Copyright © 2026 Authors retain the copyright of this article. This article is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

@article{205701,
        author = {Dr. P. Bhargavi},
        title = {Pade-Approximation Approach to 1-D Heat Conduction Moving Boundary Problem in a Slab},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {13},
        number = {1},
        pages = {8275-8279},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=205701},
        abstract = {Problems whose solutions satisfy certain conditions on the boundary are called moving boundary problems, phase change problems, or Stephan Problems. The characteristic feature of these problems is the existence of a continuously moving boundary/interface that moves at a constant rate. Tracking the position and velocity of the moving boundary is an important part of the solution. Moving boundary problems arising in phase-change processes, such as melting and solidification, are commonly modelled using Stefan-type formulations. Exact analytical solutions exist only for simplified cases and typically involve transcendental functions, such as the error function. In this study, a semi-analytical solution for a one-dimensional heat equation with a moving boundary is developed using Pade approximations. The temperature distribution is expressed in a closed rational form by approximating the error function using a Pade approximant. This approach converts the classical transcendental Stefan condition into an algebraic equation, thereby simplifying the evaluation of the moving interface. The proposed method satisfies all boundary and interface conditions and provides accurate temperature and interface predictions with reduced computational effort.},
        keywords = {Stefan problem, moving boundary, heat equation, Pade approximations, phase change, melting.},
        month = {June},
        }