Abstract
Unsteady convective flows, over an infinite, vertical, heated, circular cylinder is investigated by considering the generalized Fourier's law of the thermal process. The generalized constitutive equation of thermal flux is a partial fractional differential equation based on the generalized time-fractional derivative with Mittag–Leffler kernel, namely the generalized Atangana–Baleanu derivative. Closed forms of the analytical solutions for the temperature and velocity fields, expressed with Bessel and Struve functions, are determined using the Laplace transform and the Weber–Dirichlet transform. The ordinary case corresponding to classical Fourier's law is also obtained. Numerical simulations, obtained with the Mathcad software, are carried out and graphically illustrated to analyze the heat transfer and fluid motion. The influence of the fractional orders of the time-derivative and of the Prandtl and Grashof numbers on the fluid temperature and velocity is studied.
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