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Transient three-dimensional numerical simulations of power-law fluid flow in an annular channel with a diameter ratio of 1/2 were performed. The outcomes of the simulations using the URANS approach were contrasted with the results of the RANS and LES approaches for Newtonian and power-law fluids. It was demonstrated that comparable outcomes to those obtained through LES can be achieved through URANS with a reduced computational cost. It was determined that the RANS approach tends to underestimate turbulent kinetic energy and pressure losses. Parametric studies were conducted using the URANS approach, encompassing a range of Reynolds numbers (R e) between 100 and 10,000, dimensionless rotation rates (N) values between 0.2 and 5, and power-law indices (n) between 0.4 and 1. The following flow regimes were identified: (1) flow without vortices; (2) Taylor-type toroidal vortices; (3) Görtler-type continuous spiral vortices swirling around the inner cylinder; and (4) small-scale Görtler-type vortices near both channel walls. The numerical experiments demonstrated that the rotation of the inner cylinder resulted in three notable effects: a reduction in the apparent viscosity within the vicinity of the rotating cylinder, a decline in viscous shear stresses, and the development of Görtler-type vortex structures, which contributed to an increase in energy losses. Additionally, at Reynolds numbers below 300, high rotation led to the formation of Taylor-type vortices and a reduction in pressure losses. The power law fluid requires increased rotation of the inner cylinder to form vortices and transition the flow to turbulent. When the Reynolds number is less than 300, the first mechanism is the dominant factor, resulting in a reduction in pressure loss. At Reynolds numbers of approximately 300, the first two mechanisms are in competition, with the pressure loss dependent on the power law index, n. Finally, at Reynolds numbers greater than 300, secondary vortex structures, such as Görtler vortices, become the dominant factor, leading to an increase in pressure loss with rotation. [Display omitted] • Results of RANS, URANS and LES approaches are compared. • Flow features and vortex structures for Newtonian and power-law are described. • Parametric study was carried out by RANS and URANS. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

Fluid disinfection involving ultraviolet (UV) rays is a promising method due to its easy implementation and low cost compared to other methods. In the present work, fluid disinfection in a Taylor-Couette configuration operating with power-law fluids with different absorbance coefficients, and fluence rates were simulated using the lattice Boltzmann Method. The effects of operating parameters such as Taylor and axial Reynolds numbers, power-law index behavior, and fluence rate were analyzed. Results show that the required UV dose decreases for an increase in absorbance coefficient, while it grows for increasing power-law indexes. For Ta = 120 and Re = 3, the disinfection reaches 82.3% for pseudo-plastic fluids and is complete for dilatant fluids. Considering different absorbance coefficients, it was observed that α = 0.4 leads to complete disinfection regardless of the fluid. For α = 0.5 ⁠, fluid disinfection is complete for the dilatant fluid only. A value of 0.6 leads to partial disinfection (≠ 90%) for all fluids. [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 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 distinction between homogeneous and heterogeneous chemical reactions is crucial because many chemically reactive systems, such as hydrometallurgical processes, cooling towers, biological systems, fog dispersion, catalysis, etc., involve both types of reactions. Thus, this study analyzes the heat transmission (HT) characteristics in an MHD stagnant flow of power-law fluid caused by a spinning disk that is stretched and saturated in a porous medium. The study considers homogeneous-heterogeneous (HH) reactions and nonlinear thermal radiation subject to no-slip and convection boundary conditions. The leading equations are switched into ordinary differential equations (ODEs) employing similarity variables. The study focuses on the dimensionless concentration, velocity, temperature, Nusselt number, and skin friction coefficient, which are discussed in detail in the results and discussion section. The study observes that for power-law fluids with an index value less than 1, the skin friction coefficient decays as the power-law index grows. It also notes that the dimensionless skin friction of power-law fluids decreases as the velocity ratio increases. The dimensionless concentration increases with Schmidt and modified Prandtl numbers for both power-law fluids over a stretching spinning porous disk. The HH reaction parameters decline the concentration of power-law fluids.

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]

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.

