{
  "abstract": "Cold-to-hot heat transfer is a conspicuous non-equilibrium feature of rarefied cavity flows and is often used to judge whether a continuum closure captures higher-order transport. We examine what such agreement actually establishes. The exact heat-flux balance shows that the fourth-order contribution enters only through the divergence of the composite tensor (A_{ij}=R^{\\mathrm{cl}}*{ij}+Δδ*{ij}/3). A compactly supported Airy construction yields an infinite-dimensional family of symmetric divergence-free perturbations that preserve the flux-side wall trace. A two-dimensional-physical, three-dimensional-velocity (2D3V) description also leaves the transverse component (A_{zz}) unobserved. Heat flux therefore cannot uniquely identify the underlying fourth-order state. We test the consequences using direct simulation Monte Carlo (DSMC) ensembles and independent regularized 13-moment (R13) and regularized 26-moment (R26) solutions at two rarefaction levels. Counter-gradient transport and the dominant tensorial channel persist under changes in grid and particle number, whereas the local scalar fourth moment and the spatial organization of the counter-gradient region are more sensitive. A finite-particle-corrected fourth-moment audit shows that more than 95% of the resolved R26--DSMC composite-tensor discrepancy at the higher rarefaction lies in the discrete divergence-null space, whereas projected sampling noise hides only about half of its energy. R26 captures the circulation and heat-flux direction more closely than R13, yet the remaining differences concentrate in the wall and corner layers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27892",
  "author_total": 1,
  "authors": [
    {
      "name": "Ehsan Roohi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jmg6y643q90r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27892",
  "fulltext_url": null,
  "id": "7jmg6y643q90r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27892",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7214181737",
  "pdf_url": "https://arxiv.org/pdf/2609.27892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jmg6y643q90r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27892"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity",
  "title_text": "What does anti-Fourier heat-flux agreement validate? Observability of the fourth-order closure state in a rarefied lid-driven cavity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/7jmg6y643q90r",
  "venue": "arXiv",
  "versions": []
}