Insight into the Natural Convection Flow Through a Vertical Cylinder Using Caputo Time-Fractional Derivatives

  • Nehad Ali Shah
  • Thanaa Elnaqeeb
  • I. L. Animasaun
  • Yasir Mahsud
Original Paper


The variation in temperature distribution with time for the case of the fractional model which models the flow of fluid through a vertical cylinder is considered. This article provides an insight into the natural convective flow of a viscous fluid through a vertical heated cylinder using the fractional differential equation with Caputo derivatives. Analytical solutions for temperature and velocity functions were obtained using Laplace transform and finite Hankel integral transform methods. Stehfest’s algorithm was used to obtain the inverse Laplace transforms. Numerical simulations and graphical illustrations were carried out in order to analyze the influence of the time-fractional derivative on the transport phenomenon. The significant difference between the fractional fluid flow and ordinary fluid at various time (\( t \)) is unraveled. At the initial time, the flow of fractional fluid is faster than the ordinary fluid.


Natural convection flow Vertical cylinder Laplace and finite Hankel transforms Caputo time-fractional derivative 


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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Abdus Salam School of Mathematical SciencesGC University LahoreLahorePakistan
  2. 2.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  3. 3.Department of Mathematical SciencesFederal University of TechnologyAkureNigeria

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