Diffusion phenomenon for natural convection flow of classical Hartmann problem due to a cylindrical tube by generalized Fourier's theories: A Fractional analysis

Qasim Ali, Kamel Al-Khaled, M. Ijaz Khan*, Sami Ullah Khan, Ali Raza, Mowffaq Oreijah, Kamel Guedri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


The classical Hartmann flow problem is still interesting and novel due to its applications in MHD generators, plasma physics, power systems, etc. Owing to such importance in mind, this investigation explores the natural convection flow of viscous fluid following the Hartmann flow phenomenon due to a cylindrical tube. The heat transfer characteristics with diffusion phenomenon have been taken into consideration. The classical problem is further extended by countering the magnetic force impact. The fractional framework based on the Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) is performed. The closed-form solutions are attained with Laplace as well as finite Hankel transforms. Further, the obtained results are stated as a combination of G-functions of Lorenzo and Hartley. The particular cases for the obtained simulations have been performed. The role of flow parameters governing the flow is graphically attributed.

Original languageEnglish
Article number2350104
JournalInternational Journal of Modern Physics B
Issue number11
Publication statusPublished - Oct 19 2022
Externally publishedYes


  • Fourier's law
  • Hartmann flow
  • fractional derivatives
  • integral transforms
  • natural convection

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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