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The Meter model (a four-parameter model) captures shear viscosity–shear stress relationship (S-shaped type) of polymeric non-Newtonian fluids. We devise an analytical solution for radial velocity profile, average velocity, and volumetric flow rate of steady-state laminar flow of non-Newtonian Meter model fluids through a circular geometry. The analytical solution converts to the Hagen–Posseuille equation for the Newtonian fluid case. We also develop the formulations to determine effective viscosity, Reynolds number, and Darcy’s friction factor using measurable parameters as available rheological models do not correctly define these parameters for a given set of flow condition in circular geometry. The analytical solution and formulations are validated against experimental data. The results suggest that the effective Reynolds number and effective friction factor estimated using the proposed formulation help characterize non-Newtonian fluid flow through a circular geometry in laminar and turbulent flows.

The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting the volume concentration of dust particles in fluid dynamics. The governing PDEs of the problem for both phase models are transmuted into nonlinear coupled non-dimensional ODEs by utilizing suitable similarity modifications. The bvp4c technique was utilized in MATLAB script to acquire a graphical representation of the experimental results. This study illustrates the analysis of repercussions of pertinent parameters on non-Newtonian fluid and the dusty phase of fluid. By improving the volume concentration of dust particles and rotating parameters, the axial velocity for both phases depreciates, whereas temperature and transverse velocity for both phases have the opposite behavior. The micro-rotation distribution rises with higher contributions of rotating and material parameters, whereas it decreases against larger inputs of volume concentration of dust particles. The growing strength of the dust volume fraction (ϕd) caused the coefficient of skin friction to decrease along the x direction, and the skin friction coefficient is raised along the y direction.

In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H 1 norm and prove that their accuracy is of O ( τ + h 2 ) and O ( τ min{3–γ s ,2–α q ,2– β } + h 2 ), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.

Many subsurface engineering applications involve radial injection of non‐Newtonian fluids into fractured media, where the displacement efficiency of injected fluids profoundly impacts the injection performance. Despite its importance, how to enhance radial displacement efficiency of non‐Newtonian fluids in rough fractures remains rarely reported. Here, by conducting visualization experiments of shear‐thinning fluids radially displacing silicone oil in a rough fracture, we report a novel transition in displacement patterns from capillary fingering to compact displacement (CD) to viscous fingering with increasing injection rate, which differs from conventional expectations for Newtonian fluids. This transition induces a non‐monotonic variation in displacement efficiency, thereby enabling potential control of displacement performance. We further propose theoretical models to predict the transition and identify the optimal range of flow rate for maximizing displacement efficiency, with model predictions showing good agreement with experimental observations. This work provides guidance for predicting and enhancing displacement efficiency in engineering operations involving shear‐thinning fluids.

Purpose The purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states. Design/methodology/approach The Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC). Findings The impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < Br < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy. Originality/value This study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

The significance of velocity second slip model of non-Newtonian fluid on peristaltic pumping in existence of double-diffusivity convection in nanofluids and induced magnetic field is deliberated. Mathematical modelling of current problem is defined in fixed frame of reference and then abridges under well- known conjecture of long wavelength and low but finite Reynolds number approximation. Precise results of coupled nonlinear partial differential equations are presented. Graphical results exhibit the performance of various supportive parameters. The phenomenon of stream functions with different wave forms is also discussed in detail. The effects of thermal energy, solute concentration, and nanoparticle fraction are also described using graphical representation.

Electroosmotic flow (EOF) has been widely used in various biochemical microfluidic applications, many of which use viscoelastic non-Newtonian fluid. This study numerically investigates the EOF of viscoelastic fluid through a 10:1 constriction microfluidic channel connecting two reservoirs on either side. The flow is modelled by the Oldroyd-B (OB) model coupled with the Poisson–Boltzmann model. EOF of polyacrylamide (PAA) solution is studied as a function of the PAA concentration and the applied electric field. In contrast to steady EOF of Newtonian fluid, the EOF of PAA solution becomes unstable when the applied electric field (PAA concentration) exceeds a critical value for a fixed PAA concentration (electric field), and vortices form at the upstream of the constriction. EOF velocity of viscoelastic fluid becomes spatially and temporally dependent, and the velocity at the exit of the constriction microchannel is much higher than that at its entrance, which is in qualitative agreement with experimental observation from the literature. Under the same apparent viscosity, the time-averaged velocity of the viscoelastic fluid is lower than that of the Newtonian fluid.

In this work, we propose a novel method to quantify flows of inelastic non-Newtonian fluids in porous media based on the energy dissipation rate. Unlike the permeability of a Newtonian fluid with Darcy’s law, the permeability of a non-Newtonian fluid shows complicated behaviors due to non-separable effects of the geometry and rheology. We suggest a simple energy dissipation-based flow characterization method to resolve this problem, employing the concepts of effective viscosity and effective shear rate. These effective quantities can be defined with two flow numbers (the energy dissipation rate coefficient and the effective shear rate coefficient) independent of fluid rheology. New expressions for the permeability of Newtonian and mobility of non-Newtonian fluids were derived for model porous media in this approach. We show that the mobility (a ratio of permeability to viscosity) of a non-Newtonian fluid for a given porous media can be factored into the permeability of Newtonian fluid and the effective viscosity, exactly the same as in case of a Newtonian fluid. The proposed quantification method was validated through example problems of flows using numerical simulations (1) in two-dimensional (2D) transverse fibrous porous media (quadratic and hexagonal), (2) flows in three-dimensional (3D) regularly packed beds with spheres (faced-centered cubic and body-centered cubic), and (3) finally randomly distributed unidirectional fibers in 2D. The suggested method can quantitatively assess tortuous path in porous electrode for electrolyte transport and in the secondary oil recovery, offering the potential to optimize performance and efficiency in these applications.

This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonian fluid owing to the action of the cells’ membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonian fluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonian fluid model than for the Newtonian one.

Flow-type landslide, such as debris-flow, often exhibits high velocity and long run-out distance. Simulation on it benefits the propagation analysis and provides solution for risk assessment and mitigation design. Previous studies commonly used shallow water assumption to simulate this phenomenon, ignoring the information in vertical direction, and the Bingham model to describe constitutive law of non-Newtonian fluid can cause numerical divergence unless necessary parameter is defined. To address the issue, the full Navier–Stokes equations are adopted to describe the dynamics of the flow-type landslides. Additionally, the general Cross model is employed as the constitutive model, which ensures the numerical convergence. Rheological parameters are introduced from the Bingham model and the Mohr–Coulomb yield criterion. Subsequently, the governing equations incorporating the modified rheological model are numerically built in the smoothed particle hydrodynamics (SPH) framework and implemented into the open-source DualSPHysics code. To illustrate its performance, the 2010 Yohutagawa debris-flow event in Japan is selected as a case study. Parameters regarding the debris magnitude, i.e., the front velocity and section discharge, were also well analyzed. Simulated mass volume and deposition depth at the alluvial fan are in good agreements with the in situ observation. On the basis of the results, the developed method performs well to reproduce the debris-flow process and also benefits the analysis of flow characteristics, affected area for risk assessment and mitigation design.