International Journal of Science, Engineering and TechnologyAuthors: Dr.P.Naga Santoshi
Abstract: The mathematical modeling of coupled heat and mass transfer is undergoing rapid transformation through fractional calculus, advanced lattice Boltzmann methods, machine learning surrogates, and generalized continuum theories. This review synthesizes peer reviewed research from 2025–2026. Key advances include fractional order models capturing memory effects with velocity enhancements up to 20%, a multi speed lattice Boltzmann method achieving ≤1.5% error across ballistic to diffusive phonon transport, and machine learning models reaching R² > 0.9996 for temperature field prediction. Pore scale simulations identify optimal porosity ranges, while generalized thermoelastic diffusion models predict stress reductions exceeding 70%. These developments enable next generation thermal management, energy storage, and manufacturing design.
