Using a scale/analytical analysis approach, we model phase change (melting) for pure materials which generate constant internal heat generation for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by internal heat generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry.

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... analysis also consider constant heat flux (in a cylindrical geometry).We show the time scales in which conduction and convection heat transfer dominate. NOMENCLATURE a, b, c -constants c 1 , c 2 -constants c p -specific heat (kJ/kg K) g -gravitational constant (m/s 2 ) h f -latent heat (kJ/kg) k -thermal conductivity (W/m K) q -internal heat generation (W/m 3 ) q -surface heat flux (W/m 2 ) r -radial distance (m) s -distance from CL to phase front (m) St -Stefan number (c p T/ h f ) t -time (s) T -temperature (K) T m -melting temperature (K) u, w -velocity components (m/s) z -spatial components (m) Greek -thermal diffusivity (m 2 /s) -coefficient of thermal expansion (1/K) z -convection thermal boundary layer thickness (m) -dynamic viscosity (kg m/s) -kinematic viscosity (m 2 /s) -density (kg/m 3 )