Search

The paper investigates peristaltic flow of a Power-law fluid in contact with a Jeffrey fluid in an inclined channel with permeable walls under long wavelength and low Reynolds number approximations. Power-law fluid is considered in the core region and Jeffrey fluid in the peripheral region. Expressions for the shape of interface between the two fluids and the pressure rise are obtained. It is observed that an increase in permeability parameter increases the thickness of the core layer in the channel. It is also observed that pressure rise increases with decrease in the Jeffrey parameter.

Efficient hydraulics program of oil and gas wells has a crucial role for the optimization of drilling process. In the present paper, a numerical study of power-law fluid flow through concentric (E = 0.0) and eccentric annulus (E = 0.3, E = 0.6 and E = 0.9) was performed for both laminar and turbulent flow regimes utilizing a finite volume method. The effects of inner pipe rotation, flow behavior index and diameter ratio on the pressure drop were studied; furthermore, the appearance and development of secondary flow as well as its impact on the pressure drop gradient were evaluated. Results indicated that the increment of the inner pipe rotation from 0 to 400 rpm is found to decrease pressure drop gradient for laminar flow in concentric annulus while a negligible effect is observed for turbulent flow. The beginning of secondary flow formation in the wide region part of the eccentric annulus (E = 0.6) induces an increase of 9% and a slight increase in pressure drop gradient for laminar and turbulent flow, respectively. On the other hand, the variation of the flow behavior index and diameter ratio from low to high values caused a dramatic increase in the pressure drop. Streamlines in the annulus showed that the secondary flow is mainly induced by eccentricity of the inner pipe where both high values of diameter ratio and low values of flow behavior index tend to prevent the secondary flow to appear. [ABSTRACT FROM AUTHOR]

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

The paper investigates the influence of the inlet boundary condition on the spatial evolution of natural roll-waves in a power-law fluid flowing in steep slope channels. The analysis is carried out numerically, by solving the von Kármán depth-integrated mass and momentum conservation equations, in the long-wave approximation. A second-order accurate scheme is adopted and a small random white-noise is superposed to the discharge at the channel inlet to generate the natural roll-waves train. Both shear-thinning and shear-thickening power-law fluids are investigated, considering uniform, accelerated and decelerated hypercritical profiles as the unperturbed condition. Independently of the unperturbed profile and of the fluid rheology, numerical simulations clearly enlighten the presence of coalescence, coarsening and overtaking processes, as experimentally observed. All the considered statistical parameters indicate that the natural roll-waves spatial evolution is strongly affected by the unperturbed profile. Compared with the uniform condition, at the beginning of roll-waves development an accelerated profile reduces the growth of the roll-waves with a downstream shift of the non-linear wave interaction. The opposite behavior is observed if the roll wave train develops over a decelerated profile. The comparison with the theoretical outcomes of the linearized near wave-front analysis allows the interpretation of this result in terms of stability of the base flow. It is shown that once the coarsening process starts to take place, the roll-waves spatial growth rate is independent of the unperturbed profile. Present results suggest that an appropriate selection of the flow depth at the channel inlet may contribute to control, either enhancing or inhibiting, the formation of a roll-waves train in power-law fluids.

This paper investigates the electroosmotic micromixing of non-Newtonian fluid in a microchannel with wall-mounted obstacles and surface potential heterogeneity on the obstacle surface. In the numerical simulation, the full model consisting of the Navier–Stokes equations and the Poisson–Nernst–Plank equations are solved for the electroosmotic fluid field, ion transport, and electric field, and the power law model is used to characterize the rheological behavior of the aqueous solution. The mixing performance is investigated under different parameters, such as electric double layer thickness, flow behavior index, obstacle surface zeta potential, obstacle dimension. Due to the zeta potential heterogeneity at the obstacle surface, vortical flow is formed near the obstacle surface, which can significantly improve the mixing efficiency. The results show that, the mixing efficiency can be improved by increasing the obstacle surface zeta potential, the flow behavior index, the obstacle height, the EDL thickness.

