A computational framework for electro-osmotic flow analysis in Carreau fluids using a hybrid numerical scheme

• A novel two-stage exponential integrator is proposed, specifically designed for solving parabolic partial differential equations (PDEs) with high accuracy and stability. • The scheme incorporates compact spatial discretization techniques to achieve high-order accuracy in capturing the spatial variations of electro-osmotic flow in Carreau fluid over flat and oscillatory sheets. • Rigorous analysis of the proposed scheme, demonstrating its consistency and stability in the mean square sense, ensuring reliability in environmental simulations. • The proposed Numerical scheme is highly accurate and attains the predicted order of convergence shown through various examples. • A comparison shows that the proposed scheme consumes almost 50 % less computation time than the traditional scheme. • The continuity equation is effectively managed with first-order schemes, while the momentum, energy, and concentration equations are addressed using the proposed integrator, yielding accurate and consistent results for complex fluid flow scenarios. Developing mathematical models for electro-osmotic flow in non-Newtonian fluids is difficult since fluid mechanics and electrokinetic phenomena are interconnected. Conventional models frequently assume Newtonian behaviour, which is insufficient for accurately representing the complex characteristics of non-Newtonian fluids such as Carreau fluid. The primary objective of this work is to construct a computational scheme for solving the governing equations related to the electro-osmotic flow of Carreau fluid over a stationary sheet. The practicality of the Carreau fluid model for this study lies in its ability to accurately represent the shear-dependent viscosity observed in various biological and industrial fluids. A novel two-stage numerical scheme is introduced for solving the governing time-dependent partial differential equations. The first stage utilizes an exponential integrator, while the second stage employs a Runge-Kutta method. Spatial discretization is achieved using a high-order, accurate compact scheme, which ensures sixth-order spatial accuracy. The stability and convergence of the proposed scheme are rigorously analyzed for both scalar equations and systems of parabolic equations. The framework is applied to the dimensionless governing equations of electro-osmotic flow, with the results validated against existing first- and second-order schemes. The proposed method demonstrates superior accuracy and computational efficiency. The results reveal the influence of key parameters, such as the Weissenberg number, Forchheimer number, and Helmholtz-Smoluchowski velocity, on the flow and temperature profiles. The framework also considers the impact of heat generation, reaction kinetics, and mass diffusivity on thermal and concentration distributions. This work establishes a robust computational approach for solving complex fluid flow problems involving non-Newtonian fluids, such as Carreau fluids, driven by electro-osmotic forces and influenced by magnetic and porous media effects.