Modelling heat and mass transfer in electro-osmosis flow of williamson nano-fluids using a hybrid scheme

• A hybrid computational scheme combining an exponential integrator and the Runge-Kutta method is developed to solve time-dependent partial differential equations for the electro-osmosis flow of Williamson nanofluids. • A high-order compact numerical scheme is proposed for spatial discretization, providing fourth or sixth-order accuracy in capturing the dynamics of electro-osmotic flow with heat and mass transfer. • The stability and accuracy of the scheme are validated through consistency and stability analysis, ensuring the reliability of the numerical solution. • The scheme is applied to a mathematical model of electro-osmosis flow, with key parameters such as Helmholtz–Smoluchowski velocity influencing the velocity profile and fluid behaviour. • Simulation results demonstrate the scheme's effectiveness, revealing the impact of nanoparticle concentration and Helmholtz–Smoluchowski velocity on electro-osmotic flow and heat transfer in microfluidic channels. This paper presents a computational scheme for solving time-dependent partial differential equations (PDEs) arising from the study of electro-osmosis flow of Williamson nano-fluids, which is significant for optimizing microfluidic and biomedical applications. The scheme employs a two-stage approach: the first stage modifies the time integrator using an exponential time integration technique. In contrast, the second stage implements the second-order Runge-Kutta method. This combination utilizes the efficacy of exponential integrators for stiff equations and the reliability of the Runge-Kutta method for time stepping. The stability of the scheme is examined using a scalar PDE as a benchmark. In addition to the time integrator, spatial discretization is performed using a high-order compact scheme, providing fourth or sixth-order accuracy for space-dependent terms. The mathematical model demonstrates that increasing Helmholtz–Smoluchowski velocity enhances fluid velocity, which is crucial for improving electrokinetic performance. This study's findings have potential applications in designing advanced lab-on-a-chip devices for efficient fluid transport in microchannels.