A time-fractional model of free convection electro-osmotic flow of Casson fluid through a microchannel using generalized Fourier and Fick’s law

Abstract

Electro-osmotic flow through a micro-channel has vast applications in the modern world, that is, in different fields like biochemistry and the biomedical industry. The present paper investigates the electro-osmotic flow of Casson (non-Newtonian) fluid through a vertical microchannel. The effect of heat and mass transfer is also studied in this fluid flow. The above physical phenomenon is modeled in the terms of partial differential equations. The derived system of the differential equations is non-dimensionalized using some appropriate dimensionless variables. Moreover, the dimensionless classical system is fractionalized using generalized Fourier and Fick’s law. The definition of the Caputo derivative is used for generalization. Laplace and Fourier’s techniques are applied jointly to obtain the exact solutions of the velocity, temperature, and concentration distributions. Furthermore, the effect of various physical parameters like Casson fluid parameter, fractional parameter, zeta potential parameter, thermal and mass Grashof number, Schmidt and Prandtl number on the velocity, temperature, and concentration distributions is shown and discussed graphically. Moreover, the results show that the velocity increases by raising the values of electrokinetic parameter k. This increase in velocity is the result of the fact that the larger value of k exhibits the thinner Electric Double Layer (EDL), which enhances the flow with the larger velocity gradient.