Piezoelectric three-dimensional inkjet printing has been used to manufacture heterogeneous objects due to its high level of flexibility. The materials used are non-Newtonian inks with complex rheological properties, and their behavior in the context of inkjet printing has not been fully understood: for example, the fact that the shear-thinning viscosity affects the droplet generation. Therefore, a control strategy coping with shear-thinning behaviors is needed to ensure printing consistency. In this paper, a novel model-based approach is presented to describe the shear-thinning ink dynamics inside the piezoelectric inkjet printhead, which provides the basis to design the excitation parameters in a systematic way. The dynamic equation is simplified into a quasi-one-dimensional equation through the combination of the boundary layer theory and the constitutive equation of the power-law fluid, of which the viscosity is shear-thinning. Based on this, a nonlinear time-varying equivalent circuit model is presented to simulate the power-law fluid flow rate inside the tube. The feasibility and effectiveness of this model can be evaluated by comparing the results of computational fluid dynamics and the experimental results.

This article presents a simple and unique method for predicting the friction factor for the fully developed, laminar flow of power-law fluids in ducts with a rectangular cross-section by means of an engineering calculation for rapid equipment design. The relationship between friction factor f and the Reynolds number defined by Metzner–Reed (ReMR) for a rectangular cross-section was investigated and rearranged with very good engineering accuracy using the results of very simple correlations based on the application of the well-known and long-established coefficient for Newtonian fluid flow. The investigated value of the flow index was up to 2, and the aspect ratio ranged from 0 to 1, with calculation error not higher than 3.5%. The proposed method was compared with conventional methods from the literature, and was validated by means of numerical computations, and also with experimental data from the literature. The product of friction factor and ReMR is a linear function of geometrical parameter C and flow behavior index n and also the proposed method predicts the friction factor as accurately as conventional and traditional methods. [ABSTRACT FROM AUTHOR]

This paper emphasizes the radiative heat transfer of non-Newtonian fluid on free convection around a slender paraboloid in a non-Darcy porous medium. The Ostwald- de Waele power-law representation is employed to express the non-Newtonian behavior of fluid. Similarity analysis is applied to transform the set of non-dimensional PDE into set of ODE and then the resulting system of equations are solved by 4th order Runge-Kutta scheme with Shooting technique. The control of pertinent parameters on velocity, temperature and non-dimensional heat transfer rates are analyzed through graphical representation and explored in detail. It is evident that as the radius of the slender body increases the heat transfer coefficient decreases but the role of radiation on heat transfer rate getting reduced for all feasible values of the power-law index parameter. [ABSTRACT FROM AUTHOR]

Double-diffusive convective instability of horizontal throughflow in a power-law fluid saturated porous layer is investigated. The boundaries of this horizontal porous layer are impermeable, isothermal and isosolutal. The generalized Darcy's equation for power-law fluid is employed in the momentum balance, along with Oberbeck–Boussinesq approximation for buoyancy effect in the system. It is considered that the viscous dissipation is non-negligible. The basic temperature and concentration profiles for the considered horizontal throughflow are determined analytically, and the linear stability analysis is performed on this basic solution. The eigenvalue problem is solved numerically using bvp4c in MATLAB. The conditions for the onset of instability of base flow in terms of critical Rayleigh number and the corresponding wave number are obtained. It is found that critical values are affected by the flow governing parameters such as the Péclet number (Pe), power-law index (n), viscous dissipation (Ge), angle of inclination (α) , buoyancy ratio (N) and Lewis number (Le). For the considered range of these parameter values, the instability of the basic flow is discussed for the convective rolls. It is observed that instability of any general convective roll lies between that of the longitudinal and transverse rolls. Also, the effect of viscous dissipation on the onset of instability for both the longitudinal and transverse rolls is discussed in detail. This source of heating inside the porous layer increases the thermal instability of base flow. Further, the asymptotic analysis for vanishingly small Péclet number is presented as P e = 0 is a singular point. The boundary between the stationary and the oscillatory instabilities is given using the buoyancy ratio parameter and the Lewis number in this limiting case of P e → 0 . [ABSTRACT FROM AUTHOR]

