{
  "id": "2007.10214",
  "version": "v1",
  "published": "2020-07-20T15:54:52.000Z",
  "updated": "2020-07-20T15:54:52.000Z",
  "title": "On the Existence of Logarithmic Terms in the Drag Coefficient and Nusselt Number of a Single Sphere at High Reynolds Numbers",
  "authors": [
    "Yousef El Hasadi",
    "Johan Padding"
  ],
  "comment": "31 pages, 3 Figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "In the beginning of the second half of the twentieth century, Proudman and Pearson (JFM,2(3), 1956, pp.237-262) suggested that the functional form of the drag coefficient of a single sphere subjected to uniform fluid flow consists of a series of logarithmic and power terms of the Reynolds number. In this paper, we will explore the validity of the above statement for Reynolds numbers up to $ 2\\times 10^{5}$, by using a symbolic regression machine learning method.The algorithm is trained by using available experimental data, as well as data from a well-known correlation from the literature.The symbolic regression method finds the following expression for the drag coefficient $C_D = a+\\frac{24}{Re}+f(\\log(Re))$, where $Re$ is the Reynolds number, and the constituents of $f(\\log(Re))$ are integer powers of $\\log(Re)$. Interestingly, the value of $a$ resembles the value of $C_D$, at the point where laminar separation point occurs. We did the same analysis for the problem of heat transfer under forced convection around a sphere, and found that the logarithmic terms of $Re$ and Peclect number $Pe$ play an essential role in the variation of the Nusselt number $Nu$. The machine learning algorithm independently found the asymptomatic solution of Acrivos and Goddard (JFM, 23(2),pp.273-291).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T15:54:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high reynolds numbers",
      "drag coefficient",
      "nusselt number",
      "logarithmic terms",
      "single sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}