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A computational method is employed to solve heat transfer and entropy generation within a circular pipe. The thermal boundary condition assumes a constant wall temperature, while viscosity is taken to be dependent on temperature. A power-law type shear-thinning fluid is utilized in the analysis, with sinusoidal vibration applied horizontally perpendicular to the flow direction. Temperature distributions across the pipe are illustrated. Additionally, the entropy generation rate over the entire fluid volume under vibration was examined, comparing the results between steady flow and vibrational flow for both types of fluids. It was found that radial mixing is more pronounced in non- Newtonian fluids as vibration increases the strain rate, which is higher for low Reynolds numbers. The research provides a quantitative analysis of heat transfer and entropy generation for both Newtonian and shear-thinning fluids at different Reynolds numbers. It was observed that the effectiveness of superimposed vibrational flow is limited, especially for low Reynolds numbers and flow behavior index characteristic of shear-thinning fluids. [ABSTRACT FROM AUTHOR]

The investigation of blood flow into curved arteries is fascinating and essential to prevent the advancement of vascular disease. Motivated by electro-kinetic manipulation, gold nanoparticles, and their size applications, a mathematical model is developed to explain blood flow, entropy generation, and electro-kinetic energy conversion (EKEC) efficiency in curved arterial flow. To make this study more realistic, a patient-specific overlapped stenosis condition and non-Newtonian (power-law fluid) blood flow model have been considered. The effects of a magnetic field, external heating, and chemical reactions are also included. The Stone's strongly implicit scheme has been considered to solve the system of non-linear partial differential equations (PDE's) in the" MATLAB" software. In this numerical investigation, an error tolerance of 10 − 6 has been considered for every iteration step under Stone's scheme. The significance of various physical parameters, such as nanoparticle volume fraction (m), their size (dp), magnetic field intensity (M), inverse Debye length ( κ ¯ ), flow behavior index (Sc), heat source (H), and chemical reaction parameter (ξ) on the blood flow velocity, temperature, concentration, EKEC efficiency, and entropy generation have been explained graphically. This study also developed stream function contours to describe flow trapping patterns. The findings of this study conclude that the blood flow EKEC efficiency reduces with the presence of nanoparticles and stenosis in the artery. In addition, both flow velocity and entropy enhance by adopting large-size nanoparticles instead of small diametric nanoparticles. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries with WSS profiles, by which the severity of these conditions can be reduced. [ABSTRACT FROM AUTHOR]

We first study the existence and uniqueness of a positive self-similar solution of the 2D boundary-layer equations of an incompressible viscous power-law fluid when the external flow is accelerating, and then we derive the bounds of the wall shear stress rate. For shear-thickening fluids, we show that the matching with the external flow occurs at a finite distance. Furthermore, we also investigate the asymptotic behaviour at infinity of positive solutions in the case of shear-thinning fluids. [ABSTRACT FROM AUTHOR]

We investigate the flow dynamics within an elastic tube transporting a power-law fluid, where the tube is subject to a specified external forcing in the form of a progressive traveling wave. The oesophagus is cylindrical in shape and exhibits linear elastic properties. The flow is creeping, and the long wavelength and low Reynolds number approximations are employed for a solution. The relationship between the pressure distribution within the oesophagus and the radial variation of the tube characterizes the behavior of the tube. Findings reveal that the elasticity and the variations in the applied dilating forcing amplitude substantially impact pressure resulting from sinusoidal wave forcing. Notably, even a nominal increase in the inward radial force amplitude for dilatant fluid results in significant pressure changes compared with Newtonian fluid. We also observe a notable distinction between time-averaged volume flow rate and velocity in pseudo-plastic and dilatant forms. Our study also identifies that the radial velocity experiences either attenuation or enhancement due to the fluid's shear thickening and thinning characteristics. Moreover, our research uncovers a novel dimension by highlighting that in shifting from pseudo-plasticity to dilatancy, the fluid requires higher pressure to propel the bolus toward the hiatus. This observation has important implications, suggesting that feeding a more dilatant fluid to patients with pre-diagnosed swallowing disorders, such as sliding hiatus hernia, is not advisable, fearing increased pressure. [ABSTRACT FROM AUTHOR]

In this work, a numerical study is conducted to analyze the spreading dynamics of an insoluble and non-diffusive surfactant through the Marangoni convection mechanism on the surface of a deep layer of a shear thickening fluid, whose behavior follows the power-law fluid rheological model. The momentum and convective–diffusion equations are non-dimensionalized and solved numerically by an implicit finite-difference scheme. The dynamic of the physical problem depends on dimensionless parameters that control the decay of the temporal variations in the surfactant concentration: the Reynolds number R e , the power index n , and ɛ is the ratio between the wave amplitude and the mean surfactant concentration. The main findings show that opposite to shear-thinning fluids, shear-thickening fluids require less time to reach the uniform condition in the surfactant distribution due to a lower response to the inertia of the fluid; this time is even less than that needed for Newtonian fluids. Besides, both types, pseudoplastic and dilatant fluids, showed a similar response when varying the Reynolds number; as this parameter increases, the temporal decay of the surfactant concentration on the fluid surface increases while the distance over which the fluid motion is diffused towards the bottom of the fluid layer decreases. [ABSTRACT FROM AUTHOR]

A computational method is employed to solve heat transfer and entropy generation within a circular pipe. The thermal boundary condition assumes a constant wall temperature, while viscosity is taken to be dependent on temperature. A power-law type shear-thinning fluid is utilized in the analysis, with sinusoidal vibration applied horizontally perpendicular to the flow direction. Temperature distributions across the pipe are illustrated. Additionally, the entropy generation rate over the entire fluid volume under vibration was examined, comparing the results between steady flow and vibrational flow for both types of fluids. It was found that radial mixing is more pronounced in non-Newtonian fluids as vibration increases the strain rate, which is higher for low Reynolds numbers. The research provides a quantitative analysis of heat transfer and entropy generation for both Newtonian and shear-thinning fluids at different Reynolds numbers. It was observed that the effectiveness of superimposed vibrational flow is limited, especially for low Reynolds numbers and flow behavior index characteristic of shear-thinning fluids.

