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In this paper, the capillary is divided into several regions, and the effective pore radius is proposed. The relationship between the effective hole radius and the maximum radius is analyzed. The fractal models of fractal flow rate, average velocity and effective permeability of power-law fluid flow in fractal soil composed of circular cross section capillaries are derived. The effects of different power exponent, viscosity coefficient and fractal dimension on the average flow velocity and effective permeability model are analyzed, and the comparative analysis of different sections is carried out. The reasonable calculation results of the fractal model given in this paper verify the correctness of the model. The introduction of the effective pore radius concept and the derivation of fractal models have advanced our ability to characterize and predict flow behavior. We anticipate that these findings will stimulate further research and practical applications in various domains, benefiting both scientific knowledge and technological advancements. [ABSTRACT FROM AUTHOR]

We study the symmetric stochastic p-Stokes system, p ∈ (1 , ∞) , in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost - 1 / 2 temporal derivatives on a Besov scale. Second, we verify that the velocity u of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient V (ϵ u) = (κ + ϵ u) (p - 2) / 2 ϵ u , κ ≥ 0 , which measures the ellipticity of the p-Stokes system, has 1/2 temporal derivatives in a Nikolskii space. [ABSTRACT FROM AUTHOR]

Strengthening the thermal transfer of hot bodies is one of the topics that the old and new researches aim at due to its wide use in the fields of applied engineering. This research includes a study of thermal activity of five hot objects placed inside a cold chamber and rotating at constant speed. An equilateral triangular shape is the cross-sectional shape of the bodies. A rheologically complex fluid is poured into the chamber completely. A magnetic field of constant strength is applied to the x-direction of the chamber. The items studied here are: the rheological nature of the fluid by changing the value of power-law index (n = 0.8, 1 and 1.2), the rotational speed of the chamber is in terms of the Reynolds number (Re = 5 to 40), the magnetic field strength expressed in terms of the Hartmann number (Ha = 0 to 100) and finally buoyancy force (Ri = 0 to 50). The investigation was carried out using a numerical method adopted by a digital simulator with very high characteristics. The results showed that the thermal activity varies from one body to another. The effect of magnetic field on Nusselt number of the bodies decreases as the value of power-law increases. [ABSTRACT FROM AUTHOR]

The use of polymer microspheres is becoming increasingly widespread. Along with their most common applications, they are beginning to be used in the synthesis of photonic crystals, microstructure analysis and multiplexed diagnostics for disease control purposes. This paper presents a simple mathematical model that allows us to study the transport mechanisms involved in the deformation of an elastic microchannel under the flow stream of a power-law fluid. In particular, we analyze the momentum transfer to a non-Newtonian fluid (Polydimethylsiloxane, PDMS) due to the deformation of the elastic ceiling of a rectangular microchannel. Hooke's law is used to represent the stress–deformation relationship of the PDMS channel ceiling. Stop-flow lithography is modeled, and the pressure exerted by the deformed PDMS ceiling on the fluid when the microchannel returns to its original form is taken into account. It is found that the response time of the elastic ceiling deformation increases with the channel width and length and decreases with the channel height independently of the power-law exponent of the injected fluid. However, an increase in the power-law exponent beyond unity causes an increase in the wall-deformation response time and the maximum deformation of the channel height compared to a Newtonian fluid. [ABSTRACT FROM AUTHOR]

This study investigated the momentum and thermal characteristics of a blunt‐headed cylinder immersed in a stream of generalized Newtonian fluids (i.e., power‐law fluids) under various planar confinements. The flow and heat transfer characteristics were obtained by solving the constitutive equations with a finite‐element‐based solver for varying ranges of governing parameters. Reynolds number (Re = 1–40), Prandtl number (Pr = 5–100), power‐law index (n = 0.3–1.8), and blockage ratios (β = 2–40) were considered as the governing parameters for the study. Streamlines, drag coefficients, isotherm contours, and average Nusselt numbers were obtained as output parameters of the study. The local distribution of the pressure coefficient and Nusselt number are also presented to gain deep insight into the vicinity of the blunt‐headed cylinder. Shear‐thickening and shear‐thinning fluids exhibited an inverse trend for flow separation under planar confinements. The average Nusselt number exhibits a positive correlation with the Reynolds and Prandtl numbers while showing negative dependence on the power‐law index and blockage ratio. Overall, momentum and heat transfer show complex relationships with the governing parameters. The functional relationships are shown as correlations for flow‐separation Reynolds number, total drag force, and average Nusselt number on relevant dimensionless parameters for general applications. [ABSTRACT FROM AUTHOR]

This study explores the consequences of free convective laminar two-dimensional flow with the effects of thermal radiation of power-law non-Newtonian water–Cu nanofluids over the frustum of a cone whose sides are wavy shaped. The flow is described by some well-known equations of fluid dynamics, such as the equation of continuity, momentum and energy equation having the Rosseland diffusion model for radiation effect. These governing equations are transformed into non-dimensional boundary-layer equations, which are solved by using the marching order implicit finite difference method. The numerical results are obtained by varying pertinent parameters, such as the radiation–conduction parameter R d , the surface heating parameter θ w , power-law index n and nanoparticle volume fraction ϵ . The numerically calculated findings are reported with respect to the velocity and temperature distributions, streamlines, isotherms, local skin friction coefficient and average Nusselt number using graphs. According to the obtained results, R d , ϵ and θ w accelerate the convection process. Hence, velocity, skin friction, as well as the rate of heat transfer enhance. On the other hand, an increasing power-law index decreases the convection process. As a result, velocity, skin friction as well as the rate of heat transfer reduce. The present study of non-Newtonian nanofluid with radiation effect over a truncated wavy cone is a novel study. The motto of the existing numerical effort is to observe the situations considering non-Newtonian nanofluid fluids and how the considered parameters reflected their behaviour with non-Newtonian viscosity and radiation–conduction effects. The obtained result of this present study is validated with the work of Pop and Na (Int. J. Nonlinear Mech.34, 925, 1999). The findings of their investigation of free convective flow in a vertical cone are compared with the current work and the comparison showed an excellent agreement. [ABSTRACT FROM AUTHOR]