The purpose of the present article is to explore the influence of activation energy in the mixed convective flow of a power‐law fluid over a permeable inclined plate. The energy expression is incorporated with thermal radiation effect. Additionally, the suction/injection effect and convective thermal conditions are considered at the surface of the inclined plate. The convection along with a nonlinear Boussinesq approximation (i.e., quadratic or nonlinear convection) and usual boundary‐layer assumptions are used in the mathematical formulation. A combined local non‐similarity and successive linearization techniques are used to evaluate the highly complicated governing equations. The effect of pertinent parameters on the fluid flow characteristics and its solutions are conferred using this study with the help of graphs. This kind of investigation is useful in the mechanism of combustion, aerosol technology, high‐temperature polymeric mixtures, and solar collectors, which operate at moderate to very high temperatures. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing is a widespread stimulation technology in the petroleum industry. The retardation due to the fracture wall existence impacts the efficient placement of the proppant in fractures. Accurate prediction of the wall factor for proppant settling in fractures filled with Power-law fluids is important in predicting the transport distance and bed height of proppant in hydraulic fractures. However, few studies were conducted to analyze the wall factor of fracture on the settling proppant. In this study, a set of transparent parallel plates and a high-speed camera were used to record the settling behaviors of the proppant in the fracture. A total of 756 tests were carried out to analyze the effects of fluid properties, the dimensionless diameter, particle size, particle density, and the particle Reynolds number on the wall factor, involving the ranges of the dimensionless diameter and the particle Reynolds number are 0.04–0.9 and 0.0001–144.25, respectively. Results indicate that the wall factor is a function of both the dimensionless diameter and the particle Reynolds number. And a new model with 1.23% relative error was developed to predict the wall factor of the parallel plates on the spherical particles settling in the Power-law fluid. Finally, it was found that the wall effect vanishes when the dimensionless diameter is smaller than 0.057. The results of this study could help field engineers optimize proppant size and fracturing parameters. • The effects of fluid, particle, and slot properties on wall factor are studied. • Dimensionless diameter and Reynolds number affect wall factor in parallel plates. • A new model of the wall factor is developed by introducing Reynolds number. • Wall effect vanishes when the dimensionless diameter is smaller than 0.057. [ABSTRACT FROM AUTHOR]

Copyright of Special Oil & Gas Reservoirs is the property of Special Oil & Gas Reservoirs Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• The work characterizes mixing in a microchannel with the geometric wall modulation. • Heterogeneity prompted circulation zones generate perturbation caused higher mixing. • Mixing efficiency increased remarkably with flow behavior index and wave amplitudes. • Estimation is made to determine the optimum flow parameters with minimum pressure drop. The isothermal micromixing driven by an induced charge mechanism in a wavy patterned micro-channel is numerically analyzed. The walls of the microchannel are assumed to have modulated with the zeta potentials that vary slowly along the axial direction in a sinusoidal manner. The flow field of two miscible aqueous electrolytes are characterized by power-law model and are solved numerically using finite volume method. Contrary to the commonly held belief, our results predicted that the sinusoidal charged surface leads to an increase of interfacial contact area between two streams. It is noted that, the reduction of drag force leads to an improvement in pressure gradient due to high frequency fluctuations resulting an effective mixing compared to straight channel flow. Mixing is quantified numerically through charged patterned surfaces with the increment of flow behavior index (n). It is observed that mixing efficiency is not always beneficial in terms of performance factor since the pressure drop becomes higher with the increment of power-law index (n), Debye-H u ¨ ckel parameter (κH) and wave amplitude (α). Hence, we tried to estimate the microfluidic mixing by exploiting the optimum flow behavior indices with a controlled pressure drop. [ABSTRACT FROM AUTHOR]

• Interplay of fluid rheology and mixed convection in backward facing step channel. • Effect of baffle configurations and arrangements along with fluid rheology. • Evaluation of Nusselt number, pressure drop and entropy generation. • Increase in reattachment length with increase in Ri and decrease in n. • Interdependence of fluid rheology, buoyancy, baffle configuration and arrangement. The present study numerically investigates a two-dimensional, steady, laminar, incompressible and mixed convective flow of non-Newtonian fluid through a backward facing step channel with different baffle configurations. The power-law model is used to capture the confluence of fluid rheology and buoyancy for varying step to baffle distance, varying number of baffles and different arrangement (inline and staggered) of baffles. Different values of power-law index viz. n = 0.5, 0.8, 1, 1.2 and 1.5 are considered to encompass the shear-thinning (n < 1), shear-thickening (n > 1) as well as Newtonian fluids (n = 1) as a special case. The Reynolds number is fixed equal to 100 whereas the Richardson number has been varied within the range of 0.1–1 in the present investigation. The results obtained from the present investigation reveal the implications of power-law index, Richardson number and baffle configuration on the reattachment length, Nusselt number, pressure drop and entropy generation. The results show that the length of the recirculation zones formed in the backward facing step channel increases with increase in Richardson number and decreases with increase in power-law index. It is also found that the variation of heat transfer rate, pressure drop and entropy generation characteristics for varying step to baffle distance, different number of baffles and different arrangement and number of pairs of baffle is dictated by the interplay of power-law index and Richardson number. The findings of this study bear utility towards designing efficient thermodynamic system that can deliver maximum heat transfer with minimum irreversibility. [ABSTRACT FROM AUTHOR]