The current study presents a computational investigation of mixed convective heat transfer in a square enclosure containing power‐law fluid. An active flow modulator is employed in the form of a flat plate with negligible thickness, and the mixed convection is achieved through clockwise rotation of the plate. The rotation of the plate is modeled by incorporating a moving mesh technique. The solution is then obtained by applying the Finite Element Technique under the arbitrary Lagrangian–Eulerian framework. Numerical validation is performed with contemporary research studies consisting of rotating plates to justify the accuracy of the present study. The study is conducted at constant Prandtl number Pr = 1.0 and Reynolds number Re = 500 while varying the power‐law index (0.6 ≤ n ≤ 1.4) and the Richardson number (0.1 ≤ Ri ≤ 10.0). The results have been presented in terms of the flow and thermal fields, spatially averaged Nusselt number, spatially averaged power consumption by the plate, and the velocity and temperature profile in the enclosure. The numerical findings indicate that a higher Richardson number encourages heat transfer. For the shear‐thinning fluid, a 37% thermal augmentation is observed in comparison to the Newtonian fluid at Ri = 10. However, in the case of shear‐thickening fluid, thermal performance was reduced by 21.13%. Small thermal oscillations are observed in naturally dominated mixed convection for shear‐thinning fluids, but none are observed for shear‐thickening or Newtonian fluids. In addition, the findings demonstrate that the flow modulator has a positive impact on heat transfer for the shear‐thickening fluids (n > 1) and an adverse effect for the shear‐thinning fluids (n < 1). Furthermore, the power consumption decreases as Ri increases, and it becomes negative beyond Ri = 1.0 due to the increase in natural convection strength. [ABSTRACT FROM AUTHOR]

The present study investigates the thermal convection of a power-law fluid in a horizontal porous layer that is heated from below. The study of flow in a porous medium is important because of its applications in various fields such as agriculture, geothermal sciences, and engineering. Linear instability analysis is performed using the normal mode method to solve the governing equations after non-dimensionalization. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for linear instability. The impact of gravity parameter, Peclet number, and power-law index on linear instability has been investigated. Linear and quadratic variations of gravity field are considered. From the results, it is evident that the critical Rayleigh number exhibits a non-monotonic relationship with the Peclet number. Increasing the gravity variation parameter leads to a more stable system, particularly in the case of linear gravity variation.

The present article deals with the modulation of electroosmotic flow (EOF) and transport of ionic species within soft nanochannels. The power-law model is adopted to consider the non-Newtonian nature of bulk electrolyte. The soft layer grafted along the rigid walls often bears ionizable functional groups, which in turn leads to the net volumetric charge. Besides, the dielectric permittivity of the soft layer is in general lower than that of the ambient electrolyte solution, which in turn leads to ion partitioning effect. The net volumetric charge within the soft polymeric layer coated along the channel walls may be moderate to large. For such a case, the ion steric effect may play a pivotal role on the modulation of electrostatic potential and thereby the flow field across the channel. In the present article, we aim to study the flow modulation across the soft nanochannels considering all such intrinsic effects. The mathematical model is based on modified Poisson−Boltzmann equations based on Carnahan−Striling model, Cauchy momentum equation for flow field. The governing equations are solved via a suitable numerical scheme based on finite difference method to calculate the electrostatic potential as well as flow velocity. We further analyze the impact of pertinent parameters on the flow modulation and ion selectivity parameter. [ABSTRACT FROM AUTHOR]

In the present research article, we address the magnetically controlled thermal and solutal Marangoni convection in the ow of self-rewetting power-law liquid over a disk, in the existence of a space dependent heat source. The self re-wetting property of fluid is modelled by considering a quadratic dependence of surface tension on temperature and species concentration. The aforementioned problem is modelled by simplified Navier- Stokes equations. Identifying the appropriate transform variables is essential for developing ordinary differential equations from original partial differential equations that describe the ow conditions. The resulting ordinary differential equations are solved by using the bvp4c routine of MATLAB and numerical solutions are presented via graphs and tables, illustrating the impact of several factors on fluid velocity, temperature, and concentration. Computation of the quantities of physical interest such as Nusselt and Sherwood numbers are also done from those numerical solutions. One of the key findings of present research work is that the Marangoni convection works differently for pseudo-plastic fluid and dilatant fluid. On increasing thermal Marangoni convection the temperature of dilatant fluid reaches a peak value much closer to the disk than temperature of pseudo plastic fluid. [ABSTRACT FROM AUTHOR]

