Analog and Digital Computer Solutions

London and Seban (L8) introduced the method of lumped parameters in melting-freezing problems, whereby the partial differential equation is converted into a difference-differential equation by differencing with respect to the space variable. The resulting system of ordinary differential 

Other passive network solutions are given by Hlinka and Paschkis (H8). Otis (01) employs the Landau transformation for the problem of an ablating slab with uniform initial temperature and specified heat fluxes at the front and back faces, 

The variable coefficient is eliminated from the first term on the right-hand side of this equation by defining a new dimensionless time variable,  

The moving boundary has now been eliminated and the problem reduced to that of solving the heat conduction equation for a nonmelting solid with internal heat absorption, corresponding to the last term of Eq. (284). This system is then differenced with respect to the space variable and solved on a passive analog system. 

Baxter (B3) uses an enthalpy-flow temperature method, due originally to Dusinberre (D5, D6) and Eyres et al. (E4), whereby the movingboundary effect is reduced to a property variation. To begin with, the melting of a slab of finite thickness initially at the fusion temperature is considered. At the surface of the melt, which is of the same density as the solid, a heat transfer boundary condition is applied. The technique takes into account latent heat effects by allowing the specific heat to become infinite at the fusion temperature in such a way that 

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