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.

中文翻译：

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Hankel变换对圆管内自由对流流动的分形表征及协同效应

尽管已经用不同的横截面（例如椭圆锥、矩形或方形管道和三角形板）研究了瞬态自由对流的热传递，但没有探索通过分数阶微积分方法在正弦条件下对自由空间中的圆柱体进行的分析研究。本手稿介绍了圆柱体的分数建模，以观察瞬态自由对流在正弦边界条件下的传热。分数化数学模型通过 Hankel 和 Laplace 变换通过两种类型的分数阶微积分方法求解，称为 Atangana-Baleanu 和 Caputo-Fabrizio 微分算子。为了了解特定几何形状（即圆柱体）的隐藏作用，为了热相互作用效应，圆柱体的控制方程已被耦合。在文献中，已经通过 Mittage-Leffler 函数探索了浓度、温度和速度的解析解。基于嵌入的流变学参数，如普朗特数 (Pr)、施密特数 (Sc)、热格拉肖夫数 (Gr) 和质量格拉肖夫数 (Gc) 的传热比较研究已通过 Atangana-Baleanu 和Caputo-Fabrizio 微分算子。