Abstract
A new scheme to formulating the Caputo time-fractional model for the flow of Brinkman-type fluid between the plates was introduced by using the generalized laws of Fourier and Fick. Within a channel, free convection flow of the electrically conducted Brinkman-type fluid was considered. A newly generated transformation was applied to the heat and mass concentration equations. The governing equations were solved by the techniques of Fourier sine and the Laplace transforms. In terms of the special function, namely, the Mittag-Leffler function, final solutions were obtained. The entropy generation and Bejan number are also calculated for the given flow. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures and are often quantitatively computed and presented in tables. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases. The regression analysis shows that the variation in the velocity for time parameter is statistically significant.
Highlights
Because of its flexible and special properties, fractional calculus has evolved tremendously nowadays. e noninteger derivatives of all the orders are solved utilizing fractional calculus techniques
Fractional calculus is the extension of the classical calculus which has a history of around three centuries
Fractional calculus has been used for many applications in different areas, such as electrochemistry, ground-level water distribution, electromagnetism, elasticity, diffusion, and heat stream conduction [3,4,5]
Summary
Because of its flexible and special properties, fractional calculus has evolved tremendously nowadays. e noninteger derivatives of all the orders are solved utilizing fractional calculus techniques. Caputo fractional derivatives have been used by Vieru et al [8], Shakeel et al [9], and Ali et al [10] for the flow problems, and some interesting and useful results are obtained. E theory of frictional derivatives has been used by Sheikh et al [19, 20] for the flow problem of non-Newtonian fluids, which give exact solutions. In these articles, they discussed the difference between the two new fractional operators: Atangana–Baleanu and Caputo–Fabrizio. All the physical conditions are met and can be shown in graphs and tables
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