Present analysis deals with the impact of nonlinear convection on MHD non-Newtonian fluid flow considering exponentially stretched sheet through porous media. Additionally, the effects of radiation, Joule heating and energy dissipation have been taken into account. The considered flow situation of nonlinear PDEs is transmuted to nonlinear ODEs using similarity analysis. The numerical computations are derived using a fourth-order Runge–Kutta scheme with a shooting technique. Meaningful observations are discussed for velocity and energy profiles. Further, the impact of pertinent parameters considering pseudoplastic fluids (n = 0. 6) and dilatant fluids (n = 1. 3) is briefed through graphs. It is noted that the escalation in the values of the power-law index declines the velocity and energy profile. Higher values of the nonlinear parameter decline the energy profile. [ABSTRACT FROM AUTHOR]

In order to study the effect of tortuosity of diffusion paths on the grouting effect of shield tunnel segment, a penetration diffusion model of grouting through segments of shield tunnel considering tortuosity of diffusion paths was established for power-law fluid. The influence of grouting time, grouting pressure and grouting rate on the diffusion radius and the tunnel segment were analyzed. Finally, by using MATLAB and COMSOL Multiphysics software, a numerical simulation program for permeation and diffusion of powerlaw fluid considering tortuosity of diffusion paths was developed, and the numerical simulations of grouting for shield tunnel segment was achieved. The research results show that under the condition of other parameters unchanged, as the termination grouting pressure increases, the diffusion radius and the pressure on the tunnel segment increase. With the increasing grouting rate, the diffusion radius and the pressure on the tunnel segment first increase and then decrease. After the consideration of tortuosity of diffusion paths, the diffusion radius and the pressure on the tunnel segment decrease compared with the case without considering tortuosity of diffusion paths. With the increase of the termination grouting pressure and grouting rate, the influence of tortuosity of diffusion paths on the diffusion radius and pressure on the tunnel segment become more significant. [ABSTRACT FROM AUTHOR]

To conduct a more in-depth study of the flow mechanism of power-law fluids within sewage pumps, this paper focuses on self-priming sewage pumps, with typical power-law fluid (Carboxymethyl Cellulose, CMC) as the conveying medium. The constitutive equations for sewage and typical power-law fluid (CMC solution) were established using the power-law model. Through numerical calculation methods, the non-steady flow field inside the pump of different concentration power-law fluids was analyzed from various aspects such as velocity, pressure, vorticity, and wall shear stress. The pressure pulsations at key locations in the pump flow field were monitored and analyzed. At the rated flow rate, when the concentration of CMC solution increased from 0.5% to 2.0%, the channel pressure and tongue pressure decreased by 16.5% and 3.5%, respectively. This indicates that the pressure on the impeller blades, within the flow passages, and at the tongue of the volute all decrease with the increase in concentration of CMC solution. This may alter the fluid flow pattern, leading to more vortex motion and shear deformation, while also reducing the pump's pressure boosting capability, thereby affecting the pump's performance stability. It can be inferred from quantitative comparisons that changes in rheological properties had a significant impact on the flow characteristics of sewage pumps. This paper reveals that some flow characteristics of power-law fluids in sewage pumps, providing a theoretical and reference basis for the performance optimization and flow mechanism research of sewage pumps. [ABSTRACT FROM AUTHOR]

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, , the power-law index, , the cavity aspect ratio, , the Lewis number, , and the buoyancy ratio, . An analytical solution is obtained for shallow enclosures ( ) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters.

This paper studies the free convection of Ostwald-de Waele fluid in a Π-shaped chamber with a Π-shaped heated strip at the lower mid-section. The upper wall and the remaining sections of the lower wall are thermally insulated, while the lateral walls are maintained at a low temperature. The primary objective is to identify the optimal power-law index (n) and the geometric configurations of the strip that yield enhanced heat transfer. Furthermore, the impact of Rayleigh number (Ra) on the thermal performance of the cavity in that optimum condition is to be investigated. The Galerkin finite element approach has been employed to resolve the governing equations and auxiliary conditions. Within the study, the power-law index of the Ostwald-de Waele fluid has been systematically varied (0.6 ≤ n ≤ 1.4). At the same time, the variations in the non-dimensional height (0.1 ≤ ζ ≤ 0.5) and width (0.1 ≤ ε ≤ 0.3) of the heated strip have been explored. The results show improved thermal performance with a growth in Rayleigh number, particularly when n

Flow of non-Newtonian fluids between parallel plates has many uses including heat transfer applications. Many non-Newtonian fluids can be categorized as pseudoplastic fluids. A broader category, power-law fluids, covers in addition dilatant and Newtonian fluids. Models for developing power-law fluid flow between parallel plates include computational and integral boundary layer methods. Most published studies include partial results and apply to one of the three categories. The present work addresses the three cases and exclusively shows the transition from developing to fully developed flow. In the inlet region, viscous effects are restricted to the boundary layer. The present approach is based on the inlet-filled region concept, and includes an additional zone, called filled region in which viscous effects are present in the whole region, with the flow asymptotically reaching the fully developed solution. The integral boundary layer method is used in both regions to solve for the flow. The results are found to be in good agreement with published Newtonian, pseudoplastic and dilatant fluid results for boundary layer thickness, centerline velocity, local friction factor, pressure drop profiles, and entrance region size. The present model is fundamentally analytical with minor computational work required.

