for a given wave period.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1659-1666
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• 2001

The objective of this study was to investigate the characteristics of air flow and heat transfer caused by trapezoid rods array in impinging air jet system. Trapezoid rods have been set up on front of flat plate to act as a turbulence promoter. Local Nusselt numbers were determined as a function of three parameters : (a) the space from re(Is to heating surface(C=1, 2, 4mm), (b) the pitch between each rods(P=30, 40, 50mm), (c) the distance from nozzle exit to flat plate(H/B=2, 6, 10). The measurements were compared with those of the experiment without trapezoid rods. As a result, when rods are installed in front of the impinging palate, the acceleration of the flow and the eddies due to the rods seem to contribute to the heat transfer enhancement. Heat transfer performance was best under the condition of C=1mm and as the pitch is 30mm. The maximum rate of heat transfer augmentation is about 1.9 times greater compared to that without trapezoid rods.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.247-264
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• 2021

The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.67-84
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• 2003

A quadrature rule for the finite Hilbert Trasnform via trapezoid type inequalities is obtained . Some numerical experiments for different divisions of the interval [a, b] are also presented.