A numerical model is developed to study the combined effects of Soret and Dufour on mixed convection heat and mass transfer in a Power-law fluid saturated with Darcy–Forchheimer porous medium in the presence of nonlinear thermal radiation, chemical reaction and Ohmic dissipation. The governing boundary layer equations are solved numerically by using shooting method with Runge–Kutta Fehlberg integration scheme. The influence of Soret and Dufour numbers, chemical reaction, thermal Grashof number and solutal Grashof number on velocity, temperature and concentration fields are studied. The effects of some important physical parameters on skin-friction, Nusselt number and Sherwood number are studied in detail. [ABSTRACT FROM AUTHOR]

• Effect of screw flights on viscous dissipation in melt channels is investigated. • Three-dimensional non-Newtonian fully developed power-law flow is assumed. • Huge set of numerical solutions are approximated by symbolic regression models. • These models remove the need for time-consuming numerical simulations. • Models also apply to injection molding machines and to predicting drive power. Modeling the flow of non-Newtonian melts in single-screw extruders generally requires numerical methods. In this study, we analyze viscous dissipation for fully developed flow of non-Newtonian fluids within three-dimensional metering channels of single-screw extruders. Applying the theory of similarity we identified a set of four independent dimensionless influencing parameters that fully describe the underlying physics of the considered problem: the channel height-to-width ratio h / w , the screw-pitch ratio t / D b , the power-law exponent n , and the dimensionless down-channel pressure gradient Π p, z. Based on a comprehensive numerical parametric design study we developed two generalized symbolic regression models predicting dimensionless viscous dissipation – one for given pressure gradient, and the other one for given throughput. As a result of the three-dimensional modeling approach our regression models take the effects of flight flanks, transverse flow, and non-Newtonian fluid behavior into account. The accuracy of these developed models was proven by means of an error analysis using an independent data set. These models allow fast, stable and accurate predictions of viscous dissipation, thus contributing to the optimal design of extruder screws without the need for numerical simulations. Furthermore they are applicable to injection molding machines and for predicting the required drive power. [ABSTRACT FROM AUTHOR]

The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube. In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified, and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or ϕ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid. [ABSTRACT FROM AUTHOR]

Natural convection of power‐law fluids over a horizontal flat plate with constant heat flux is studied. The stretching transformations relating the similarity forms of the boundary layer velocity, pressure, and temperature profiles are applied to the governing boundary layer equations. The resultant set of coupled ordinary differential equations are solved analytically and numerically using the integral method and the finite difference method, respectively. The results are presented for the details of the velocity and temperature fields for various values of the non‐Newtonian power‐law viscosity index (n) and the generalized Prandtl number (Pr*). At a fixed value of the viscosity index, increasing the Prandtl number increases the skin friction and wall temperature. For Pr* > 1, a lower viscosity index results in larger wall skin friction, temperature scale, and thermal boundary layer thickness, and thus lower Nusselt number. The reverse trend is observed for Pr* < 1. By using an integral solution and the numerical results, a semi‐analytical correlation for the Nusselt number is obtained, valid for 0.5≤n≤1.5 and 0.1≤Pr*≤10. [ABSTRACT FROM AUTHOR]

In this article, we explore the heat transfer of non-Newtonian liquid food in the heating process in a channel connecting a tank. To achieve a rapid heat diffusion, several cylindrical agitators are inserted into the tank. We pay special attention to a Chinese traditional food, i.e. the black sesame paste, which is predicted by the power-law model. The fluid flow and heat transfer are investigated numerically, under the impacts of the angular velocity of cylinder, the stirrer size and the rotational direction. Three different settings are investigated: the two-stirrer, the three-stirrer, and the 2 × 2 stirrer settings. Several applicable strategies could be applied to improve the heat transfer in food engineering practices, including changing the size, the rotational velocity, the direction, and the number of stirrers in the heat exchanger. [ABSTRACT FROM AUTHOR]