In the process of oil and gas drilling, it is of great significance to accurately predict the drag coefficient and settling rate of cuttings in the drilling fluid for hydraulic parameters and borehole cleaning. In this paper, particle settling experiments were used to obtain the final settling velocity of 196 groups of spherical particles and 224 groups of terrestrial high-clay pure-shale cuttings in the power-law fluid. Based on data analysis, a settlement drag coefficient model suitable for irregular- shaped shale cuttings was established. The model can be used to predict the settlement drag coefficient and settling velocity of irregular-shaped shale cuttings in power-law fluid, which can provide theoretical guidance for wellbore cleaning and hydraulic parameter optimization in Daqing Gulong shale oil drilling operations. [ABSTRACT FROM AUTHOR]

AbstractIn the present investigation, the onset of Marangoni convection in the flow of self-rewetting fluid over a stretching disk has been discussed. The self-rewetting fluid is considered to be electrically conducting and the flow problem is discussed under the influence of an induced magnetic field. The fluid flow is mainly induced due to two different mechanisms: (i) onset of Marangoni convection due to presence of temperature gradient along the liquid-gas interface and (ii) induction of magnetic field due to presence of an external magnetic field, which modifies the original field. The governing partial differential equations are written, following Navier-stokes equations and Prandtl boundary layer equation. With the use of similarity transformations, the governing equations are turned into a system of ordinary differential equations. Nonlinear systems of ordinary differential equations are solved by the bvp4c technique. The reciprocal of the magnetic Prandtl number diminishes the induced magnetic profile. [ABSTRACT FROM AUTHOR]

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge. [ABSTRACT FROM AUTHOR]

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In the present study, laminar pulsating power‐law momentum and heat transfer in a uniformly heated plane duct is studied analytically. Assuming that fully developed conditions exist both hydrodynamically and thermally, a perturbation series method is utilized to derive analytical solutions for the momentum and energy balance equations, and the amplitude is prescribed as the perturbation parameter. For varying values of the power‐law index (n $n$), representing pseudoplastic, Newtonian, and dilatant fluids, effects of dimensionless amplitude (ϵ $\epsilon $) and frequency (F $F$) on periodic and period‐averaged friction factor and Nusselt number are obtained. The results obtained for Newtonian fluid are shown to be in good harmony with the corresponding findings in the open literature. [ABSTRACT FROM AUTHOR]

This paper introduces an exponential time integrator scheme for solving partial differential equations in time, specifically addressing the scalar time-dependent convection-diffusion equation. The proposed second-order accurate scheme is demonstrated to be stable. It is applied to analyze the heat and mass transfer mixed convective flow of power-law nanofluid over flat and oscillatory sheets. The governing equations are transformed into a dimensionless set of partial differential equations, with the continuity equation discretized using a first-order scheme. The proposed time integrator scheme is employed in the time direction, complemented by second-order central discretization in the space direction for the momentum, energy, and nanoparticle volume fraction equations. Quantitative results indicate intriguing trends, indicating that an increase in the Prandtl number and thermophoresis parameter leads to a decrease in the local Nusselt number. This modified time integrator is a valuable tool for exploring the dynamics of unsteady power-law nanofluid flow over moving sheets across various scenarios. Its versatility extends to the examination of unstable fluid flows. This work improves engineering and technological design and operation in nanofluid dynamics. Improving numerical simulations' precision and computational efficiency deepens our comprehension of fundamental physics, yielding helpful information for enhancing systems that rely on nanofluids. [ABSTRACT FROM AUTHOR]

Many scholars have studied the interporosity flow function (IFF) and shape factor. However, the existing research does not consider the complex microstructure of dual media and the influence of fluid types on interporosity flow. In this paper, the anisotropic IFF and shape factor model of power-law fluid in smooth and rough fracture dual media are established by using the rough capillary bundle model and considering the influence of the microstructure of dual media and the type of fluid. The relationship between IFF, shape factor, and relative roughness in dual media is studied. It is found that the relative roughness is inversely proportional to the IFF and inversely proportional to the shape factor. In addition, the model is compared with the existing research and experimental data to verify the rationality of the model. [ABSTRACT FROM AUTHOR]

Previous studies have given little consideration to the influence of soil unloading effect on permeation grouting. A spherical permeation diffusion model considering the influence of soil unloading effect was established based on the theory of spherical permeation grouting to study the permeability and diffusion characteristics of a power-law fluid in unloaded soil. The permeation grouting model was compared and verified with the grout diffusion experiment conducted in the unloaded soil. A parametric analysis with the proposed model was performed. The result shows that the final diffusion radius of the grout increases with the increase of soil unloading degree, grouting pressure, water–cement ratio, and initial permeability coefficient but decreases with the increase of underground water pressure. The increment value of grouting pressure is equal to the increment value of underground water pressure under the same grouting time and grout diffusion radius. The influence of soil stress history, soil initial permeability coefficient, underground water pressure, and water–cement ratio should be comprehensively considered to determine the reinforcement range of permeation grouting. The proposed permeation grouting diffusion model is suitable for sandy soil with normal loading and unloading conditions, and the results analyzed by this model can provide some theoretical guidance for the tunnel vault grouting and bored pile postgrouting process. [ABSTRACT FROM AUTHOR]