The settlement drag coefficient of irregular particles in power-law fluids is a crucial parameter in the field of petroleum engineering. However, the irregular shape of the particle and the non-Newtonian rheological properties of the fluid make it challenging to predict the settlement drag coefficient. In this study, the spherical and irregular particle sedimentation processes in power-law fluids have been analyzed using a visual device and a high-speed camera system. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of 114 spherical particle experimental results, and a prediction model of the drag coefficient of spherical particles in the power-law fluid was established with a mean relative error of 3.85%. On this basis, considering the influence of geometric shape on the law of particle sedimentation, a new irregular particle sedimentation resistance coefficient model in power-law fluid is established via the incorporation of the parameter circularity of 2D shape description c into the spherical particle sedimentation resistance coefficient predictive model. The parameters in the new irregular particle sedimentation resistance coefficient predictive model can be obtained via nonlinear data fitting of the 211 groups of irregular particles using experimental results in the power-law fluid. The model has high prediction accuracy for the drag coefficient of irregular particles in power-law fluid, with a mean relative error of 4.47, and expands the scope of engineering applications, which is of great significance for fracturing scheme design and wellbore cleaning. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effect of heat transfer and flow of non-Newtonian power-law fluids towards a stretching sheet in the appearance of transverse magnetic field with slip boundary conditions. Suitable similarity transformations are used to change the non-linear partial differential equations to ordinary differential equations. For the numerical solution Maple software by applying built-in command dsolve with numeric is utilized. It is noticed from the obtained results that an increase in the magnetic parameter results in a decrease in the dimensionless velocity profile and in the stream function while the temperature profile increases for the Newtonian, dilatant, and pseudo-plastic fluids. Increasing the velocity slip parameter, a reducing behavior can be seen in the stream function and in the velocity profile while temperature profile is enhancing. Moreover, with increasing thermal slip, a decrease occurs in the dimensionless temperature. The variations in the velocity and temperature profiles under dimensionless parameters are significant for n = 0.8 (pseudo-plastic fluid) rather than for n = 1 (Newtonian fluid) and n = 1.02 (dilatant fluid). [ABSTRACT FROM AUTHOR]

We investigate the existence of weak solutions to a certain system of partial differential equations, modeling the behavior of a compressible non‐Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack of the L∞$$ {L}^{\infty } $$ estimate on the divergence of the velocity field. The result was obtained by combining the regularity theory for singular operators with a certain logarithmic integral inequality for BMO$$ BMO $$ functions, which allowed us to adjust the method from Feireisl et al. (2015) to more relaxed conditions on the velocity. [ABSTRACT FROM AUTHOR]

In this article, electro-osmotic thrusters (EOTs), which are full of non-Newtonian power-law fluids with a flow behavior index n of the effective viscosity, are theoretically investigated in a microchannel. Different values of the flow behavior index represent two kinds of non-Newtonian power-law fluids, pseudoplastic fluids (n < 1) and dilatant fluids (n > 1), which have not yet been considered to be used as propellants in micro-thrusters. Analytical solutions of the electric potential and flow velocity are obtained using the Debye–Hückel linearization assumption and the approximate scheme of hyperbolic sine function. Then, thruster performances of power-law fluids, including specific impulse, thrust, thruster efficiency, and thrust-to-power ratio, are explored in detail. Results show that these performance curves strongly depend on the flow behavior index and electrokinetic width. It is noted that the non-Newtonian pseudoplastic fluid is most suitable as a propeller solvent in micro electro-osmotic thrusters owing to its improving or optimizing deficiencies in the performances of the existing Newtonian fluid thrusters. [ABSTRACT FROM AUTHOR]

To guarantee the transporting efficiency of microdevices associated with fluid transportation, mixing, or separation and to promote the heat transfer performance of heat exchangers in microelectronics, the hydrodynamic behaviors at unsteady and steady states, as well as the thermal characteristics at the steady state in a pressure-driven electrokinetic slip flow of power-law fluid in a microannulus are studied. To present a more reliable prediction, the slip phenomenon at walls and nonlinear rheology of liquid are incorporated. The modified Cauchy momentum equation applicable to all time scales and energy equations, are analytically solved in the limiting case of a Newtonian fluid and numerically solved for power-law fluids. The transient velocity profile, time evolution of flow rate, temperature profile, and heat transfer rate are computed at different flow behavior indices, electrokinetic width, slip lengths, and Brinkman numbers, thereby, the coupling effect of nonlinear rheology, slip hydrodynamics, and annular geometry on flow and thermal behaviors is explored. The unsteady flow takes a longer time to achieve the steady state for shear thinning fluids or greater slip lengths. The flow behavior index and slip length play a significant role in the flow rate and heat transfer performance. The relevant discussion can serve as a theoretical guide for the operation and thermal management of annular geometry-related flow actuation systems. [ABSTRACT FROM AUTHOR]

