Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through Hankel transform

Although heat transfer by transient free convection has been investigated with different cross sections such as elliptical cones, rectangular or square ducts, and triangular plates, none of the analytical study of a circular cylinder in free space via fractional calculus approaches with sinusoidal conditions is explored. This manuscript presents fractional modeling of a circular cylinder to observe the heat transfer by transient free convection flow subject to the sinusoidal boundary conditions. The fractionalized mathematical model is solved via Hankel and Laplace transforms through two types of fractional calculus approaches called Atangana–Baleanu and Caputo–Fabrizio differential operators. The governing equations of the circular cylinder have been coupled for the sake of thermally interacting effects for knowing the hidden role of a particular geometry, viz., circular cylinder. In the literature, the analytic solutions for concentration, temperature, and velocity have been explored by means of Mittage–Leffler functions. The comparative investigation of heat transfer based on embedded rheological parameters such as the Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gc) has been depicted as graphs via Atangana–Baleanu and Caputo–Fabrizio differential operators.