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

Abstract

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.