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]

Effect of external-recycle operations on the heat-transfer efficiency, specifically for the power-law fluid flowing in double-pass concentric circular heat exchanger under sinusoidal wall fluxes, is investigated theoretically in the developed countries. Given that the fluid is heated twice on both sides of the impermeable sheet, four flow patterns proposed in recycling double-pass operations are expected to make substantial improvements in the performance of heat exchanger device in this study. Theoretical predictions point out that the heat-transfer efficiency increases with the ratio of channel thickness of double-pass concentric circular heat exchanger for all new designs under the same working dimension and the operational condition. The fluid velocity within the double-pass heat exchanger is increased by the fluids flowing through divided subchannels, which contributed to the higher convective heat-transfer efficiency. A simplified mathematical formulation was derived for double-pass concentric circular heat exchangers and would be a significant contribution to analyze heat transfer problems with sinusoidal wall fluxes at boundaries. The results deliver the optimal performance for the proposed four configurations with the use of external recycle compared to those conducted in single-pass, where an impermeable sheet is not inserted. The influences of power-law index and impermeable-sheet position on average Nusselt numbers under various flow patterns are also delineated. The distribution of dimensionless wall temperature was lower at the level of relative smaller thickness of annular channel, and the average Nusselt numbers for four external-recycle configurations and single-pass device were more suitable for operating under same condition. The ratio of the power consumption increment to heat-transfer efficiency enhancement demonstrates the economic feasibility among various configurations of double-pass concentric circular heat exchanger. The results also show that the external-recycle configuration (say Type B in the present study) serves as an important economic advantage in designing concentric circular heat exchangers for heating power-law fluids due to the smaller volumetric flow rate in annular channel with exiting outlet temperature.

The main objective of the present paper is to construct a new class of space–time discretizations for the stochastic p -Stokes system and analyze its stability and convergence properties. We derive regularity results for the approximation that are similar to the natural regularity of solutions. One of the key arguments relies on discrete extrapolation that allows us to relate lower moments of discrete maximal processes. We show that, if the generic spatial discretization is constraint conforming, then the velocity approximation satisfies a best-approximation property in the natural distance. Moreover, we present an example such that the resulting velocity approximation converges with rate 1 / 2 in time and 1 in space towards the (unknown) target velocity with respect to the natural distance. The theory is corroborated by numerical experiments. [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]

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 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]

An analytical formulation, referred to as conjugated Graetz problems, is developed to predict the temperature distribution and Nusselt numbers for the power-law fluid flowing in a double-pass concentric circular heat exchanger under sinusoidal wall fluxes. A new design of inserting an impermeable sheet into a concentric tube, in parallel, to conduct recycling double-pass operations has been studied theoretically in the fully developed region, resulting in substantial improvements in the performance of heat exchanger device. The analytical solution was derived using the complex functions by transforming the boundary value problem into ordinary differential equations with the aid of the Frobenius method. The influences of power-law index and impermeable-sheet position on average Nusselt numbers with various designs and operating parameters are also delineated. The theoretical predictions show that the heat transfer efficiency is considerably improved through operating the double-pass device compared to via a single-pass circular heat exchanger (where an impermeable sheet is not inserted). The economic feasibility of operating double-pass concentric circular heat exchanger for power-law fluids is exemplified by the ratio of the heat-transfer efficiency enhancement and the increment in power consumption. The double-pass effect from increasing the convective heat-transfer coefficient can compensate for the rise in power consumption, which serves as important economic advantage of this design.

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]

In this paper, a numerical investigation is done to understand the two-dimensional flow behaviorof power-law fluids past a rotating elliptic cylinder in unconfined domain. The flow field around the cylinder is calculated using ANSYS (FLUENT 15) The sliding mesh method (SMM) is used to treat moving solid–fluid boundary. The engineering parameters like drag coefficient, lift coefficient and complete kinematic variables such as stream function and vorticity have been calculated for the range of dimensionless parameters namely aspect ratio of the cylinder e = 0. 1 and 0.7, rotational speed (1 ≤ α ≤ 4), Reynolds number (5 ≤ R e ≤ 40) and power-law index (0. 4 ≤ n ≤ 1. 8). The emphasis has been given to see the effect of the power-law index (n) and Reynolds number (R e), rotational speed α and aspect ratio of cylinder e on flow characteristics around the cylinder in laminar flow regime. Before presenting the results, a qualitative as well as a quantitative comparison has been done between the present result and experimental and numerical result presented in the literature. Further, a detailed streamline and vorticity patterns in the vicinity of the cylinder is shown to demonstrate the wake formation phenomenon around the cylinder. The increase in rotational speed and power-law index exhibit a similar effect on wake formation phenomena. Due to rotational motion of the cylinder drag and lift coefficient vary in periodic manner with time/orientation of cylinder. The average value of drag is seen to decrease with R e and α and a complete trend is displayed with power-law index, n. The negative lift coefficient is observed due to anticlockwise motion of the cylinder for all parameters considered here. The results of this work clearly show the strong dependency of flow phenomenon around the rotating elliptic cylinder on power-law index, rotational speed, aspect ratio, and Reynolds number. [Display omitted] • Flow phenomenon of power-law fluids around a rotating elliptic cylinder is numerically investigated using ANSYS (FLUENT). • Effect of power-law index (n), Reynolds number (R e), and rotational speed (α) on streamlines and vorticity contours and engineering parameters ( C D , C L ) are studied. • Enveloping vortex around the cylinder grow in size as the rotational speed (α) and power-law index (n) increases. Similar increasing trend observed for detached vortex with R e. • The drag and lift coefficient decreases with rotational speed (α) and Reynolds number (R e). However, the dependency on power-law index is complex and no trend is found. [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 paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.