In the present work, heat transfer and entropy generation due to the natural convection of Newtonian and non-Newtonian fluids in two types of shear thinning and shear thickening inside a righttriangular cavity under the effect of uniform and non-uniform magnetic field by multiple relaxation time lattice Boltzmann methods have been investigated. The aspect ratio of the cavity is variable and the magnetic field is applied in two different angles" is replaced by" the magnetic field is applied from left to right and perpendicular to the gravity of the cavity". The present work is validated with previous references and results presented in the form of tables, diagrams and streamlines, isothermal lines, and entropy lines. The simulation is done by writing the computer code in the Fortran language. The effect of Rayleigh number, aspect ratio, power-law index of fluid, Hartmann number and angle, and type of magnetic field applied on fluid flow and heat transfer characteristics has been evaluated. The results show that in all cases, increasing the Hartmann number and fluid power-law index leads to a decrease in the strength of flow, heat transfer rate, and entropy generated and the percentage of this effect varies depending on the number of other variables. By applying a magnetic field non-uniformly, the flow strength and heat transfer rate can be increased to about 45% and 20%, respectively. At higher Hartmann numbers, the effect of changing the type of magnetic field applied is more pronounced. The angle of the magnetic field applied is a determinant parameter on the amount of heat transfer so that the average Nusselt number in the horizontal mode is on average 15% less than in the vertical mode. Increasing of power-law index dramatically reduces the magnetic field effect so that it is ineffective for the shear thickening fluid, the type of magnetic field applied. By increasing the Rayleigh number and the aspect ratio of the cavity, the flow strength and the rate of heat transfer increase and the effect of the magnetic field becomes more pronounced. This study can be useful in the optimal design of industrial and engineering equipment, including electronic coolers. [ABSTRACT FROM AUTHOR]

The forced convection flow and heat transfer aspects of an isothermal sphere in an oscillating stream of power‐law fluids in the range of 5 ≤ Re ≤ 120 and 0.3 ≤ n ≤ 1.5 are numerically investigated. The effects of shear‐dependent viscosity and oscillatory flow features on the temporal variation of streamlines, patterns of streaming flows, drag coefficient, and Nusselt number are examined in depth. The power‐law index modulates the transition of the steady streaming flows between two distinct streaming regimes. Overall, shear‐thinning fluids at low oscillation frequencies are observed to yield significant increase in heat transfer. Due to the phase lag in the momentum boundary layer, the drag coefficient exhibits a phase lag ranging from π/2 to 4π/5 whereas the Nusselt number lags by about 50 % of these values. [ABSTRACT FROM AUTHOR]

The aim of this present work assesses heat transfer and entropy generation arising from free convection of power-law fluids in a trapezoidal chamber under the effect of uniform and non-uniform magnetic field with heat absorption/generation by using LBM. The impact of Rayleigh number (103, 104 and 105), wall slope (11.5°, 26.5° and 38.5°), power-law index (0.75, 1.0 and 1.25), Hartmann number (0, 15, 30 and 45), type of magnetic field applied (uniform and non-uniform) with heat absorption/generation (− 10, − 5, 0, + 5 and + 10) on fluid flow and heat transfer characteristics has been evaluated. By enhancement of the Rayleigh number and decreasing wall slope of the chamber, the flow strength, the rate of heat transfer and entropy generation increase and the effect of the magnetic field becomes more remarkable. By applying a magnetic field non-uniformly, the flow strength and heat transfer rate can be grown to about 25% and 15%, respectively. At higher Hartmann and Rayleigh numbers, the effect of changing the type of magnetic field applied is more notable. By increasing the heat absorption/generation coefficient, the average Nusselt number decreases and the effect of the magnetic field increases. In the heat generation mode, the total entropy generation increases with increasing Hartmann number, while in the heat absorption mode, the opposite effect was obvious. A salient and distinctive feature of the present work compared to previous studies is the application of non-uniform magnetic field (specific type of application) in the presence of heat absorption/generation for non-Newtonian fluids, which is not researched. [ABSTRACT FROM AUTHOR]

A novel analytical model is derived based on fractal geometry theory to characterize the permeability of power-law fluids through fractured porous media with fractal asperities on surfaces. The proposed model is expressed as a function of structure parameters of fractured porous media, fractal dimensions for porous matrix and for fracture as well as the index n of power-law fluid behavior. The influences of these parameters on the permeability are analyzed in detail. It is found that the relationship between permeability and roughness exhibits nonlinear characteristics. A higher power-law fluid behavior index significantly affects the reduction rate of permeability with relative roughness. Moreover, permeability is sensitive to the perturbation due to the rate of aperture to length. The proposed fractal model can clearly reveal more physical mechanisms for power-law fluid in fractured porous media than the existing models. Compared with the experimental data available in the literature, the validity of model predictions is verified. [ABSTRACT FROM AUTHOR]

