Outward spherical solidification of a superheated melt with time dependent boundary flux
- 61 Downloads
Abstract
Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.
Keywords
Boundary Condition Temperature Distribution Grid Point Finite Difference Efficient MethodPreview
Unable to display preview. Download preview PDF.
References
- 1.S.C. Gupta, Axisymmetric solidification in a long cylindrical mold, Applied Scientific Research 42 (1985) 229–244.Google Scholar
- 2.R.I. Pedroso and G.A. Domoto, Inward spherical solidification solution by the method of strained coordinates, Int. J. Heat Mass Transfer 16 (1973) 1037–1043.Google Scholar
- 3.R.I. Pedroso and G.A. Domoto, Perturbation solutions for spherical solidification of saturated liquids, ASME J. Heat Transfer 95 (1973) 42–46.Google Scholar
- 4.D.S. Riley, F.T. Smith and G. Poots, The inward solidification of spheres and circular cylinders, Int. J. Heat Mass Transfer 17 (1974) 1507–1516.Google Scholar
- 5.C.L. Huang and Y.P. Sih, A perturbation method for spherical and cylindrical solidification, Chem. Eng. Sci. 30 (1975) 897–906.Google Scholar
- 6.G.B. Davis and J.M. Hill, A moving boundary problem for the sphere, IMA J. Appl. Math. 29 (1982) 99–111.Google Scholar
- 7.K. Stewartson and R.T. Waechter, On Stefan's problem for spheres, Proc. Roy. Soc. Lond.A 348 (1976) 415–426.Google Scholar
- 8.A.M. Soward, A unified approach to Stefan's problem for spheres and cylinders, Proc. Roy. Soc. Lond.A 373 (1980) 131–147.Google Scholar
- 9.P. Grimado and B.A. Boley, A numerical solution for the symmetric melting of spheres, Int. J. Num. Methods in Eng. 2 (1970) 175–188.Google Scholar
- 10.Y.F. Lee and B.A. Boley, Melting of an infinite solid with a spherical cavity, Int. J. Engng. Sci. 11 (1973) 1277–1295.Google Scholar
- 11.B.A. Boley, A method of heat conduction analysis of melting and solidification problems, J. math. Phys. 40 (1961) 4300–313.Google Scholar
- 12.R.M. Furzeland, A comparative study of numerical methods for moving boundary problems, J. Inst. Maths. Applics. 26 (1980) 411–429.Google Scholar
- 13.W.D. Murray and F. Landis, Numerical and machine solutions of transient heat conduction problems involving melting or freezing, Part I — Method of analysis and sample solutions, ASME J. Heat Transfer 81 (1959) 106–112.Google Scholar
- 14.H.L.R.M. Levy, A.J. Lockyer and R.G.C. Arridge, The coating of fibres, Int. J. Heat Mass Transfer 21 (1978) 435–443.CrossRefGoogle Scholar
- 15.H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, 2nd Edn., Clarendon Press, Oxford (1959).Google Scholar
- 16.S.C. Gupta and A.K. Lahiri, Heat conduction with a phase change in a cylindrical mould, Int. J. Engng. Sci. 17 (1979) 401–407.CrossRefGoogle Scholar
- 17.M. Abramovitz and Z.A. Stegun, Handbook of Mathematical Functions, Dover, New York (1972).Google Scholar