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.

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.

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]

In the current study, the settling, interaction, drafting, kissing, and tumbling of two identical and non-identical circular particles were simulated in a two-dimensional box in shear-thinning, Newtonian, and shear-thickening fluids by using the combined lattice Boltzmann-smoothed profile methods. Furthermore, the drag coefficient of one particle settling for different power-law indexes and Archimedes numbers was calculated. Also, the effect of the diameter ratio of the two particle pairs was considered during settling. The developed method was validated by simulating the settling of one particle and two identical particles in a Newtonian fluid. To consider two non-identical particles, two cases were examined. In Case A, the larger particle was above the smaller one and in the Case B, the smaller particle was above the larger one. The results showed that the two non-identical particles were separated more easily than the identical ones. In the settling of two particles under the same Archimedes number, the drafting and kissing time considerably increased by changing the non-Newtonian fluid behavior from a shear-thinning one to a shear-thickening one. Also, when the larger particle was above the smaller one, the time duration of the kissing stage increased with the decrease in the diameter ratio. [ABSTRACT FROM AUTHOR]

This work evaluates the benefits of using the Anderson acceleration method in a finite volume context to solve convective-dominant power-law non-Newtonian fluid flows. We use a pressure-correction fractional step approach adapted to the finite volume method as a segregation strategy with the Picard linearization scheme. We evaluate the accuracy and performance of the Anderson method when we use TVD and non-TVD convective schemes. The work emphasizes algorithmic and programming aspects. We conduct several numerical tests to support the findings and evaluate the sensitivity of the methods concerning numerical parameters. First, we evaluate the convective schemes when solving two problems with analytical solutions to validate the implementation and accuracy. Subsequently, we use the Anderson acceleration method to solve the square lid-driven cavity flow problem for a steady case defined by Re = 7500 and for unsteady solutions defined by Re = 10 , 000 and 20,000. In this case, we analyze the robustness and performance of the schemes when solving nonlinear convection-dominant flows. Finally, we solve the lid-driven cavity flow problem for power-law fluids of shear-thinning and shear-thickening behavior defined by a power-law index n = 0. 5 and n = 1. 5. In this last case, we resolve a steady flow defined by Re = 5000, and then, we evaluate the methods to approximate unsteady solutions defined by Re = 15,000 with n = 0. 5 and Re = 25,000 with n = 1. 5. As the most important result, we reduce the number of nonlinear iterations using Anderson by 91.6% in the steady case and 79.9% in the time-dependent one in the Newtonian case. In the case of shear-thinning and shear-thickening fluids, the nonlinear iterations were reduced up to 49.7% and 64.3% when using acceleration in an unsteady, highly convective flow. • Efficient Picard–Anderson acceleration schemes for unsteady power-law fluid flows. • Assessment of TVD and non-TVD schemes for unsteady convective-dominant power-law fluid flows. • Anderson method allows the use of larger time steps in unsteady convection-dominant flows. • Anderson method improves convergence of Picard in unsteady convection-dominant flows. • Anderson acceleration method decreases nonlinear iterations drastically. [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]