This study aims to investigate the roles of pertinent parameters on the mixed convection of complex liquids in annular devices. The investigated area consists of two circular cylinders with fixed and heat walls. Both cylinders are enclosed within a circular room with a cold wall and rotate regularly. The zone between the inner obstacles and the outer space contains complex power‐law fluids. This investigation is numerically achieved by using the package ANSYS‐CFX, which is based on the finite‐volume method. The parameters studied in this study are the arrangement and size of inner tubes (d/D), the rotational speed of outer space, the rheological nature of fluids (n), and the relative concentration of thermal buoyancy force. These pertinent parameters were quantitatively expressed for the following values: d/D (= 0.1, 0.25, and 0.45); Reynolds number (Re = 1 to 20); flow behavior index (n = 0.6, 1 and 1.6); Richardson number (Ri = 0 to 100), respectively. It was found that increasing the thermal buoyancy value and the rotational speed of the outer container increases the rate of heat transfer of the cylinders in the vertical and horizontal arrangement. For example, for shear‐thinning fluid (n = 0.6), raising the value of Ri from 0 to 100 increases Nu by 59.67% for d/D = 0.1. Also, the arrangement of the two cylinders differently affects the dynamic behavior of the fluid within the studied space. [ABSTRACT FROM AUTHOR]

This work is an evaluative study of heat transfer in the helical-type heat exchanger. The fluid used is non-Newtonian in nature and is defined by Oswald's model. The work was performed numerically by solving each of the Navier–Stokes equations and the energy equation using the package ANSYS-CFX. Following are the aspects that have been dealt with in this paper: the effects of thermal buoyancy, fluid nature and the tube shape on the heat transfer, and the fluid comportment. The interpretation of the obtained results was done by analyzing the isotherms and the streamlines. The mean values of the Nusselt number were also obtained in terms of the studied parameters. The results of this research enabled us to arrive at the following conclusion: the intensity of thermal buoyancy and the nature of the fluid affect the heat transfer distribution but keep the overall rate of heat transfer the same. [ABSTRACT FROM AUTHOR]

The steady flow of non‐Newtonian power‐law fluids across a periodic square array of infinitely long circular cylinders is studied numerically using an unstructured finite volume method. The local and global flow characteristics have extensively been explored by the systematic variations of the pertinent dimensionless parameters as follows: fluid volume fraction (ϕf =.70–.99), Reynolds number (Re = 1–40), and power‐law index (n =.4–1.8). Qualitatively, the dense and curved streamlines are seen with the increasing inertial forces and shear‐thinning behavior across all the fluid volume fractions. Further, the pressure coefficient over the surface of periodic cylinders is significantly influenced by the governing parameters and found to be maximum and minimum for the upstream and downstream cylinders, respectively. The individual and total drag coefficients have shown complex dependence on n, ϕf, and Re. For shear‐thinning fluids (n < 1), the pressure drag coefficient dominates over the friction drag coefficient, whereas an opposite response is seen for the shear‐thickening fluids (n > 1) except at Re = 40. Further, both individual and total drag coefficients are observed to increase and decrease in the ranges of ϕf of.70–.90 and.92–.99, respectively, with increasing n. The strong interactions between the periodic cylinders, at smaller ϕf, diminish with a corresponding increase in ϕf. In addition, simple predictive correlations for the pressure, friction, and total drag coefficients have been developed to gain further physical insights into the detailed flow kinematics. Finally, the present findings display a good agreement with the available literature. [ABSTRACT FROM AUTHOR]

This work deals with a practical approach for the determination of the rheological parameters of the purely viscous power–law fluids in the rectangular channel and concentric annulus. The rectangular channels with a height to width ratio (aspect ratio) of less than 0.1 and concentric annulus of large aspect ratios are used for the determination of the shear viscosity of the non‐Newtonian fluids. For rectangular channels of aspect ratio greater than 0.1, the determination of the shear viscosity for the power–law model requires two geometrical parameters, according to conventional methods. In this work, a practical method is introduced in order to determine rheological parameters of the power–law fluids for rectangular channels and concentric annulus with the aspect ratios between 0 and 1 using one geometric parameter. The validity of the suggested one‐parameter method is firstly compared with the conventionally used two‐parameter model analytically. Then, verification is carried out by experimental method using slit viscometer and a rectangular channel with an aspect ratio of 0.2. Obtained wall shear rate‐wall shear stress values from both geometries are compared, and finally obtained rheological parameters are verified by numerical methods. It has shown that the suggested method is successful for the determination of shear viscosity, and results reveal that rectangular channels with an aspect ratio greater than 0.1 can be used to obtain rheological parameters for power–law fluids. [ABSTRACT FROM AUTHOR]

We study the stability of the two-dimensional boundary-layer flow of a power-law (Ostwald de Waele) non-Newtonian fluid over a moving wedge. The mainstream velocity is assumed to have a power of distance from the leading boundary layer, such that the system admits to the self-similar solutions. We discuss the problem in question for both shear-thickening and shear-thinning fluids which lead to a non-uniqueness (double solutions) in the base flow solutions. We then address an issue of the stability of the non-unique solutions. A linear eigenvalue analysis of the double solution reveals that the basic flow represented by the first solution is always stable, and this flow is practically encountered. The system becomes unstable to the second solutions which have the mode-two perturbations with larger boundary-layer thickness. The first and second solutions form a tongue-like structure in the solution space. Furthermore, the modification of the viscosity for the power-law fluids reveals that the system predicts an infinite viscosity in the confinement of the boundary-layer region. Extensive comparisons of the solutions with the existing models with Newtonian fluid are made, and a physical explanation behind these solutions is proposed. [ABSTRACT FROM AUTHOR]