The problem of boundary layer flow of a non-Newtonian power-law fluid (which is assumed to be incompressible) is considered. Existence and uniqueness of similarity solutions are considered for all values of the power-law index n>0. Conditions are determined (values of n and various parameters within the problem) where existence and uniqueness of solutions hold and where they do not hold. Exact solutions in some cases are exhibited. The asymptotic behavior of solutions is also determined for all values of n>0 of the non-Newtonian fluid. [ABSTRACT FROM AUTHOR]

Abstract The stability of shear-thinning fluid down an inclined plane is investigated theoretically with application to process engineering (coating process) and natural hazards as well (debris flow impact). The power-law model is used to describe the fluid rheological behavior. A linear stability analysis is brought out for building a generalized Orr-Sommerfeld model with appropriate definition of non-dimensional numbers in order to overcome the inconsistency of the existing shallow-water models. The solution to the secular equation showed that at zeroth order, there is no instability with respect to the long wave perturbations considered. Waves propagate without dispersion, at the same dimensional speed for any wavenumber. Moreover, the interface and the stream function are in phase, while the components of the perturbation velocities are respectively in phase and in quadrature of phase. Finally, the perturbation celerity decreases for increasing power law index, with a value of 2 as minimum for the Newtonian fluid. At first order, the effect of the different forces acting on the flow has been pointed out. It was particularly shown that pressure and surface tension have a stabilizing effect, while inertia and rheofluidification have a destabilizing effect. Moreover, the relative variation of critical Reynolds number increases with increasing reduced wavenumber for all values of slope tested while it decreases with increasing power-law index for all values of reduced wavenumber tested. Highlights • A generalized Orr-Sommerfeld equation was built and solved by a perturbation method. • Order zero: waves propagate without dispersion at the same speed for any wavenumber. • Perturbation celerity decreases for increasing power law index, with 2 as minimum. • Order one: the celerity correction only affects its growth rate but not its value. • Effects of all forces acting on flow stability have been respectively characterized. [ABSTRACT FROM AUTHOR]

In this work, the streamline topologies and their bifurcations for peristaltic transport of shear-thinning and shear-thickening fluids characterised by power-law model are analysed. The flow is assumed in a two-dimensional symmetric channel. The analytical solution is obtained in a wave frame of reference under low Reynolds number and long wavelength approximations. To study the streamline topologies, a system of non-linear autonomous differential equations is formed and the method of dynamical system is employed to investigate the bifurcations and their changes. Three different types of flow situations occur: backward flow, trapping and augmented flow. The conversions of backward flow to trapping and then trapping to augmented flow correspond to bifurcations. The stability and nature of bifurcations and their topological changes are explained graphically. For this purpose, a global bifurcation diagram is constructed. The backward flow and trapping regions are significantly affected by fluid behaviour index. In fact, the trapping region expands and the backward region shrinks by increasing the fluid behaviour index. Theoretical results are verified by comparing them with the experimental data, which is available in the literature. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Extending previous electrokinetic analyses based on a Newtonian fluid to power-law fluids, we investigate the behaviors of the ion current rectification (ICR) and the ion selectivity S of a conical nanopore having a pH-regulated surface. The bulk salt concentration C bulk , the solution pH, and the power-law index n are examined in detail for their influences on these behaviors. We show that the ICR ratio for the case where pH is lower than the isoelectric point (IEP) of the nanopore surface is different both quantitatively and qualitatively from that for the case where pH > IEP. The relative magnitude of the ICR ratio as n varies depends largely on the level of C bulk. In contrast, S (pH < IEP) is qualitatively similar to that for S (pH > IEP), where | S | decreases with increasing C bulk and/or decreasing n. In addition, S is very sensitive to n , for example, a decrease of n from 1.0 (Newtonian fluid) to 0.9 (pseudoplastic fluid) can yield a 245% increase in S at C bulk = 100 mM. Implying that the performance of ion separation can be improved by tuning the fluid viscosity. Mechanisms are proposed for explaining the observed behaviors in the ICR ratio. [ABSTRACT FROM AUTHOR]