This work numerically studies the momentum and thermal characteristics of the power-law fluids flowing through a rectangular-shaped orifice fitted in a two-dimensional channel, over wide ranges of conditions: fluid behavior index, n (0.3–1.0), Reynolds number, Re (1–50), Prandtl number, Pr (10−100), aspect ratio, β (0.3–0.7) and three different locations of the orifice, C o (0.5–0.75). Extensive results have been analyzed in terms of streamlines, separation zones, discharge coefficient, isotherm contours, temperature profiles and local Nusselt number. Multiple separation zones are formed in downstream section depending upon the combinations of parameters, which, in turn, influence the discharge coefficient and the local Nusselt number. Separated flow regions formed on the bottom wall expand with increasing Reynolds number (Re), while it decreases with n and β and shows a complex dependence on C o. The local Nusselt number, Nu L , observed herein which is found to be more pronounced at high C o and low n and β for the upper wall. Further, it bears an inverse relation with n , on both walls while a strong effect of orifice location, C o and aspect ratio, β is seen over the range of conditions spanned here. • Influence of orifice location on the flow and thermal characteristics of power-law fluids. • Effect of orifice aspect ratio on the momentum and heat transfer characteristics. • Discussion on the flow visualization and isotherm contours. • Demonstration of the orifice discharge coefficient. • Effect of orifice location and aspect ratio on the local Nusselt number. [ABSTRACT FROM AUTHOR]

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

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]

• Developed is a two-layer model for non-isothermal film flow of power-law fluids on a porous incline. • An expression for the critical Reynolds number for long-wave instability is obtained. • A reduced dimensionality model is used to study the nonlinear effects. • Important correlation found between substrate filtration and thermocapillary instability. The stability of the steady uniform flow of a power–law fluid down an inclined porous layer heated from below is investigated by means of a two–layer model. Under the long-wave approximation, the flow model is deduced starting from the continuity and momentum equations in the fluid film, the continuity and the generalized Darcy's law in the porous layer, and the energy balances in both the film and the porous layer. The associated boundary conditions account for the surface tension and the Beavers-Joseph velocity slip at the film bottom. A linear stability analysis of both two–dimensional and one–dimensional, i.e. depth–integrated, formulations is performed to define the neutral stability conditions, separately analyzing the S- and H-mode contributions. The influence of all the dimensionless governing parameters on the stability is discussed. Finally, the numerical solution of the depth–integrated model allows for an investigation of the nonlinear growth of H-mode unstable perturbations up to the formation of permanent waves and a discussion of the role of the magnitude of thermocapillary effects on the wave shape. Present results, taken collectively, indicate that, similarly to the isothermal case, the presence of a porous medium strongly modifies the stability bounds even in non-isothermal conditions, suggesting its potentiality as a passive control for the themocapillary instability for both H- and S-modes. Moreover, it is found that the shear-thinning behaviour leads to flows which are less stable but also less susceptible to thermocapillary effects. [ABSTRACT FROM AUTHOR]

Abstract Enhanced Oil Recovery (EOR) is a process that extends reservoir life through field operations that aim to increase reservoir displacement efficiency. Injection of polymeric solutions, which is a chemical EOR process, improves sweep efficiency by decreasing the mobility of the injected fluids. One challenge in polymer flooding is to model the non-Newtonian rheological behavior of the injected solutions due to the complex interdependence between fluid flow velocity, fluid viscosity and shear rate. Proper reservoir management requires a thorough understanding of non-Newtonian fluid flow behavior through porous media, thus the need for new and improved mathematical models that describe the transient pressure behavior in wells. In this work we consider the flow of non-Newtonian pseudoplastic fluids in homogeneous isotropic porous media. To describe the rheological polymer behavior, we used the well-known power-law model, which leads to a nonlinear problem. In this paper, a novel semi-analytical solution is obtained by combining spatial domain discretization with pseudotime, so the flow problem is rewritten as a system of linear equations in Laplace domain. We also presented a variation of the proposed solution by assuming a pseudostationary behavior of the non-Newtonian velocity. Both approaches are compared to previously published approximated analytical solutions. One interesting aspect of our work is that it can be extended to more realistic polymer rheological models. Highlights • A new semi-analytical solution for pressure transient behavior of a power-law fluid in porous media. • Two different approaches: pseudotime and pseudostationary. • This procedure may be extended to other rheological models. [ABSTRACT FROM AUTHOR]