This study explores cost-effective and customized composite applications by strategically placing carbon fiber-reinforced thermoplastics in multi-material designs. The focus is on developing a model for the simultaneous processing of non-reinforced and reinforced thermoplastic layers, with the aim of identifying essential parameters to minimize insert flow and ensure desired fiber orientation and positional integrity. The analysis involves an analytical solution for two layered power-law fluids in a squeeze flow setup, aiming to model the combined flow behavior of Newtonian and pseudo-plastic fluids, highlighting the impact of the non-Newtonian nature. The behavior reveals a non-linear trend in the radial flow ratio towards the logarithmic consistency index ratio compared to a linear trend for Newtonian fluids. While a plateau regime of consistency index ratios presents challenges in flow reduction for both layers, exceeding this ratio, depending on the height ratio of the layers, enables a viable overmolding process. Therefore, attention is required when selectively placing tailored composites with long-fiber-reinforced thermoplastics or unidirectional reinforcements to avoid operating in the plateau region, which can be managed through appropriate cavity or tool designs. [ABSTRACT FROM AUTHOR]

In petroleum engineering, accurately predicting particle settling velocity during various stages of a well's life cycle is vital. This study focuses on settling velocities of both spherical and non-spherical particles in Newtonian and non-Newtonian fluids. Utilizing a dataset of 931 experimental observations, an artificial neural network (ANN) model with a 7-42-1 architecture is developed (one input layer, one hidden layer with 42 neurons, and one output layer). This model effectively incorporates particle settling orientation and the inclusion of the settling area ratio, enhancing its predictive accuracy. Achieving an average absolute relative error (AARE) of 8.51%, the ANN model surpasses traditional empirical correlations for settling velocities in both Newtonian and power-law fluids. Key influencing factors, such as the consistency index and particle equivalent diameter, were identified. This approach in ANN model construction and data analysis represents a significant advancement in understanding particle dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study bioconvection radiative flow of power-law nanofluid. Nanofluid characteristics are incorporated by utilizing the Buongiorno model. The influence of motile gyrotactic microorganism is retained. Magnetohydrodynamics and time-dependent aspects are under consideration. Related governing expressions are transformed into dimensionless partial differential system. The resulting nonlinear system is tackled through finite difference technique. Outcomes of emerging variables like Prandtl number, Hartmann number, Buoyancy ratio parameter, Grashof number, Peclet number, bioconvection Rayleigh number, Peclet number, radiation and Schmidt number are graphically discussed. Velocity is controlled by higher Hartman number while it boosts against higher Grashof and bioconvection Rayleigh numbers, buoyancy ratio and stretching parameters. Higher radiation, Brownian and thermophoresis parameters lead to intensification in temperature profile while it reduces for higher Prandtl number. Bioconvection profile reduces against higher Peclet and Lewis numbers. [ABSTRACT FROM AUTHOR]

To improve the effectiveness of fracturing treatment, it is vital to understand how multiple fractures interact with each other. This study presents a fully coupled hydraulic fracture model that considers both Newtonian fluids and power-law fluids to investigate the effect of stress shadowing in different propagation regimes, from toughness- to viscosity-dominated, under limited entry conditions. The dimensionless parametric space for a plane-strain fracture driven by power-law fluids is outlined, and numerical analysis is performed in the parametric space to simplify the problem. Moreover, the numerical scheme for the coupled hydromechanical problem is verified by comparing the results to the existing analytic solutions. It is shown that the simultaneous propagation of multiple fractures is significantly influenced by the fracture propagation regime and cluster spacing. Fractures tend to grow uniformly in the viscosity-dominated regime, and the fracture reorientation can be observed if both the cluster spacing and stress anisotropy are small. In contrast, fractures propagating in the toughness-dominated regime tend to propagate in the opposite direction of the adjacent fractures to avoid each other, resulting in minimal overlap between fracture lengths. The influence of fracture propagation regime is consistent for Newtonian and power-law fluids. Additionally, as the cluster spacing increases, the effect of stress shadow decreases, and the behavior of each individual fracture resembles that of an isolated fracture. Highlights: A fully coupled hydraulic fracture model for studying the simultaneous growth of multiple fractures driven by Newtonian and power-law fluids is developed. A dimensionless parametric space for a plane-strain fracture driven by power-law fluid is established. The effect of fracture propagation regimes and cluster spacing on the simultaneous growth of multiple fractures is revealed. [ABSTRACT FROM AUTHOR]

The locomotion state and motion type of elliptical squirmers in a channel flow of power-law fluids are simulated numerically. Three locomotion states (independent, coupled, related) and three types of motions (upstream, intermediate, downstream) for pairs of squirmers are found and identified. The effect of height difference (0.5 ~ 10) between the initial positions of two squirmers, aspect ratio (0.3 ~ 1.0), particle Reynolds numbers (0.5 ~ 10), self-propelling strength of the squirmers (− 9 to 9), and power-law index (0.4 ~ 1.5) of the fluid on the locomotion state and motion type of a pair of squirmers are explored, and the corresponding hydrodynamical characteristics are analyzed in detail. Head-to-head coupled structures and body-to-body coupled structures are observed for a pair of pullers and a pair of pushers, respectively. It is found that coupled structures are easy to be broken for squirmers with larger aspect ratio or larger particle Reynolds number and self-propelling strength. The movement characteristics of squirmers are closely related to the initial positions of squirmers in strong shear-thinning fluid, but not to the initial positions in strong shear-thickening fluid. The dependence of viscosity on shear will also significantly affect the flow velocity, thus changing the motion type of squirmers. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, RT, the power-law index, n, the cavity aspect ratio, A, the Lewis number, Le, and the buoyancy ratio, N. An analytical solution is obtained for shallow enclosures (A >> 1) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters. [ABSTRACT FROM AUTHOR]