Measurement and prediction of suspension flow properties in cylindrical geometries represent a significant challenge for both the experimentalist and modeler. In this paper, results of a computational study of the suspension flow in a pipe geometry using a computational method based on the smoothed particle hydrodynamics are presented. Flow fields and the spatial distribution of solid spherical inclusions for the case of pipe flow will be shown as a function of the matrix fluid properties (including Newtonian, shear thinning, and shear thickening), driving force, and volume fraction of particles. Simulation results of suspension flow are consistent with a previous work of suspensions with a Newtonian fluid matrix. A strong effective slip phenomenon is shown for the case of a suspension with a shear thinning fluid matrix despite adherence to no-slip boundary conditions. A simple scaling ansatz is given to describe the change of flow rate with driving force. At a volume fraction of approximately 40 % and higher, there is strong evidence of ordering. This feature is illuminated using a small-angle scattering algorithm and compared to experimental studies using neutron scattering. Issues related to proper experimental characterization of rheological properties for pumping and printing of cement-based materials are discussed. [ABSTRACT FROM AUTHOR]

The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 < n < 1) flows from the shear-thickening fluid (n > 1) flows while the Newtonian fluid (n = 1) flows remain unaffected by this parameter no matter what be the value of S. [ABSTRACT FROM AUTHOR]

Summary: A formulation has been derived for the flow of non‐Newtonian (power‐law) fluids in deformable, fractured porous media. The formulation is enhanced with a subgrid scale model to accurately represent the flow of the power‐law fluids inside the cracks. The resulting equations have been discretised using standard (Lagrangian) finite element shape functions and with non‐uniform rational B‐splines (NURBS), which have been cast into a standard finite element datastructure using Bézier extraction. The effect of the power‐law index on the velocity inside the fracture and on the total fluid flow through the porous medium has been analysed for a typical boundary‐value problem. It is shown that large differences between non‐Newtonian and linearised Newtonian fluids can occur for the fluid velocity inside the fracture. This can significantly influence the total fluid transport through the domain. A mesh sensitivity study has been carried out as well and shows that markedly smaller element sizes are required in order to obtain accurate results for the local flow inside the fracture, compared with the element sizes necessary for obtaining accurate results inside the porous medium away from the fracture. Moreover, a comparison has been made between the results obtained using standard Lagrange polynomials and those obtained using NURBS. It is shown that while both discretisation methods are able to accurately simulate the deformations and pressures in the porous medium, the higher interelement continuity of NURBS is mandatory for obtaining correct values of the fluid velocities inside the fracture, especially near the tips. [ABSTRACT FROM AUTHOR]

The extensional extruder is a novel method of polymer processing which generates high elongation stress within a polymer. A mathematical model is proposed which describes the velocity distribution during polymer processing in such an extruder. The modeling results indicate that the dimensionless velocity profiles for power-law fluids decrease as the power-law index increases. Overall, the extensional extruder has an advantage for dispersion effects over traditional screw extruders based on the extensional rheology. [ABSTRACT FROM AUTHOR]

Due to the increasingly wide application of electroosmotic flow in micromachines, this paper investigates the electroosmotic flow of the power-law fluid under high zeta potential in a cylindrical microcapillary for different dimensionless parameters. The electric potential distribution inside a cylindrical microcapillary is presented by the complete Poisson-Boltzmann equation applicable to an arbitrary zeta potential. By solving the Cauchy momentum equation of power-law fluids, the velocity profile, the volumetric flow rate, the average velocity, the shear stress distribution and dynamic viscosity of electroosmotic flow of power-law fluids in a cylindrical microcapillary are studied for different low/high zeta potential, flow behavior index, dimensionless electrokinetic width. The velocity profile gradually changes from parabolic to plug-like shape as the flow behavior index decreases or as the dimensionless electrokinetic width increases. For shear thinning fluids, the viscosity is greater in the center of the microchannel than that near the channel wall, the reverse is true for the shear thickening fluids. Greater volumetric rate and average velocity can be achieved by enhancing the dimensionless electrokinetic width, flow behavior index and zeta potential. It is noted that zeta potential and flow behavior index are important parameters to adjust electroosmotic flow behavior in a cylindrical microcapillary. [ABSTRACT FROM AUTHOR]

In situations involving large zeta potential, the classical Poisson-Boltzmann theory of electrolytes breaks down and a modified Poisson-Boltzmann equation which takes into account the finite size of the ions must be utilized. In addition, most biofluids cannot be treated as Newtonian, therefore, simultaneous effects of finite size of the ions and non-Newtonian behavior of the fluid in combined electroosmotic and pressure driven flows have been examined in the present study. The Governing equations are solved by a finite-difference-based numerical procedure in a rectangular microchannel. The ion size is introduced into the modified Poisson-Boltzmann equation by the steric factor, which allows considering the ions as point charges or finite sizes. Considering the ionic finite size; generally enhances the velocity of the shear-thickening fluid, while reducing the velocity of shear-thinning fluid. The Cross sectional aspect ratio is also considered and it was found that the adverse pressure gradient greatly affects the velocity profile, when aspect ratio increases, while velocity profile is less sensitive to aspect ratio variations in favorable pressure gradients. Furthermore, friction coefficient of both shear thinning and thickening fluids increases with the increase in zeta potential for point charge model, which for finite size charges decreases. Cross sectional averaged velocity reduces under steric effects for shear thinning fluids at large zeta potentials, while it is slightly influenced by shear thickening fluids. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive computational work on hydrodynamic and thermal phenomena of flow separation around a confined circular cylinder by superimposed thermal buoyancy. For that purpose, let us consider a confined flow of Non-Newtonian power-law fluid around a heated square cylinder in a twodimensional vertical channel. The effects of thermal buoyancy and power-Law index on the flow separation and the average Nusselt number are studied for the conditions: (10 ≤ Re ≤ 40), (0.4 ≤ n ≤ 1.2), (0 ≤ Ri ≤ 0.8), Pr = 50 and blockage ratio β = 0.2. The Reynolds numbers of flow are chosen in low range such that the flow remains steady and separated without imposition of the thermal buoyancy. In the steady flow regime the results show that the augmentation of the power-law index in the absence of thermal buoyancy causes a separation to grow. The thermal buoyancy delays the separation in different power-law indexes gradually and at some critical value of the buoyancy parameter it completely disappears resulting a stuck flow around a cylinder. Moreover, the recirculation length and skin friction are calculated to support the above finding. The decrease in the power-Law index increases the heat transfer rate. The Nusselt numbers are computed to predict the heat transfer rates of power-law fluids under the superimposed thermal buoyancy condition. [ABSTRACT FROM AUTHOR]

