Exact closed-form solutions of some Stefan problems in thermally heterogeneous cylinders

• Stefan problem is recast as asymptotically stable differential-difference equations.
• Differential-difference equations are reduced by Clarkson–Kruskal's direct method.
• Difference equation reductions and compatible interfacial evolutions are obtained.
• New integrable Stefan problems in heterogeneous cylinders are realized.
• Their exact solutions are obtained in closed-form.

It will be shown that one can obtain from a differential-difference equation reformulation exact closed-form solutions to a class of Stefan problems in cylinders with inverse-square thermal heterogeneity: in particular, new interfacial evolutions were discovered for this class of problems, which Gottlieb's approach [Appl. Math. Lett. 15 (2002) 167–172] had not been able to produce, alongside their associated exact closed-form temperature distributions.