AbstractThermosolutal natural convection originates in a fluid when the density changes due to the presence of two distinct components with varying rates of diffusion. This convection is driven by buoyancy resulting from concurrent temperature and concentration gradients. This study focuses on the thermosolutal free convection flow within a parallelogrammic enclosure. The functioning fluid under consideration is non-Newtonian and formulated by the viscosity model (power-law). The top and bottom walls of the chamber are adiabatic and are assumed to be impermeable. The temperature and concentration on the left side are maintained at a high level, while the conditions on the right side are cold and low. The controlling parameters for the present case include Rayleigh number (105≤Ra≤106), Lewis number (Le = 5, 10), Prandtl number (Pr = 6.2), buoyancy ratio (N = 0.8, −0.8) along with power-law index (n = 0.6, 1, 1.4). The results obtained from this numerical study are validated with existing results and indicate the correctness of the code. The output of the study is shown in terms of velocity and temperature profiles, streamlines, isotherms, and iso-concentrations, the average rate of heat and mass transmission in terms of the average Nusselt number (Nu¯) and the average Sherwood number (Sh¯). The correlation equation derived from the RSM approach demonstrates the relationship between the output responses and the input parameters. It concludes that n negatively affects both heat and mass transfer, while Ra affects positively. The findings of this study could be helpful for understanding of thermosolutal natural convection behavior of non-Newtonian (power-law) fluid in an enclosure and therefore accelerate the industrial application of such fluid in the relevant field, such as HVAC (heating, ventilation, and air conditioning) system. [ABSTRACT FROM AUTHOR]

This research delves into the complexities of backflow phenomena in finite-length and flat-walled fractures with elastic walls, specifically focusing on power-law fluids, whose shear-thinning behavior distinguishes them from Newtonian fluids. We model the backflow process under the lubrication approximation and by incorporating the linear Navier slip law. We numerically examine the influence of parameters such as slip length, fluid rheology, and external pressure on the backflow propagation of the carrier fluid. Our findings underscore the significant role played by the rheological index in determining the fracture closure rate. Additionally, our investigations highlight the marked effect of external pressure variations on pressure distribution within the fracture. Notably, the friction coefficient at the fracture walls, as denoted by a dimensionless slip number, exhibits limited influence on the fundamental dynamics of the problem. These insights advance our understanding of power-law fluid backflow and have wide-ranging applications across various engineering disciplines. [ABSTRACT FROM AUTHOR]

Trying to understand to what extent active methods (the angle of placement chamber + the change of temperature of the barrier included inside the chamber) and passive methods (the application of MF + HAP) can be used in controlling and managing EP regarding to HT of non-Newtonian FF has been one of the goals of this numerical study. Since in this study, in addition to convection process, heat conduction in the solid is also considered, in addition to Ha, PL index, Ra, HAPC, TMF, the barrier temperature and the chamber inclination angle, TCR is presumed as the controller variable. The utmost momentous obtained outcomes are as follows: (A) On average, a decrease of up to 38% in the flow power and a decrease of up to 45% in HT amount are the result of an augmentation of in the value of Ha and PL index. (B) The impact of exerting MF becomes more noticeable with diminish in PL index. Augmentation of Ha to the highest value causes decline in the mean Nu by about 52% and 18% for n = 0.75 and n = 1.25, respectively. (C) To achieve a flow with higher power and higher the mean Nu, MF can be used non-uniformly, especially TMF1. The more noticeable influence of changing TMF is the result of augmentation of the amount of Ha. The influence of the change in TMF to the shear thickening fluid is lowest. (D) As TCR increases, the maximum mean Nu is acquired, in which case the impact of increasing Ha and the HAPC becomes more pronounced. (E) The minimum amount of HT, current power and MF influence is obtained when the chamber is at an angle of + 90°, in which case the mean Nu is up to about 75% less than the zero angle. (F) Although enhancement of HAPC reduces the mean Nu, it nevertheless increases the flow power and influence of MF on EP. In the case of heat production, the increment of in EP is the result of the enhancement of in Ha, unlike in other cases. (G) EP and current vigor increase by placing the barrier at hot temperature while the mean Nu diminishes. The contribution of MF in EP increases with enhancement of block temperature. (H) Be value increases with increment of HAPC, augmentation of Ha and decrement of TCR, and maximum Be value is obtained at an angle of + 90°. [ABSTRACT FROM AUTHOR]

The present study aims to numerically explore Fluid-Structure Interaction (FSI) induced mixed convection characteristics in a square cavity filled with a non-Newtonian power-law fluid. The side walls of the cavity under consideration are subjected to constant low temperature having motion in opposite directions while the insulated top wall and the bottom hot wall are kept stationary. A flexible fin is mounted on the bottom wall that essentially serves as a passive flow modulator. To solve the transient flow, thermal, and stress fields, the FSI problem is presented in an arbitrary Lagrangian-Eulerian framework employing the Galerkin finite element method. Different non-Newtonian fluids are represented by the power-law index (n) varied within the range, of 0.6 ≤ n≤ 1.4. Besides, the dynamic as well as mixed convection condition of the flow is analyzed by variation of Reynolds number (100 ≤ Re ≤ 300) and Richardson number (0.1 ≤ Ri ≤ 10.0) respectively. System characteristics have been evaluated in terms of streamline and isotherm contours, spatial and time-averaged Nusselt number as well as Normalized Nusselt number in regard to the “No Fin” case. The outcome of the present study reveals that the efficacy of a flexible fin for a given system depends on both the system dynamic condition (Re) and the mixed convection regime (Ri). The presence of a flexible fin has been found to have positive impact on heat transfer performance for both the shear-thinning and shear-thickening fluids for higher values of Re and Ri. However, for lower values of Re, the inclusion of a flexible fin has been found to adversely affect the heat transfer performance for shear-thickening fluids. Moreover, the thermal field exhibits periodic oscillation properties at Ri = 10, which can be attributed to the induced motion of the flexible fin. This phenomenon has been further elucidated through Power Spectrum Analysis. Results obtained in the present study might provide valuable insights into FSI-induced mixed convection with non-Newtonian fluids having versatile industrial applications such as solar thermal collectors with strategically positioned passive flexible flow modulators.

