This study develops a comprehensive predictive mathematical modelling framework for analyzing heat transfer and phase change phenomena in sustainable buildings. The work integrates multiple aspects of thermal behaviour, including heating and cooling loads, ground temperature distribution, periodic heat transfer through walls, roofs, and windows, as well as the effects of ventilation, furnishings, and auxiliary heating. Special emphasis is given to solidification and phase change processes, which are critical in applications such as concrete hydration, phase change materials (PCMs), and waste solidification for sustainable construction. Governing equations are formulated using thermodynamic principles, heat conduction theory, and response functions, and solved analytically and numerically through finite element analysis. Computational investigations demonstrate how temperature gradients, solar radiation, and soil depth influence building energy performance, while solidification modelling highlights the relationship between cooling rates, interface dynamics, and material strength development. The proposed framework provides valuable predictive insights for optimizing material selection, improving energy efficiency, and enhancing durability in green building design. Overall, this research bridges building physics, thermal energy storage, and materials science, offering engineers and architects a robust tool for advancing sustainable construction technologies.
Jitendra Kumar (Thu,) studied this question.