Abstract In the present study, the momentum and heat transfer aspects from an isothermally rotating cylinder immersed in a power-law fluid, confined symmetrically and asymmetrically between two parallel walls are considered. The governing equations are solved numerically for the rotational Reynolds number ( 10 − 3 ≤ R e ≤ 40) , Prandtl number (1 ≤ P r ≤ 100) , power-law index (0.02 ≤ n ≤ 1) , blockage ratio ( 10 − 3 ≤ β ≤ 0.9999) and asymmetry ratio ( 10 − 4 ≤ γ ≤ 1) to elucidate the role of these parameters on the momentum and heat transfer characteristics. The results reported herein pertain to the two dimensional, steady, incompressible power-law fluid in the laminar flow region. The numerical strategy and method used here are validated by comparing the present results with some of the available experimental and numerical studies, showing good agreements. As far as can be ascertained, it is the first systematic numerical study of a rotating cylinder immersed in power-law fluids elucidating the complex interplay between the rheological and kinematic parameters. The flow field is visualized by plotting the streamlines and, hydrodynamic forces and torque acting on the rotating cylinder are computed. The numerical results are supplemented by a lubrication approximation analysis relevant to highly confined cases, i.e., large values of β. In this case, when confinement increases, the asymptotic scaling of the torque is given by ε − 1 / 2 where ε denotes the non-dimensional gap between the cylinder surface and the nearest wall. The heat transfer characteristics are presented in terms of the isotherm contours, and the local and average Nusselt numbers as functions of the aforementioned governing parameters. The rate of heat transfer exhibits a positive dependence on the Reynolds number, Prandtl number, confinement and the degree of asymmetry while the shear-thinning behavior decreases the rate of heat transfer above the corresponding value in Newtonian fluids. Finally, the present results are consolidated by fitting them in the form of a predictive correlation for the average Nusselt number for different blockage ratios studied herein. Highlights • Confinement and asymmetry enhances the torque up to 23%. • Shear-thinning behavior decreases the torque. • Lubrication expression for torque correction factor matches with numerical results. • Heat transfer is less in power-law fluid, counterintuitive result explained by thin boundary layer. • 56–58% additional heat can be transferred due to confinement and asymmetry. [ABSTRACT FROM AUTHOR]

Summary: This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power‐law fluid. The purpose of this study is to investigate the influence of anisotropy and power‐law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak‐off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated. [ABSTRACT FROM AUTHOR]

Highlights • Fluid–structure interaction between a microchannel with a soft top wall and a power-law fluid flow is analyzed. • The coupled problem is reduced to the solution of a single nonlinear first-order ODE. • The theory applies to both thin and thick plate-like microchannel top walls. • The theoretical predictions are benchmarked against full two-way coupled 3D simulations in ANSYS. Abstract We study fluid–structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff–Love theory of thin plates and Reissner–Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between the flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical theory for the flow rate–pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory. [ABSTRACT FROM AUTHOR]

The fountain flow of a non‐Newtonian fluid during a circular pipe filling is investigated. Mathematical description of the process is based on the equations of motion and continuity. The system of equations is completed by the Ostwald‐de Waele rheological equation. The slip condition is used at the contact line. The numerical solution of the formulated problem is obtained using a computational technology based on the finite volume method, SIMPLE procedure, and invariant method, which is used for numerical realization of the boundary conditions on the free surface. The results of parametric studies of the flow kinematic characteristics are presented depending on the governing dimensionless criteria and power‐law index. © 2018 American Institute of Chemical Engineers AIChE J, 65: 850–858, 2019 [ABSTRACT FROM AUTHOR]

Copyright of Journal of Drainage & Irrigation Machinery Engineering / Paiguan Jixie Gongcheng Xuebao is the property of Editorial Department of Drainage & Irrigation Machinery Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Hydrodynamic interaction between swimmers in power-law fluid is systematically investigated by using an immersed boundary-lattice Boltzmann method. The squirmer model is applied to mimic swimmers and distinct kinematic features are found for them in different types of power-law fluids. For parallel interactions, pushers (a type of swimmers) attract each other to certain orientation angles eventually while pullers (another type of swimmers) push themselves away and turn to the head-to-head state. For interactions with initial swimming towards each other, puller eventually departs away from the other one while pusher is more easily locked at certain location. The feature of power-law fluid is responsible for the trajectories of locomotion. In addition, the distribution of viscosity around the swimmer deeply relies on the tangential velocity at the boundary. The peaks and valleys of the viscosity locate at sites where the streamlines are parallel and normal to the surface of the swimmer, respectively. Finally, the collision time for neutral swimmer (β = 0) and a kind of puller (β = 2. 5) decreases as power-law index increases while a non-monotonic relation is found for another kind of puller (β = 5). Highlights • Hydrodynamic interaction between swimmers in power-law fluid is studied. • Distinct kinematic features are found in different types of power-law fluids. • Viscosity around swimmer deeply relies on the tangential velocity at the boundary. • Collision time for swimmer and a puller decreases as power-law index increases. [ABSTRACT FROM AUTHOR]