It is proposed that an impregnation model can predict the porosity of composites for power-law fluids impregnation in fabric. The impregnation model takes the material properties and fabric characteristic dimensions into account. In order to verify the model, glass fabric reinforced polypropylene (PP) composites are fabricated by using compression molding procedure. The impregnation model is validated by a series of comprehensive experiments, and the experimental results are perfectly consistent with the impregnation model’s value. The impregnation process is studied respectively through the model and the experiment. The results of it have shown that the impregnation time can indeed be shortened for compression molding procedure by increasing the processing temperature or increasing the applied pressure. [ABSTRACT FROM AUTHOR]

Microfluidic droplet technology has been developing rapidly. However, precise control of dynamical behaviour of droplets remains a major hurdle for new designs. This study is to understand droplet deformation and breakup under simple shear flow in confined environment as typically found in microfluidic applications. In addition to the Newtonian-Newtonian system, we consider also both a Newtonian droplet in a non-Newtonian matrix fluid and a non-Newtonian droplet in a Newtonian matrix. The lattice Boltzmann method is adopted to systematically investigate droplet deformation and breakup under a broad range of capillary numbers, viscosity ratios of the fluids, and confinement ratios considering shear-thinning and shear-thickening fluids. Confinement is found to enhance deformation, and the maximum deformation occurs at the viscosity ratio of unity. The droplet orients more towards the flow direction with increasing viscosity ratio or confinement ratio. In addition, it is noticed that the wall effect becomes more significant for confinement ratios larger than 0.4. Finally, for the whole range of Newtonian carrier fluids tested, the critical capillary number above which droplet breakup occurs is only slightly affected by the confinement ratio for a viscosity ratio of unity. Upon increasing the confinement ratio, the critical capillary number increases for the viscosity ratios less than unity, but decreases for the viscosity ratios more than unity. [ABSTRACT FROM AUTHOR]

We develop the a posteriori error analysis of finite element approximations to implicit power-law-like models for viscous incompressible fluids in d space dimensions, d ∈ {2,3}. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi-valued, maximal monotone r-graph, with .... We establish upper and lower bounds on the finite element residual, as well as the local stability of the error bound. We then consider an adaptive finite element approximation of the problem, and, under suitable assumptions, we show the weak convergence of the adaptive algorithm to a weak solution of the boundary-value problem. The argument is based on a variety of weak compactness techniques, including Chacon’s biting lemma and a finite element counterpart of the Acerbi–Fusco Lipschitz truncation of Sobolev functions, introduced by [L. Diening, C. Kreuzer and E. Süli, SIAM J. Numer. Anal. 51 (2013) 984–1015]. [ABSTRACT FROM AUTHOR]

Fully developed turbulent pipe flows of power-law fluids are studied by means of direct numerical simulation. Two series of calculations at generalised Reynolds numbers of approximately 10000 and 20000 were carried out. Five different power law indexes n from 0.4 to 1 were considered. The distributions of components of Reynolds stress tensor, averaged viscosity, viscosity fluctuations, and measures of turbulent anisotropy are presented. The friction coefficient predicted by the simulations is in a good agreement with the correlation obtained from experiment. Flows of power-law fluids exhibit stronger anisotropy of the Reynolds stress tensor compared with the flow of Newtonian fluid. The turbulence anisotropy becomes more significant with the decreasing flow index n. An increase in apparent viscosity away from the wall leads to the damping of the wall-normal velocity pulsations. The suppression of the turbulent energy redistribution between the Reynolds stress tensor components observed in the simulations leads to a strong domination of the axial velocity pulsations. The damping of wall-normal velocity pulsations leads to a reduction of the fluctuating transport of momentum from the core toward the wall, which explains the effect of drag reduction. [ABSTRACT FROM AUTHOR]

In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤ Ri≤5; Reynolds number, 1≤ Re≤100; Prandtl number, 1≤ Pr≤100; power-law index, 0.3≤ n≤1.8, and aspect ratio, 0.2≤ e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates ( e < 1) than that for prolates ( e > 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape ( e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio ( e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor. [ABSTRACT FROM AUTHOR]

