In this work, we aim to develop a mathematical model for capillary filling dynamics of electromagnetohydrodynamic flow of non-Newtonian fluids. An axially applied electric field and a transverse magnetic field are considered to elucidate the electromagnetohydrodynamic transport through the microcapillary. Assuming a non-Newtonian power-law obeying fluids, we analyze the transient evolution of the electromagnetohydrodynamic capillary positions by considering the magnitude of the total force balance via finite volume-based numerical formalism. We have highlighted the various rheological regimes in the horizontal capillary through a scaling analysis. For the Newtonian fluids, corresponding inviscid linear Washburn regime is also analyzed and compared with the power-law obeying fluids. Furthermore, we have also derived closed-form analytical expressions for the electromagnetohydrodynamic velocity, pressure gradient, and transient evolution of the capillary positions by using couple stress parameter model to characterize the fluid rheological behaviors. We perform a comparison test of the coupled stress parameter model with the results from the literature for a similar set of fluid rheological parameters. The comparison results are found to be in good agreement.

No abstract

No abstract

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non‐Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in‐house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.

This work presents theoretical and numerical studies related to micromixing phenomena using two different shapes of microchannel systems (i.e., X-and Y-shaped, respectively). In this study, we consider a system that consists of a primary fluid, an aqueous phase (Fluid A), and a secondary fluid (distributed phase), Rhodamine B, in water (Fluid B). In this study, a two-dimensional closed-form generalized analytical model is developed and solved using the method of separation variables to understand the fluid flow mixing behaviour under the influence of a convective-diffusive mass transport process. In addition, numerical simulations are also performed by solving the continuity,