Open Access

ARTICLE

High Accuracy Simulation of Electro-Thermal Flow for Non-Newtonian Fluids in BioMEMS Applications

Umer Farooq¹, Nabil Kerdid^2,*, Yasir Nawaz³, Muhammad Shoaib Arif ⁴

1 College of Mathematical Sciences, Harbin Engineering University, Harbin City, 150001, China
2 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh, 11623, Saudi Arabia
3 Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan
4 Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

* Corresponding Author: Nabil Kerdid. Email:

(This article belongs to the Special Issue: Applications of Modelling and Simulation in Nanofluids)

Computer Modeling in Engineering & Sciences 2025, 144(1), 873-898. https://doi.org/10.32604/cmes.2025.066800

Received 17 April 2025; Accepted 02 July 2025; Issue published 31 July 2025

Abstract

In this study, we proposed a numerical technique for solving time-dependent partial differential equations that arise in the electro-osmotic flow of Carreau fluid across a stationary plate based on a modified exponential integrator. The scheme is comprised of two explicit stages. One is the exponential integrator type stage, and the second is the Runge-Kutta type stage. The spatial-dependent terms are discretized using the compact technique. The compact scheme can achieve fourth or sixth-order spatial accuracy, while the proposed scheme attains second-order temporal accuracy. Also, a mathematical model for the electro-osmotic flow of Carreau fluid over the stationary sheet is presented with heat and mass transfer effects. The governing equations are transformed into dimensionless partial differential equations and solved by the proposed scheme. Simulation results reveal that increasing the Helmholtz–Smoluchowski velocity by 400% leads to a 60%–75% rise in peak flow velocity, while the electro-osmotic parameter enhances near-wall acceleration. Conversely, velocity decreases significantly with higher Weissenberg numbers, indicating the Carreau fluid’s elastic resistance and increased magnetic field strength due to improved Lorentz forces. Temperature rises with the thermal conductivity parameter , while higher reaction rates diminish concentration and local Sherwood number values. The simulation findings show the scheme’s correctness and efficacy in capturing the complicated interactions in non-Newtonian electro-osmotic transport by revealing the notable impact of electrokinetic factors on flow behaviour. The proposed model is particularly relevant for Biological Micro-Electro-Mechanical Systems (BioMEMS) applications, where precise control of electro-thermal transport in non-Newtonian fluids is critical for lab-on-a-chip diagnostics, drug delivery, and micro-scale thermal management.

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