A biomimetic design rule is proposed for generating bifurcating microfluidic channel networks of rectangular cross section for power-law and Newtonian fluids. The design is based on Murray's law, which was originally derived using the principle of minimum work for Newtonian fluids to predict the optimum ratio between the diameters of the parent and daughter vessels in networks with circular cross section. The relationship is extended here to consider the flow of power-law fluids in planar geometries (i.e. geometries of rectangular cross section with constant depth) typical of lab-on-a-chip applications. The proposed design offers the ability to precisely control the shear-stress distributions and predict the flow resistance along the bifurcating network. Computational fluid dynamics simulations are performed using an in-house code to assess the validity of the proposed design and the limits of operation in terms of Reynolds number for Newtonian, shear-thinning and shear-thickening fluids under various flow conditions. [ABSTRACT FROM AUTHOR]

This paper is focused on the study for the effects of constant heat flux and thermal buoyancy on the steady two-dimensional flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching vertical surface in the presence of thermal radiation. Highly nonlinear momentum and thermal boundary layer equations which governing the flow and heat transfer are reduced to a set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of fourth order Runge-Kutta method coupled with the shooting technique. The effects of various parameters like the buoyancy (mixed convection) parameter, the radiation parameter, power-law index parameter and the local Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Favorable comparisons of numerical results with previously published work on various special cases of the problem are obtained. [ABSTRACT FROM AUTHOR]

The governing partial differential equations have been solved numerically for the 2-D and steady powerlaw fluid flow over two square cylinders in tandem arrangement. Extensive numerical results spanning wide ranges of the governing parameters as Reynolds number (0.1≤Re≤40), power-law index (0.2≤n≤1) and inter-cylinder spacing (2≤L/d≤6) are presented herein; limited results for L/d=24 are also obtained to approach the single cylinder behavior. The detailed flow visualization is done by means of the streamline and vorticity contours in the vicinity of two cylinders. The global characteristics are analyzed in terms of the surface pressure distribution and pressure drag coefficient. The drag coefficient shows the classical inverse dependence on the Reynolds number irrespective of the value of the powerlaw index; the drag on the upstream cylinder is always greater than that for the downstream cylinder. [ABSTRACT FROM AUTHOR]

This study elucidates a relationship between the Fanning friction factor and the Reynolds number for the laminar propagation of constant-flux gravity currents. The particular motivation for this study was related to the pipeline disposal of dredged fluid-mud where non-Newtonian bottom gravity currents form. The power-law rheology model, which has been shown to model fluid-mud rheology well, was incorporated in the theoretical analysis. The proposed Fanning friction factor–Reynolds number relationship includes a proportionality constant (henceforth, the shape factor) that considers the shape of the current. For non-Newtonian fluid-mud gravity currents, a relationship for the shape factor was developed through laboratory experiments. Different potential applications of the developed friction factor–Reynolds number relationship are discussed. In this regard, a new viscous propagation model was developed and evaluated through comparisons with laboratory experimental data for fluid-mud gravity currents. The approach presented in this manuscript can be extended for currents of different fluids propagating over smooth and rough bottoms. [ABSTRACT FROM AUTHOR]

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids. [ABSTRACT FROM AUTHOR]

The steady flow and mass transfer of nanofluids with power-law type base fluids over a free-rotating disk are investigated. Previously, we have modeled the volume fraction of nanoparticles and verified the experimental conclusion through the numerical simulation of particle distribution in nanofluid in a Petri dish under the influence of movement using a power-law model of mass diffusivity. We further this study by a similar model of the mass diffusivity following a power-law type to consider the laminar non-Newtonian power-law flow in a rotating infinite disk with angular velocity about the z-axis. The coupled governing equations are transformed into ODEs. Homotopy analysis method (HAM) is applied to solve the ODEs while special attention is paid to deal with the nonlinear items in the ODEs. In the last section, we provide images of nanoparticles suspended in power-law fluids in a rotating disk as obtained using the laser speckle method. When they are compared with the analytical results gained by the HAM, they qualitatively matched the solutions of the concentration equation of nanofluids. [ABSTRACT FROM AUTHOR]

Our experiment reported here adopts water, alcohol (100 %), carboxymethyl cellulose (CMC) aqueous solution with different concentrations as the base-fluid of nano-fluids. We show diffusion, aggregation and precipitation of nano-size particles in the optical quartz glass Petri dishes filled with nano-fluids flat with the help of a rotating cone. The experimental results illustrate that nanoparticles are preferably suspended in CMC aqueous solution than in water or alcohol, which means the effective Hamaker constant of water- or alcohol-particle suspensions is bigger than that of CMC-particle suspension. In the experiment with CMC as the base solution, increasing the viscosity of the solution can alleviate the settling velocity of particles and make the suspension better. The experiment also discovers that in static condition, the mutual attractive force between nanoparticles plays an important role in the suspension; however, if external forces, which are higher than the attraction, exist, they are decisive parts. In addition, AlO solution is much more sensitive than the Cu solution with the varying concentration and status in the experiment because the density of AlO particles is smaller than that of Cu-nanoparticles. [ABSTRACT FROM AUTHOR]

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge-Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases. [ABSTRACT FROM AUTHOR]

The effects of non-uniform heat generation/absorption and viscous dissipation on heat transfer of a non-Newtonian power-law fluid on a non-linearly stretching surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations by using suitable similarity transformation. The transformed system of ordinary differential equations is solved numerically using fourth order Runge-Kutta method with the shooting technique. Graphical solutions for the dimensionless temperature are presented and discussed for various values of the power-law index parameter, the Prandtl number, the heat generation/absorption parameter and the Eckert number. The results show that the local Nusselt number is reduced with increasing the Eckert number or the heat generation parameter, whereas the heat absorption parameter has the effect of enhancing the local Nusselt number. [ABSTRACT FROM AUTHOR]

