Numerical methods for predicting melting through the gap applied to the one-dimensional Stefan problem using Taylor series

Abstract

There is always a gap in melting process in the contact surfaces of two materials. The gas trapped in the gap can inhibit heat transfer and cause the contact resistance. The purpose of the study was to determine the effect of the gap to the melting rate. Numerical methods applied to the one-dimensional Stefan problem using a Taylor series expansion is used to calculate the melting rate and the influence of the material properties of the melt rate. The result is a greater temperature difference between the inlet temperature (To) to the melting temperature (T m) caused the melting speed difference Δu will be larger, the smaller of the melting time difference Δt. The greater of Stefan number will cause melting speed difference Δu greater. The small value of latent heat (C) and density (ρ) will cause the small energy requirements for melting causing the Δu a large, otherwise the small value of thermal conductivity (k) will lead to small Δu so that the ratio of the value of k/ρC is the variable values of Δu.

Numerical solution of Stefan problem with variable space grid method based on mixed finite element/finite difference approach

“…Different numerical methods and their use for different types of problems are systematized by Minkowycz et al (2006). Esen and Kutluay (2004), Mennig and Özişik (1985), Furzeland (1980), Rizwan-uddin (1999), Savović and Caldwell (2003), Singh et al (2011), Vitorino et al (2010), Irawan et al (2013) and Reutskiy (2011) report various solutions of Stefan problems and include linear, exponential and periodical variation of the surface temperature or the flux with time.…”