In the process of oil and gas drilling, it is of great significance to accurately predict the drag coefficient and settling rate of cuttings in the drilling fluid for hydraulic parameters and borehole cleaning. In this paper, particle settling experiments were used to obtain the final settling velocity of 196 groups of spherical particles and 224 groups of terrestrial high-clay pure-shale cuttings in the power-law fluid. Based on data analysis, a settlement drag coefficient model suitable for irregular-shaped shale cuttings was established. The model can be used to predict the settlement drag coefficient and settling velocity of irregular-shaped shale cuttings in power-law fluid, which can provide theoretical guidance for wellbore cleaning and hydraulic parameter optimization in Daqing Gulong shale oil drilling operations.

A mathematical model is used to study the impact of elasticity on the peristaltic flow of a Power-Law fluid including nanoparticles in a cylindrical tube. Long wavelength and low Reynold's number approximations and non-dimensionalization are used in the governing equations to get non-linear equations. Homotopy Perturbation Method is an approximate analytical method, which is used here to solve coupled equations of Temperature profile and nanoparticle phenomena. Then the expression for axial velocity and flux flow rate are calculated. The techniques of Rubinow, Keller, and Mazumdar are used to compute the flux variation. The impact of various factors on flow is addressed. The change in Heat and Mass transfer coefficients are studied at the end. A number of intriguing behaviors are reported by the results obtained for the current flow characteristics, which call for more research on physiological fluids in elastic tubes with peristalsis. In this work, the wide variety of applications of nanofluids is presented with an emphasis on their enhanced, regulated heat transfer qualities. Because of their special qualities, these nanofluids are appropriate for a variety of uses. The work has applications in pharmacological engineering, such as peristaltic micropumps and innovative drug delivery methods.

Power-law fluids have recently received increasing attention because of their applications in different industrial fields. In previous works, the energy and momentum equations for power-law fluids were considered the same as those for Newtonian fluids. However, as the heat transfer of fluids results from thermomolecular motions, the heat-transfer behavior of non-Newtonian power-law fluids should be different from that of Newtonian fluids. The flow of fluids on a smooth plate is a classical problem. In most situations, the plates are rough. In particular, in industrial fields, many plates are deliberately designed to be rough to enhance heat transfer. Herein, according to the Taylor expansion and boundary-layer theory, the boundary-layer equations for the Ostwald–de Waele power-law fluids with a variable thermal conductivity along a horizontal wavy surface are reduced to partial differential equations. An energy equation with a variable thermal conductivity is constructed, where the heat-conduction coefficient is assumed to be a power-law function dependent on the temperature gradient. Through the introduction of a series of transformations, including nondimensional and coordinate transformations, the original wavy-surface problem is transformed into a system of partial differential equations describing the flow problem with boundary conditions on a flat plate, which is solved numerically using the Keller-box method. The effects of some parameters, such as the amplitude–wavelength ratio \begin{document}$ \alpha $\end{document}, power-law index \begin{document}$ n $\end{document}, and generalized Prandtl number \begin{document}$ {N_{{\rm{zh}}}} $\end{document}, on the local friction coefficient and heat-transfer coefficient are discussed. Numerical results show that the velocity of power-law fluids on the surface and pressure gradient varies periodically along the wavy plate. Furthermore, the cycles of the velocity and pressure gradients are the same as the one of the wavy-shape plate. The results show that the local Nusselt number and the friction coefficient vary periodically in a wavelike manner and increase gradually with the amplitude–wavelength ratio, although a sudden change exists near the zero point. With the increasing amplitude, the friction coefficient oscillates more considerably. With the increasing power-law index, the local Nusselt number decreases. For a special case in which the plate is flat, the local Nusselt number and friction coefficient are in a stable state for a short distance along the plate, although initial oscillations appear near the zero point. Owing to the effects of different parameters on the periodicity, the peak and trough of the local Nusselt number and friction coefficient are not consistent, despite occurring in the same cycle.

Heat transport (HT) efficiency in boundary layer flow (BLF) across wedges is critical for many industrial processes, as well as aerospace and defence research. The HT analysis in a power-law fluid along a moving permeable wedge is described in this paper. A changeable parameter is the injection velocity at the wedge surface. The governing equations are dimensionless, and the shooting technique is used to achieve a non-similar solution. Graphs depict the impacts of various factors on the velocity and temperature contours, local Nusselt number, and skin friction coefficient. The results show that the dilatant fluid has a velocity decline near the wedge surface and achieves its maximum velocity away from the wedge surface. The findings of this study may aid in the development of better HT systems for a variety of applications.

