The combined influence of magnetic field, electro-osmotic flow (EOF), and pressure gradient on the unsteady magnetohydrodynamic fluid flow through a parallel microchannel is investigated. The Burger's liquid model is used for the fractional partial differential equation, which allows us to study the behavior of viscoelastic liquid velocity profile in the parallel microchannel. The Laplace transform (LT) in concert with the Fourier cosine transform are used to obtain the analytical solution of the velocity profile. Furthermore, using the method of separation of variables, the energy equation, Joule heating, energy dissipation, and electromagnetic effects are calculated to obtain the temperature within the microchannel. The influence of some relevant parameters like heat transfer, temperature distribution, Hartmann number (Ha), and Brinkman number (Br) on fluid flow velocity are presented graphically and discussed. The results obtained show that temperature decreases with Ha and Br of the transverse electric field for slip flow. Close to the middle of the microchannel, fluid flow velocity increases with decrease in the delay time parameter value and increase in the Burger's parameter value, while the opposite trend is found for the velocity near to the middle of the microchannel. In addition, Burger's liquid is quite general, such that Oldroyd-B, Maxwell, and Newtonian liquids are readily obtained as limiting cases. The study is significant in the application fields of chemical analysis and biological analysis, drug delivery, bacteria detection, and some others.

No 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,