Fractional Stefan problems exhibiting lumped and distributed latent-heat memory effects

Area of Science:

• Thermodynamics
• Phase Transitions
• Mathematical Modeling

Background:

• Fractional Stefan problems model phase transitions with memory effects.
• Latent heat accumulation is a key factor in melting and solidification processes.
• The nature of the phase transition interface (sharp vs. diffuse) impacts memory representation.

Purpose of the Study:

• To investigate how memory of latent-heat accumulation is recorded in fractional Stefan melting problems.
• To compare memory representation in sharp-interface versus diffuse-interface models.
• To determine conditions under which sharp- and diffuse-interface models are equivalent.

Main Methods:

• Analysis of fractional Stefan melting problems.
• Mathematical modeling of phase transitions.
• Comparison of memory "lumping" in sharp interfaces versus memory "distribution" in diffuse interfaces.

Main Results:

• Memory of latent-heat accumulation is "lumped" in interface speed history for sharp interfaces.
• Memory is "distributed" throughout the liquid phase for diffuse interfaces.
• Sharp- and diffuse-interface models are equivalent only in the absence of memory.

Conclusions:

• The representation of latent-heat memory is fundamentally different in sharp- versus diffuse-interface models.
• Memory effects are critical in distinguishing between these modeling approaches.
• Absence of memory is a necessary condition for the equivalence of sharp and diffuse interface models in Stefan problems.