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

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.