Solidification of a Finite Medium Subject to a Periodic Variation of Boundary Temperature

Abstract

The motion of a solid-liquid interface in a finite one-dimensional medium, subject to a fluctuating boundary temperature, is analyzed. The fluctuations are assumed to be periodic. The solution method involves a semi-analytic approach in which, at any given time, the spatial temperature distributions are represented in infinite series. The effect of the solid, liquid Stefan numbers and the unsteady boundary temperature variation is investigated. The results showed a retrograde motion of the solidification front for large liquid Stefan numbers.

An approximate analytical solution of one-dimensional phase change problems in a finite domain

“…It is seen from the figure that more time is required to cover an interface position with the increase in liquid Stefan number. This implies that the movement of interface decreases with the increase in liquid Stefan number, which is in complete agreement with the result of Dursunkaya and Nair[10].…”

“…Many useful accounts of analytical methods are given by [5][6][7]. Dursunkaya and Nair [8,10] applied the spectral approach for the solution of solidification problem in finite domains with constant and time dependent boundary conditions. Rai and Singh [9] presented a numerical solution for a two phase Stefan problem in finite domain.…”

Accuracy of the two-iteration spectral method for phase change problems

“…An analytical series solution of the solidification problem in a semi-infinite medium is obtained using the approach of [8,9]. Unlike [8,9], the iterative integration of the resulting integro-differential equation is obtained analytically, and the result enabled a direct comparison with the existing analytical solution.…”

“…doi:10.1016/j.apm.2005.07.006 accounts of the methods used. The spectral approach was used in the solution of solidification problems in finite domains with constant and time dependent boundary temperatures [8,9]. After fitting a Fourier series for the spatial variation of temperatures, the resulting differential equation for the interface location was solved numerically and the temperature distributions were computed.…”

Heat Transfer Model for Thin Solidified Material in Continuous Casting

“…22,23) These studies suggest their applicability to the general boundary condition. However, the conventional method requires significant cost; implicit solution method and/or tolerable numerical integrations for each basis function are necessary.…”