Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition

Abstract:

Article Preview

The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.

Info:

Periodical:

Edited by:

Bale V. Reddy, Shishir Kumar Sahu, A. Kandasamy and Manuel de La Sen

Pages:

145-148

Citation:

R. Chiba, "Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition", Applied Mechanics and Materials, Vol. 627, pp. 145-148, 2014

Online since:

September 2014

Authors:

Export:

Price:

$38.00

* - Corresponding Author

[1] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Clarendon, Oxford, (1986).

[2] F. Civan, C.M. Sliepcevich, Limitation in the apparent heat capacity formulation for heat transfer with phase change, Proc. Oklahoma Acad. Sci. 67 (1987) 83-88.

[3] R. Chiba, Application of differential transform method to thermoelastic problem for annular disks of variable thickness with temperature-dependent parameters, Int. J. Thermophys. 33 (2012) 363-380.

[4] P.L. Ndlovu, R.J. Moitsheki, Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins, Commun. Nonlinear Sci. Numer. Simul. 18 (2013).

[5] M.J. Jang, C.L. Chen, Y.C. Liu, Two-dimensional differential transform for partial differential equations, App. Math. Comput. 121 (2001) 261-270.

[6] S.H. Chang, I.L. Chang, A new algorithm for calculating two-dimensional differential transform of nonlinear functions, Appl. Math. Comput. 215 (2009) 2486-2494.

DOI: https://doi.org/10.1016/j.amc.2009.08.046

[7] M.J. Jang, Y.L. Yeh, C.L. Chen, W.C. Yeh, Differential transformation approach to thermal conductive problems with discontinuous boundary condition, Appl. Math. Comput. 216 (2010) 2339-2350.