• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1541-1547
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• 2001

The non-dimensional fin length for optimum heat loss from a thermally asymmetric rectangular fin is represented as a function of the ratio of the bottom surface Biot number to the top surface Biot number, fin tip surface Biot number and the non-dimensional fin width. Optimum heat loss is taken as 98% of the maximum heat loss. For this analysis, three dimensional separation of variables method is used. Also, the relation between the ratio of the bottom surface Biot number to the top surface Biot number and the ratio of the right surface Biot number to the left surface Biot number is presented.

• International Journal of Air-Conditioning and Refrigeration
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• v.9 no.2
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• pp.94-101
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• 2001

Fin effectiveness and efficiency of a thermally asymmetric rectangular fin are represented as a function of non-dimensional fin length, width, fip tip surface Biot number and the ratio of fin bottom surface Biot number to top surface Biot number. For this analysis, three dimensional separation of variables method is used. One of the results shows that fin effectiveness can be increased or decreased depending on the fin length as the fin tip surface Biot number increases while fin efficiency decreases without depending on that as the fin tip surface Biot number increases.

• Journal of the Korean Society of Propulsion Engineers
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• v.7 no.1
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• pp.1-9
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• 2003

The rectangular profile annular fin with fixed volume is optimized using 2-dimensional analytic method. For a base boundary condition, convection from fluid within the pipe to the inside wall of the pipe and conduction from the inside wall of the pipe to the fin base are considered. Heat loss from the fin tip radius is not ignored. The maximum heat loss, the optimum fin tip radius and the optimum fin half thickness corresponding to the maximum heat loss are presented as a function of fin base radius, Biot number over the fin surface and Biot number within the pipe. Results show 1) the maximum heat loss increases as both Biot number over the fin surface and Biot number within the pipe increase and as fin base radius decreases 2) the optimum fin thickness increases as Biot number within the pipe decreases or as fin base radius and Biot number over the fin surface increase.

• Journal of Industrial Technology
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• v.22 no.B
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• pp.21-26
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• 2002

The non-dimensional heat loss from a thermally asymmetric triangular fin is investigated as a function of a ratio of upper and lower surface Biot numbers (Bi2/Bi1), the non-dimensional fin length and tip surface Biot number using the two-dimensional separation of variables method. The effect of fin tip surface Biot number on the variation of the non-dimensional temperature along the sloped upper and lower surfaces for the thermally asymmetric condition is presented. The relationship between the non-dimensional fin length and the fin tip surface Biot number for equal amount of heat loss is also discussed as well as the relationship between upper surface Biot number and tip surface Biot number for equal amount of heat loss.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.1
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• pp.66-73
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• 2002

Fin effectiveness and efficiency of a thermally asymmetric triangular fin are represented as a function of the ratio of fin lower surface Biot number to upper surface Biot number and the non-dimensional fin length. For this analysis, two dimensional separation of variables method is used. When fin effectiveness is 2 and efficiency is 90%, the relationship between the non-dimensional fin length and the ratio of fin lower stir(ace Biot number to upper surface Biot number is shown. The relationship between the non-dimensional fin length and the upper surface Biot number for the same condition is also presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.3 no.4
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• pp.173-180
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• 1979

Temperature distriburion in a hollow chlinder has been analyzed mathematically. Unsteady condition considered assumed a constant heat flux input from the inside. The results are compared with experimental results of surface temperature rise of a gun barrel during continuous firing. Their agreements are acceptable. Effects of various dimensionless parameters on the surface temperature rise are discussed. For small Biot numbers, the external survface temperature approaches more rapidly to the steady temperature. Temperature difference between internal and external surfaces becomes greater for small Biot number. Steady solution assumed that the gas temperature inside the cylinder varies periodically. Relative amplitude and phase angles between the gas temperature and the internal or external surface temperature are obtained. Phase angles become smaller for large radiancy of gas temperature variation, small external Biot number, or large internal biot number. Relative amplitudes become samller as radiancy of gas temperature variation and internal Biot number become smaller. or external Biot number becomes larger. The solution obtained in this paper can be applied to gun barrels, heat pipes used in heat excangers, and reciprocation engines.

• International Journal of Air-Conditioning and Refrigeration
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• v.13 no.3
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• pp.145-151
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• 2005

A thermally asymmetric straight rectangular fin is analysed and optimized using the two-dimensional separation of variables method. The optimum heat loss is presented as a function of bottom to top Biot number ratio, fin base length and top Biot number. Decreasing rate of the optimum fin length with the increase of the fin base length is listed. The optimum fin tip length is shown as a function of bottom to top Biot number ratio, fin base length and tip to top Biot number ratio. One of the results shows that the optimum heat loss and the actual optimum fin length decrease while the optimum fin tip length increases as the fin base length increases.

• Journal of the Korean Society of Propulsion Engineers
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• v.3 no.3
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• pp.16-24
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• 1999

Performance of the trapezoidal fins having different upper side slope is investigated by the three dimensional analytic method. It is shown that one equation can be used to analyse the trapezoidal fins having different upper side slope by adjusting the slope factor only. The performances for these fins are represented as a function of the non-dimensional fin length, fin width, Biot number and the slope factor when the remaining variables are fixed arbitrarily. One of the results is that the fin effectiveness increases as Biot number, the non-dimensional fin width and the slope factor decrease and as the non-dimensional fin length increases in the case of Bi $\leq$ 0.1 but the trend of the fin shape effect on the effectiveness is somewhat irregular for higher Biot number(i.e. Bi = 0.3).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.153-163
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• 2000

The non-dimensional convective heat losses from each surface are investigated as a function of the non-dimensional fin length, width and the ratio of upper surface Biot number to bottom surface Biot number (Bi2/Bi1) using the three-dimensional separation of variables method. Heat loss ratio in view of each surface with the variation of Bi2/Bi1 is presented. The variation of the non-dimensioal temperare profile along the fin center line for a thermally asymmetric conditions is also presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.109-120
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• 2002

The dimensionless heat loss from a modified asymmetric rectangular fin is investigated as a function of the fin top and tip Biot numbers using the two-dimensional separation of variables method. A rectangular fin is modified by attaching the wing on the top side of the fin. Fin effectiveness and efficiency with the variation of the location of the wing and the width of the wing are presented. The relationship between top surface Biot number and bottom surface Biot number as well as the relationship between the dimensionless wing height and the location of the wing for equal amount of heat loss is also discussed.