{
  "abstract": "In this work, the Maxwell--Cattaneo--Vernotte (MCV) equation is used to model the one-dimensional hyperbolic Stefan problem in the limit of a small Stefan number (Ste $\\ll$ 1). The solutions are approximated with perturbation series expansions using a reformulation in which time is expressed as a function of the solid-liquid interface position. The first proposed solution is derived in a framework that considers diffusive heat transfer at the phase change interface, for analytic tractability. Two rectification strategies are proposed to address the asymptotic divergence present in this formulation: a rescaled inner solution which is then combined with the outer solution to yield a composite solution, and size-dependent thermo-physical system parameters for better capture of hyperbolic effects at the phase change interface. The resulting interface profiles exhibit a characteristic parabolic-like shape, consistent with diffusive Stefan problem findings, with pronounced early-time hyperbolic effects at larger thermal relaxation times. Parametric studies are done over three pertinent variables in the dimensionless system: the Stefan number ($\\mathrm{Ste}$), the dimensionless thermal relaxation time ($\\widetilde τ$), and the thermal diffusivity ($α$). The studies suggest that model error scales with the Stefan number in accordance with the theoretical truncation error of the perturbation expansion. Additionally, larger values of $\\widetilde τ$ amplify early-time hyperbolic effects, thereby increasing model error, while larger $α$ extends the relative temporal domain over which these hyperbolic effects remain significant, also corresponding to an increase in model error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12102",
  "author_total": 3,
  "authors": [
    {
      "name": "Matthew Van Ham"
    },
    {
      "name": "Minghan Xu"
    },
    {
      "name": "Samuel Huberman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24a6dn6m9bzyc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12102",
  "fulltext_url": null,
  "id": "24a6dn6m9bzyc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12102",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2206|Heat Transfer and Numerical Methods"
    ]
  ],
  "openalex": "W7168388856",
  "pdf_url": "https://arxiv.org/pdf/2607.12102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24a6dn6m9bzyc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2607.12102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Analytical and numerical solutions to the non-diffusive Stefan problem",
  "title_text": "Analytical and numerical solutions to the non-diffusive Stefan problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/24a6dn6m9bzyc",
  "venue": "arXiv",
  "versions": []
}