This paper introduces an exponential time integrator scheme for solving partial differential equations in time, specifically addressing the scalar time-dependent convection-diffusion equation. The proposed second-order accurate scheme is demonstrated to be stable. It is applied to analyze the heat and mass transfer mixed convective flow of power-law nanofluid over flat and oscillatory sheets. The governing equations are transformed into a dimensionless set of partial differential equations, with the continuity equation discretized using a first-order scheme. The proposed time integrator scheme is employed in the time direction, complemented by second-order central discretization in the space direction for the momentum, energy, and nanoparticle volume fraction equations. Quantitative results indicate intriguing trends, indicating that an increase in the Prandtl number and thermophoresis parameter leads to a decrease in the local Nusselt number. This modified time integrator is a valuable tool for exploring the dynamics of unsteady power-law nanofluid flow over moving sheets across various scenarios. Its versatility extends to the examination of unstable fluid flows. This work improves engineering and technological design and operation in nanofluid dynamics. Improving numerical simulations’ precision and computational efficiency deepens our comprehension of fundamental physics, yielding helpful information for enhancing systems that rely on nanofluids.

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than 1 0 0 % has been observed in f Re , whereas maximum decrease in dilatant fluid is around 3 0 % , when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic flow, heat transfer and entropy generation of pseudoplastic, Newtonian and dilatant fluids through a porous microchannel (of which the top wall is moving at constant velocity while the bottom wall kept fixed) are investigated under the combined influence of time-dependent variable injection–suction, temperature boundary condition, power-law fluid-dependent slip conditions and buoyancy force. Some typical base fluid temperatures are utilized to determine the physical properties of water and hence to calculate the values of governing parameters. The governing equations are solved with an efficient numerical procedure: staggered grid for variable arrangement, finite volume method for space discretization (and then QUICK scheme for convective terms), three-level implicit for time derivative and a pressure correction-based iterative SIMPLE algorithm. All the flow parameters (two Reynolds numbers due to the top wall movement and injection–suction velocity, Prandtl number, Grashof Number, Hartman number, Brinkman number and Richardsons number) are locally depends on the power-law fluid. Effects of various regulatory flow parameters (variable injection/suction and temperature boundary condition, and power-law fluid-dependent slip) on contours of velocities, vorticity, streamline, isothermal lines, Nusselt number and local as well as normalized-global entropy generation are studied here. Our bird's-eye view would be to search some situation at which a vortex is generated without any obstacle inside the channel, also to pick out some flow situation where the heat transfer from the walls and energy loss inside the channel is maximum/minimum. [ABSTRACT FROM AUTHOR]

The equilibrium position yep/H of a particle in a microchannel flow of Newtonian and power-law fluids with an obstacle is numerically studied using the lattice Boltzmann method in the range of the ratio of an obstacle to particle diameter 0.5 ≤ β ≤ 2, fluid power-law index 0.4 ≤ n ≤ 1, Reynolds number 20 ≤ Re ≤ 60, and blockage ratio 0.15 ≤ k ≤ 0.3. Some results are validated by comparing them with the available results. The results showed that, when a particle migrates around an obstacle in the flow behind and near the obstacle, the particle with a different initial, y/H, migrates downstream in a different lateral position, yep/H, and the larger the value of β, the closer the value of yep/H is to the centerline. Therefore, the value of yep/H can be controlled by changing β in the wake zone of the obstacle. However, in the flow far downstream from the obstacle, the particle with a different initial y/H tends to have the same yep/H when n, Re and k are fixed, but the values of yep/H are different for different n, Re and k; i.e., the larger the values of n, Re and k, the closer the value of yep/H is to the centerline. The value of β has no effect on the value of yep/H. In the flow far downstream from the obstacle, the flow distance required for the particle to reach yep/H increases with increasing β and n but decreases with decreasing Re and k. [ABSTRACT FROM AUTHOR]

The current study presents a mathematical model to simulate a power-law fluid hammer problem in pipelines. The flow is considered two-dimensional, isothermal, weakly compressible, and laminar. The governing equations consisting of mass and momentum balances are solved by the method of characteristics. The model results are compared to other numerical model values and validated against measured data found in the literature. The comparisons show that the two-dimensional model agrees better with experimental data than the one-dimensional approach. Two dimensionless parameters (a dissipative parameter and the power-law index) are identified to govern the phenomenon, and a sensitivity analysis with respect to these parameters is conducted. It can be anticipated that the first pressure overshoot due to line packing and pressure wave dissipation increase with the dissipative parameter and with the power-law index. [ABSTRACT FROM AUTHOR]

We suggest symmetric variational physics-informed neural networks (symmetric VPINN) to learn the symmetric fluid flow and physical properties of fluids from a limited set of data. Symmetric VPINN is based on the VPINN framework and guarantees the symmetry of the solutions by modifying the network architecture. The effectiveness of the symmetric VPINN is demonstrated by predicting the velocity profiles and power-law fluid properties in the Poiseuille flow of a parallel channel. Symmetric VPINN models robustly and accurately learn power-law fluid flow in both forward and inverse problems. We demonstrate that the symmetric VPINN can be particularly useful when the power-law index is small and the data are extremely limited. The modified network architecture in the symmetric VPINN guides the neural network towards an exact solution by reinforcing symmetry. We show that symmetric VPINN is effective in obtaining unknown physical properties in practical experiments where data are scarce, suggesting the possibility of introducing known conditions of the system directly into the network structure to improve the accuracy of the network. [ABSTRACT FROM AUTHOR]