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Numerical Modeling of Time-Fractional Phase-Change Problems
Azrak, Sura
Azrak, Sura
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29.232-2025.10a Sura Azrak.pdf
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Description
A Master of Science thesis in Mathematics by Sura Azrak entitled, “Numerical Modeling of Time-Fractional Phase-Change Problems”, submitted in July 2025. Thesis advisor is Dr. Youssef Belhamadia. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
Abstract
Phase-change problems, such as melting and solidification, are central to numerous natural and industrial applications. Mathematically, phase-change problems involve heat-diffusion equations in the solid and liquid regions, coupled with an interfacial condition that balances latent heat release with the motion of the solid-liquid interface, together with prescribed initial and boundary conditions. However, classical models often fail to capture the memory-dependent behavior observed in complex materials. This thesis proposes a time-fractional extension of the phase-change problem using Caputo derivatives to incorporate memory effects into the modeling of phase-change processes. A one-domain enthalpy-based formulation is derived, allowing for smooth phase transitions without explicit interface tracking. The resulting model is solved numerically using a finite difference scheme and the L1 approximation for the Caputo derivative. Several simulations are presented, demonstrating the impact of fractional order on thermal behavior and validating the model’s consistency with classical results as the order approaches one.