Flow, heat and mass transfer of three-dimensional fractional Maxwell fluid over a bidirectional stretching plate with fractional Fourier's law and fractional Fick's law

摘要

This paper investigates the flow, heat and mass transfer of fractional Maxwell fluid over a bidirectional stretching sheet, and research is carried out for the three-dimensional case. By analogy with the constitutive equation of fractional Maxwell fluid, fractional derivative is introduced into Fourier's law and Fick's law. Meanwhile, the magnetic field and chemical reaction are considered. Furthermore, the stretching speeds are not only power-law-dependent on time, but also power-law-dependent on the distance of each space direction. Combining with L1-algorithm, a newly finite difference method is developed to solve the governing equations, and convergence of the method is verified by constructing a numerical example. The influences of various physical parameters on velocity, temperature and concentration are analyzed through three-dimensional graphs. The velocity fractional parameter presents an interesting effect on the velocity. When the powers of each space direction coincide, the smaller the velocity fractional parameter is, the thinner the velocity boundary layer is. On the contrary, larger velocity fractional parameter results in decreasing velocity at first and then increasing for different powers of each space direction. Furthermore, fractional Fourier's law leads to more obvious heat transfer phenomena, which is similar with the effect of fractional Fick's law on the mass transfer. (C) 2019 Elsevier Ltd. All rights reserved.