Phase Transformation in a Thin Film with a Moving Boundary and Convective Boundary Conditions
The IUP Journal of Mechanical Engineering, Vol. IX, No. 1, February 2016, pp. 7-24
Posted: 10 Jul 2017
Date Written: July 18, 2016
Modification of thin surface films by focused energy sources and sinks is described by heat and mass transfer equations. Convective boundary conditions are applied and coupled diffusion equations are set up with suitable approximations. The problem is solved for small Stefan numbers. This work uses certain novel methods to bypass this handicap and obtain solutions which can be readily computed. Parametric analysis yields the time scales in this particular problem for heat conduction and for phase transformation velocity. In the case of the spherical model, where a sphere of solid melts or the reverse, the convective boundary conditions are applied and an exact solution is obtained. A comparison is made with the approximate perturbation solution for the coupled heat and mass equations and small non-dimensional parameters obtained for the perturbation solution in terms of the Stefan, Fourier and Biot numbers. When a sinusoidal fluctuating heat source is used as in laser heating the variations are attenuated in the boundary layer. It is shown however that some cases can lead to possible build up of oscillations depending on the values of the parameters, and an estimate of the possible time of oscillation is obtained in the region of 10-12 seconds.
Keywords: Moving boundary problem, Perturbation analysis, Solidification
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