Computer simulation of transient electroosmotic flow of Oldroyd-B fluid in a micro-channel with Caputo fractional derivative and heat transfer: Computer simulation of transient electroosmotic flow

Adamu Garba Tahiru; Ali Muhammad Baba; Muhammed Abdulhameed; Dauda Gulibur Yakubu

doi:10.54117/aytfa348

Authors

Adamu Garba Tahiru Sa'adu Zungur University
Ali Muhammad Baba Abubakar Tafawa Balewa University
Muhammed Abdulhameed Federal Polytechnic, Bauchi
Dauda Gulibur Yakubu Abubakar Tafawa Balewa University

DOI:

https://doi.org/10.54117/aytfa348

Keywords:

Fractional derivative, Electro-kinetic width, Micro-channel, Oldroyd-B fluid, Transient electroosmotic flow

Abstract

The Oldroyd-B fluid electroosmotic flow is described using the Caputo fractional derivative in a microchannel, where the Poisson-Boltzmann equation is used to describe the potential electric field applied along the length of the microchannel. By combining the Laplace transform with the classical method of partial differential equations and the finite Fourier sine transform, the component of the velocity profile of the equation is analytically solved. Laplace and finite Fourier sine transforms are used to solve the temperature component analytically. The inverse Laplace transform is obtained by the virtue of the Gave Stehfest technique, and Mathcad software is used for numerical simulation. As a memory effect, we see that the fluid velocity and temperature distribution diminish with increasing values of the fractional-order parameters. The graphical results are discussed in detail, demonstrating the impacts of time, relaxation time, retardation time, electro-kinetic width, and fractional parameters on the fluid velocity as well as the effects of time and fractional parameters on the microchannel temperature distribution. These are examined, and discovered that they are helpful for designing microfluidic devices. These tools could be helpful for diagnosing and analyzing biomedical conditions as well as for the clinical detection of bacteria and viruses in biological processes.

Author Biographies

Adamu Garba Tahiru, Sa'adu Zungur University

Department of Mathematical Sciences, Bauchi State University Gadau, Bauchi, Nigeria
Ali Muhammad Baba, Abubakar Tafawa Balewa University

Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria
Muhammed Abdulhameed, Federal Polytechnic, Bauchi

School of Science and Technology, Federal Polytechnic Bauchi, Nigeria
Dauda Gulibur Yakubu, Abubakar Tafawa Balewa University

Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria

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Computer simulation of transient electroosmotic flow of Oldroyd-B fluid in a micro-channel with Caputo fractional derivative and heat transfer