Abstract
In this article, the influence of a magnetic field is studied on a generalized viscous fluid model with double convection, due to simultaneous effects of heat and mass transfer induced by temperature and concentration gradients. The fluid is considered over an exponentially accelerated vertical plate with time-dependent boundary conditions. Additional effects of heat generation and chemical reaction are also considered. A generalized viscous fluid model consists of three partial differential equations of momentum, heat, and mass transfer with corresponding initial and boundary condition. The idea of non-integer order Caputo time-fractional derivatives is used, and exact solutions for velocity, temperature, and concentration in terms of Wright function and function of Lorenzo–Hartley are developed for ordinary cases. Graphical analysis of flow and fractional parameters is made by using computational software MathCad, and discussed. The results obtained are also in good agreement with the published results from the literature. As a result, it is found that temperature and fluid velocity can be enhanced for smaller values of fractional parameters.
Highlights
Over the last few years, different publications on exact solutions of Newtonian and non-Newtonian fluids via fractional derivatives approach have been published
They particularized their results for ordinary Casson fluid, viscous fluid with fractional derivative, and ordinary viscous fluid
Magnetic field effect is studied on fractional model of viscous fluid with double convection due to simultaneous effects of heat and mass transfer
Summary
Over the last few years, different publications on exact solutions of Newtonian and non-Newtonian fluids via fractional derivatives approach have been published. Khan et al.[1] introduced Caputo time-fractional derivative in the constitutive model of a generalized Casson fluid past an infinite flat plate oscillating in its own plane. They particularized their results for ordinary Casson fluid, viscous fluid with fractional derivative, and ordinary viscous fluid. Khan and Zaman[2] used the idea of fractional derivatives and solved the viscoelastic second grade fluid problem over an impulsive plate in the presence of a uniform magnetic field and porous medium. Few other important attempts among them are those made by Qi and Jin,[4] Qi and Xu,[5] Wang and Zhao,[6] Wang et al.,[7] Mahmood et al.,[8] Fetecau et al.,[9,10] Jamil et al.,[11,12] Khan et al.,[13] and Kamran et al.[14]
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