An Analytical Solution for the Unsteady Close-Contact Melting by Convective Heating

- Journal title : Transactions of the Korean Society of Mechanical Engineers B
- Volume 24, Issue 3, 2000, pp.450-458
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.22634/KSME-B.2000.24.3.450

Title & Authors

An Analytical Solution for the Unsteady Close-Contact Melting by Convective Heating

Yoo, Ho-Seon;

Yoo, Ho-Seon;

Abstract

This study deals with the unsteady close-contact melting of solid blocks on a flat surface subject to convective heating. Normalizing the model equations in reference to the steady solution successfully leads them to cover constant heat flux and isothermal limits at small and large extremes of the Biot number, respectively. The resulting equations admit a compactly expressed analytical solution, which includes the previous solutions as a subset. Based on the steady solution, the characteristics of close-contact melting can be categorized into constant heat flux, transition, and isothermal regimes, the boundaries of which appear to be nearly independent of the contact force. The unsteady solutions corresponding to Biot numbers in the transition regime show intermediate behaviors between those of the two limits. With a proper approximation, the present solution procedure can cope with the case of variable fluid temperature and heat transfer coefficient. Regardless of imposed conditions, the mean normalized Nusselt number during the unsteady process asymptotically approaches to a constant value as the Biot number comes close to each limit.

Keywords

Close-Contact Melting;Unsteady Analysis;Analytical Solution;Convective Heating;

Language

Korean

References

1.

Moallemi, M. K., Webb, B. W., and Viskanta, R., 1986, 'An Experimental and Analytical Study of Close-Contact Melting,' ASME J. Heat Transfer, Vol. 108, pp. 894-899

2.

Bejan, A., 1994, 'Contact Melting Heat Transfer and Lubrication,' Adv. Heat Transfer, Vol. 24, pp. 1-38

3.

Bejan, A., 1989, 'The Fundamentals of Sliding Contact Melting and Friction,' ASME J. Heat Transfer, Vol. 111, pp. 13-20

4.

Fowler, A. J. and Bejan, A., 1993, 'Contact Melting during Sliding on Ice,' Int. J. Heat Mass Transfer, Vol. 36, pp. 1171-1179

5.

Colback, S. C., Najarian, L., and Smith, H. B., 1997, 'Sliding Temperature of Ice Skates,' American J. Physics, Vol. 65, pp. 488-492

6.

Hong, H. and Saito, A., 1993, 'Numerical Method for Direct Contact Melting in Transient Process,' Int. J. Heat Mass Transfer, Vol. 36, pp. 2093-2103

7.

유호선, 1997, '등온가열에 의한 접촉융해의 초기 과도과정에 대한 근사적 해석해,' 대한기계학회논문집(B), 제21권, 제12호, pp. 17I0-1719

8.

Saito, A., Kumano, H., Okawa, S. and Yamashita, K., 1996, 'Analytical Study on Transient Direct Contact Melting Phenomena,' Trans. of the JAR, Vol. 13, pp. 97-108 (in Japanese)

9.

유호선, 1998, '등열유속에 의한 평판 위 비정상 접촉융해에 대한 근사적 해석해,' 대한기계학회논문집(B), 제22권, 제12호, pp. 1726-1734

10.

유호선, 1999, '열전도가 주도적인 삼차원 접촉융해에 대한 비정상 해석,' 대한기계학회논문집(B), 제23권, 제8호, pp. 945-956

11.

Sparrow, E. M. and Patankar, S. V., 1977, 'Relationship among Boundary Conditions and Nusselt Numbers for Thermally Developed Duct Flows,' ASME J. Heat Transfer, Vol. 99, pp. 483-485

12.

Bejan, A., 1995, Convection Heat Transfer, 2nd Edn., Wiley, New York, pp. 118-121

13.

Taghavi, K., 1990, 'Analysis of Direct-Contact Melting Under Rotation,' ASME J. Heat Transfer, Vol. 112, pp. 137-143