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A fractional study with Newtonian heating effect on heat absorbing MHD radiative flow of rate type fluid with application of novel hybrid fractional derivative operator

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Arab Journal of Basic and Applied Sciences 2023年第1期30卷 482-495页

作者： Rehman, Aziz Ur Hua, Song Riaz, Muhammad Bilal Awrejcewicz, Jan Xiange, Sun Department of Mathematics University of Management and Technology Lahore Lahore Pakistan School of Electronics and Information Yangtze University Jingzhou China Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon Department of Automation Biomechanics and Mechatronics Lodz University of Technology Lodz Poland Artificial Intelligence Research Institute Yangtze University Jingzhou China

The present work examines the analytical solutions of the mathematical fractional Maxwell fluid model near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimensional form. For the sake of better rheology of rate type fluid, developed a fractional model by applying the new definition of Constant Proportional Caputo (CPC) fractional derivative operator that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler functions for velocity and temperature, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, some limiting models such as ordinary Newtonian model had been recovered from fractional model. It is also analyzed that for Newtonian heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity and energy distribution. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models. © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.

关键词： Analytical solution CPC derivative heat transfer Laplace transformation physical parameters system parameters

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