Electro‐osmotic flow of fractional second‐grade fluid with fractional Cattaneo heat flux through a vertical microchannel

Abstract

AbstractThis study investigates the unsteady electro‐osmotic flow (EOF) of a fractional second‐grade fluid through a vertical microchannel with convection heat transfer. The fractional Cattaneo heat flux model will be used to modify the heat equation. The solutions for the velocity and the temperature have been derived by employing the Laplace and finite Fourier sine transforms and their numerical inverses. The results show that at the beginning of the time period, the fractional parameter postpones the movement of the fluid. Furthermore, the results show that at the high values of retardation time (non‐Newtonian case), the required time for the velocity and the flow rate to reach the steady state increases. Moreover, the heat relaxation time reduces the heat transfer until a critical time, and then the effect reverses.