In the lubrication limit, the time needed for the drainage of the liquid film between two particles or between particles and walls is of industrial importance, because it controls the dynamics and aggregation of nondilute suspensions. This problem is also of fundamental interest in the application of the dynamic surface force apparatus to nanorheology. Even if this problem has an exact solution in Newtonian fluid when the sphere moves steadily and slowly towards or away from a plane wall, this problem remains, to our knowledge, without any exact analytical solution in non-Newtonian fluids with negligible viscoelastic components. But Rodin, using the method of asymptotic expansions, gives an asymptotic solution to this problem in the lateral unbounded power-law fluid. Therefore, in this study, we give a numerical result using the dynamic mesh technique and an asymptotic analytical formula valid in the lubrication regime, for a fluidity index $$0.5 < n\, \leqslant \,1.8.$$ The comparison between the two results confirms their mutual validity. [ABSTRACT FROM AUTHOR]

Purpose – Most studies of power-law fluids are carried out using stress-based system of Navier-Stokes equations; and least-squares finite element models for vorticity-based equations of power-law fluids have not been explored yet. Also, there has been no study of the weak-form Galerkin formulation using the reduced integration penalty method (RIP) for power-law fluids. Based on these observations, the purpose of this paper is to fulfill the two-fold objective of formulating the least-squares finite element model for power-law fluids, and the weak-form RIP Galerkin model of power-law fluids, and compare it with the least-squares finite element model. Design/methodology/approach – For least-squares finite element model, the original governing partial differential equations are transformed into an equivalent first-order system by introducing additional independent variables, and then formulating the least-squares model based on the lower-order system. For RIP Galerkin model, the penalty function method is used to reformulate the original problem as a variational problem subjected to a constraint that is satisfied in a least-squares (i.e. approximate) sense. The advantage of the constrained problem is that the pressure variable does not appear in the formulation. Findings – The non-Newtonian fluids require higher-order polynomial approximation functions and higher-order Gaussian quadrature compared to Newtonian fluids. There is some tangible effect of linearization before and after minimization on the accuracy of the solution, which is more pronounced for lower power-law indices compared to higher power-law indices. The case of linearization before minimization converges at a faster rate compared to the case of linearization after minimization. There is slight locking that causes the matrices to be ill-conditioned especially for lower values of power-law indices. Also, the results obtained with RIP penalty model are equally good at higher values of penalty parameters. Originality/value – Vorticity-based least-squares finite element models are developed for power-law fluids and effects of linearizations are explored. Also, the weak-form RIP Galerkin model is developed. [ABSTRACT FROM AUTHOR]

This work studies the flow characteristics of power-law fluids in the fractal-like tree network. A fractal model is developed for the permeability of power-law fluid flow in fractal-like tree network based on straight capillary model, generalized Darcy's law and constitutive equation for power-law fluids. Analytical expression for permeability of power-law fluids in the network is presented and found to be a function of network microstructural parameters such as the branching diameter ratio, the branching length ratio, the total number of branching levels, the bifurcation angle, the branching number, the diameter of the zeroth branching level and the power exponent of power-law fluids. Both the phase permeabilities and the relative permeabilities are also derived and found to be a function of power exponent for the wetting phase and non-wetting phase, the saturation and other microstructural parameters and independent of the bifurcation angle. [ABSTRACT FROM AUTHOR]

The steady forced convection flow of a power-law fluid over a horizontal plate embedded in a saturated Darcy-Brinkman porous medium is considered. The flow is driven by a constant pressure gradient. In addition to the convective inertia, also the “porous Forchheimer inertia” effects are taken into account. The pertinent boundary value problem is investigated analytically, as well as numerically by a finite difference method. It is found that far away from the leading edge, the velocity boundary layer always approaches an asymptotic state with identically vanishing transverse component. This holds for pseudoplastic (0 < n < 1), Newtonian ( n = 1), and dilatant ( n > 1) fluids as well. The asymptotic solution is given for several particular values of the power-law index n in an exact analytical form. The main flow characteristics of physical and engineering interest are discussed in the paper in some detail. [ABSTRACT FROM AUTHOR]

The flow and heat transfer of a power-law fluid over an unsteadily stretched surface with variable thermal conductivity is studied. The governing equations are reduced to a class of non-linear ordinary differential equations by means of similarity transformations and an approximate analytical solution is obtained by using a modified homotopy perturbation method. The effects of the various parameters (power-law index, unsteadiness parameter, Prandtl number and variable thermal conductivity) on the velocity and temperature fields are graphically illustrated and analyzed. [ABSTRACT FROM AUTHOR]

The mixed convection of power-law fluids along a wedge in a porous medium is investigated numerically using an implicit finite difference method. Robin boundary condition is applied at the wedge surface. To explore the effects of mixed convection, both forced and free convection dominated regimes are considered separately. Non-similarity solutions are obtained for the variable heat transfer coefficient. Local dimensionless skin friction and Nusselt number are presented in tabular and graphical forms for the selected values of wedge and convective parameters. The wedge angle geometry parameter r m, power index of pseudoplastic fluids n and mixed convection parameter ξ range from 0 to 1 in both regimes, whereas different values of convective parameter h are considered for investigating the behavior of skin friction and heat transfer rates. [ABSTRACT FROM AUTHOR]