The Transient Electroosmotic Flow of Maxwell Fluids and Heat Transfer in a Parallel Microchannel Using Caputo Fractional Derivative

Abstract

In this work, we consider transient electroosmotic flow of fractional Maxwell fluids model derived for both velocity and temperature in a micro-channel. We use the Poisson-Boltzmann equation to describe the potential electric field applied along the length of the micro-channel. Exact solutions of both velocity and temperature were obtained using Laplace transform combined with finite Fourier sine transform. Due to the complexity of the equations for velocity and temperature, the inverse Laplace transform was obtained using the numerical inversion formula based on Gaver Stehfest’s algorithms. The numerical solutions were simulated with the help of Mathcard software and the graphical results showing the effects of time, relaxation time, electrokinetic width and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameter on the temperature distribution in the microchannel were presented and discussed. The results show that the applied electric field, the electroosmotic force, electrokinetic width, and relaxation time play vital role on the velocity profile in the micro-channel and the fractional parameter can be used to regulate both the velocity and temperature in the micro-channel. The effects of the various influential parameters on both fluid velocity and temperature distribution were found to be useful for the design of microfluidic devices. These devices could be useful for biomedical diagnosis and analysis, for clinical detection of viruses and bacteria in biological processes. Keywords: Caputo fractional derivative, Electro kinetic width, Electroosmotic flow, Heat transfer, Zeta potential,