Results for the time required to melt or freeze a slab or cylinder of a pure substance initially at the fusion temperature and with convection at the surface are presented. The “enthalpy-flow temperature” method of Dusinberre and Eyres is used, and the lumped equations solved on an analog computer. Correlated results are given for the ambient temperature ranges cT/L up to 2, and Nusselt number greater than 1. These represent an extension of the “no-capacity” solutions of London and Seban. The “enthalpy-flow temperature” method involves use of the dependent variables  
H(T)=0+TcdTand
 
φ(T)=0TkdT
and so reduces the essential nonlinearity at the fusion temperature to one easily handled in an analog computer simulation.
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