• The paper examines the power-law nanofluid flows due to a shrinking sheet with mass transpiration under inclined MHD. • The governing PDEs are similarly transformed into nonlinear ODEs and solved analytically. • The magnetic field significantly increases the magnitude of the skin friction and mass transpiration. • Cu-H 2 O nanofluid is used to examine the entaire calculation. This paper examines the power-law nanofluid flows due to a shrinking sheet with mass transpiration under inclined MHD. The governing partial differential equations are similarly transformed into nonlinear ordinary differential equations and solved analytically. The mathematical model through analytical solutions graphically shows that the flow's dynamics depending on the Chandraselhar number, mass transpiration, nanofluid and inclined angle parameters. The main findings and methods of the present work includes the closed-form exact solutions are examined for some special cases and one of them is an algebraic solution. Specific and quantitative analytical solutions provide important understanding to the boundary layer flow for power-law nanofluid. The present study reveals that the magnetic field significantly increases the magnitude of the skin friction and mass transpiration. Cu-H 2 O nanofluid is used to examine the entaire calculation. Nanofluids are suspensions of nanoparticles in fluids that show significant enhancement of their properties at modest nanoparticle concentration. [ABSTRACT FROM AUTHOR]

• Comparison of ellipsoidal particle migration with equivalent spheres is explored. • Effects of fluid rheology and inertia on the migration behaviour are analysed. • Effects of particle shape and size on the migration behaviour are obtained. • Shear-thinning fluid with high fluid inertia is beneficial for fast focusing particles. We numerically investigate the migration of an ellipsoidal particle in square channel flow of power-law fluids with equivalent spheres. The effects of particle shape and blockage ratio (k), power-law index (n) and Reynolds number (Re) of the fluid on the equilibrium position and travel distance are explored. The results show that the equilibrium positions of prolate ellipsoidal particle, oblate ellipsoidal particle and two equivalent spheres approach the channel centreline with increasing particle size, fluid power-law index, and with decreasing Reynolds number. The second stage travel distance for the ellipsoidal particles to reach the final equilibrium position at the wall bisector decreases with increasing Re , and with decreasing n , while the effect of k depends on the particle shape. The equivalent sphere with the same volume can predict the equilibrium position of prolate ellipsoidal particle in log-rolling (LR) rotational mode, while the second stage travel distance of prolate ellipsoidal particle is greater than two equivalent spheres. The equivalent spheres with the same rotational diameter can be used to predict the equilibrium position and the second stage travel distance of oblate ellipsoidal particle. The results are helpful for designing microfluidic devices with high precious and efficiency. [Display omitted] [ABSTRACT FROM AUTHOR]

The measurement and the investigation of the errors in a Couette rheometer have been a topic of considerable interest in many rheometric studies. In the present study, a more accurate predictor-corrector method based on CFD and the analytical solution of the problem is described. Comparing to the previous CFD-based method, in addition to considering the effect of the end parts, the presented correction factors also take into account the effect of the wide gap into a single coefficient. The correction factors are computed for both Newtonian and non-Newtonian fluids in wide and narrow gap rheometry. Results showed that the shear rate distribution across the gap is highly non-linear in non-Newtonian wide gap rheometry. Moreover, for very shear thinning fluid i.e. n < 0.4 in narrow gap rheometry, there is a need to apply correction factor to the calculated fluid properties. Comparing the presented CFD approach and the current approach, the correction factor can be enhanced up to 16% depending on the fluid behavior and the gap distance.

