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<p>We revisit the classical problem of fully developed Darcy–Brinkman flow through a tube with elliptic cross section. Building upon the exact velocity field originally derived by Narasimhacharyulu and Pattabhiramacharyulu (Proc. Indian Acad. Sci. Sect. A 87:79–83, 1978), we find, for the first time, an exact series expression for the Poiseuille number in this regime. Our results match the earlier Ritz-based approximations and are in close agreement with the finite-element solutions presented here.</p>

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Revisiting Darcy–Brinkman Flow Through an Elliptic Tube

  • 期刊论文

  • 发表日期：

    2025年12月7日

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  • André Borries Lopes,
  • Mohammad Erfan Fahim Far,
  • Vinícius Coutinho da Silva

摘要

We revisit the classical problem of fully developed Darcy–Brinkman flow through a tube with elliptic cross section. Building upon the exact velocity field originally derived by Narasimhacharyulu and Pattabhiramacharyulu (Proc. Indian Acad. Sci. Sect. A 87:79–83, 1978), we find, for the first time, an exact series expression for the Poiseuille number in this regime. Our results match the earlier Ritz-based approximations and are in close agreement with the finite-element solutions presented here.