To help in the efficient design of fluid flow in electroosmotic pumps, electroosmotic flow of non-Newtonian fluid through porous polymer membrane at high zeta potentials is studied by mainly evaluating the total flow rate at different physical parameters. Non-Newtonian fluid is represented by the power-law model and the porous polymer membrane is considered as arrays of straight cylindrical pores. The electroosmotic flow of non-Newtonian fluid through a single pore is studied by solving the complete Poisson–Boltzmann equation and the modified Cauchy momentum equation. Then assuming the pore size distribution on porous polymer membrane obeys Gaussian distribution, the performance of electroosmotic pump operating non-Newtonian fluid is evaluated by computing the total flow rate of electroosmotic flow through porous polymer membrane as a function of flow behavior index, geometric parameters of porous membrane, electrolyte concentration, applied voltage, and zeta potential. It is found that enhancing zeta potential and bulk concentration rather than the applied voltage can also significantly improve the total flow rate in porous polymer membrane, especially in the case of shear thinning fluid.

Non-Newtonian fluid flow in porous and fractured media is of considerable technical and environmental interest. Here, the flow of a non-Newtonian fluid in a variable aperture fracture is studied theoretically, experimentally and numerically. We consider a shear-thinning power-law fluid with flow behavior index n. The natural logarithm of the fracture aperture is a two-dimensional, spatially homogeneous and correlated Gaussian random field. An experimental device has been conceived and realized to allow the validation of the theory, and several tests are conducted with Newtonian and shear-thinning fluids and different combinations of parameters to validate the model. For Newtonian fluids, experimental results match quite well the theoretical predictions, mostly with a slight overestimation. For non-Newtonian fluids, the discrepancy between experiments and theory is larger, with an underestimation of the experimental flow rate. We bear in mind the high shear-rates involved in the experiments, covering a large range where simple models seldom are effective in reproducing the process, and possible interferences like slip at the wall. For all test conditions, the comparison between analytical and numerical model is fairly good.

The results of an experimental study on the condition of incipient transport of non-cohesive particles due to the flow of a power-law fluid in a rectangular pipe are presented in this article. The pipe can change its inclination, and experiments were carried out with positive and negative slopes. From a dimensional analysis, the parameters that define the condition of incipient motion were found and validated with experimental data. Thus, the threshold condition is well defined by a particle Reynolds number and a Galileo number, properly modified to take into account the power-law rheology of the fluid. The experimental data are also presented in a standard Shields diagram, including the data obtained in other studies carried out in open-channel laminar flows of Newtonian and power-law fluids.

The steady flow with heat transfer through a porous medium of a non- Newtonian power-law fluid due to the uniform rotation of a disk of infinite extent is studied. The porous medium is assumed to obey Darcy's model which accounts for the drag exerted linearly by the porous medium on the steady flow. Von Karman similarity transformation is used to transform the governing boundary layer partial differential equations to ordinary differential equations. Therefore, the resulting momentum equations as well as the energy equations including the viscous dissipation term are solved asymptotically for large values of the porosity parameter and Prandtl number.

Abstract Three-dimensional simulations on the flow and wake behaviour of shear-thinning non-Newtonian fluids past spherical particles are carried out using a computational fluid dynamics based solver with the aim to investigate the critical Reynolds numbers for the onset of steady axisymmetric flow separation point and steady non-axisymmetric flow separation point. The present solver is thoroughly benchmarked through the conventional steps of domain independence, grid independence, and validation of the existing literature results. Before obtaining the critical Reynolds numbers for the case of shear-thinning fluids, the same for the case of Newtonian fluids are obtained and found to be in excellent agreement with literature values. The major findings of this work indicate that for the case of shear-thinning fluids, the first critical Reynolds number for the onset of steady axisymmetric flow separation increases with the decreasing power-law index of the non-Newtonian fluids; whereas the reverse is true for the case of second critical Reynolds number at which steady non-axisymmetric flow separation occurs. Furthermore, the non-axisymmetry is observed in both xy and xz planes for power-law fluids when n = 0.61 and 0.54; whereas in the case of fluids with n = 0.87, 0.73 and 0.66, the non-axisymmetry is observed only along the xz plane. Finally, correlations are proposed for both the critical Reynolds numbers as function of the power-law behaviour index. Graphical abstract Unlabelled Image Highlights • Critical Re of shear-thinning fluid flow past spheres based on 3D CFD results • Critical Re for onset of axisymmetry separated flow increases with decreasing n. • Critical Reynolds number for non-axisymmetry flow decreases with decreasing n. • Lift coefficient vs. Re are presented for varying values of power-law index. • Correlations for the critical Reynolds numbers as function of n are proposed. [ABSTRACT FROM AUTHOR]