Highlights • The tortuosity fractal dimension is introduced to the model. • The diffusion coefficient of power-law fluids is derived. • The W-M function is applied to manifest the fractal characters of the pores. • The comparisons between the simulation and experiment show validity of the new model. Abstract The study of fluid diffusion is an important aspect of heat and mass transfer of the porous fibrous materials. This work established a fractal model for the diffusion of power-law fluids in porous fibrous materials by considering the pore size distribution and the tortuosity of the capillary. Adopting the Darcy's law and the Hagen–Poiseuille's law, the diffusion coefficient of power-law fluids is derived as a function of the tortuosity fractal dimension, the pore size fractal dimension and the flow behavior index, in which the phase transition and the adsorption effect of fiber as well as the influence of gas diffusion and temperature change are taken into consideration. And the Weierstrass–Mandelbrot (W-M) function is applied to manifest the detailed fractal characters of the pores. Focusing on an analytical expression of the diffusion of power-law fluids in porous fibrous materials, the changes of liquid volume fraction, gas concentration and temperature distribution subjected to the specification initial and boundary conditions are simulated numerically. The test of this approach on the height of fluids when the bottom of cotton fabrics is immersed in the water display the clear diffusion of fluid in fiber. Our preliminary results indicate the important roles that the porosity and flow behavior index play in the fluids transfer in the porous fibrous materials: the fluids with lower power law index rise higher heights and diffuse more rapidly, meanwhile, the height increases with the porosity. [ABSTRACT FROM AUTHOR]

Highlights • Shear-thinning promotes heat transfer. • Cylinder rotation may improve or impede heat transfer. • Nusselt number initially decreases with rotation and then increases. • Nusselt number bears positive relation with Grashof and Prandtl number. • For weak buoyancy effects, rotation augments heat transfer. Abstract Laminar natural convection heat transfer in a power-law fluid from an isothermal rotating cylinder placed coaxially in a square duct has been studied numerically over the following ranges of conditions: Grashof number (10 ⩽ Gr ⩽ 10 3) ; Prandtl number (0.72 ⩽ Pr ⩽ 100) ; power-law index (0.2 ⩽ n ⩽ 1.5) and non-dimensional rotational velocity (0 ⩽ S ⩽ 4). The spatial variation of the velocity and temperature fields are visualised in terms of the streamline and isotherm patterns, and temperature and vertical velocity at a few locations, respectively. Indeed, a range of flow patterns including twin-celled and single-celled recirculating regions can be observed depending upon the relative strengths of the buoyancy-induced and forced flow. The rate of heat transfer is described in terms of the distribution of the local Nusselt number over the surface of the cylinder together with its surface averaged value. As expected, the mean Nusselt number shows a positive dependence on the both Grashof and Prandtl numbers irrespective of the values of the power-law index and rotational velocity. For a non-rotating cylinder (S = 0), shear-thinning fluid behaviour promotes heat transfer, whereas shear-thickening viscosity impedes it with reference to that in Newtonian fluids otherwise under identical conditions. For the case of a rotating cylinder (S ≠ 0), the rotation has positive influence on the rate of heat transfer at low values of the Grashof or Rayleigh number (Ra < 500) irrespective of the type of fluid behaviour, i.e., shear-thinning or shear-thickening or Newtonian. However, at high values of the Grashof or Rayleigh numbers, the gradual increase of rotation of the cylinder first lowers the rate of heat transfer, and then increases it for shear-thickening (n > 1) and Newtonian fluids (n = 1). On the other hand, a reverse trend is seen for shear-thinning fluids. These non-monotonous trends in the overall heat transfer stem from the interactions between the rate of variation of the fluid viscosity and the temperature gradient on the surface of the cylinder. Therefore, a prudent choice of the operating conditions and the fluid behaviour can be used to regulate the rate of heating or cooling from a rotating cylinder. Finally, the present values of the average Nusselt number are correlated in order to facilitate the interpolation of the present results for the intermediate values of Gr , Pr , S and n and/or the estimation of heat transfer duty in a new application. [ABSTRACT FROM AUTHOR]

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in the liquid phase at a gas volume fraction of 6%. The flow is driven downward by a constant volumetric flow rate corresponding to a friction Reynolds number of Reτ≈127.3. The Eötvös number is varied between Eo=0.3125 and Eo=3.75 in order to investigate the influence of quasi-spherical as well as wobbling bubbles and thus the interplay of the bubble deformability with the power-law behavior of the liquid bulk. The resulting first- and second-order fluid statistics, i.e., the gas fraction, mean velocity and velocity fluctuation profiles across the channel, show clear trends in reply to varying power-law indexes. In addition, it was observed that the bubble oscillations increase with decreasing power-law index. In the channel core, the bubbles significantly increase the dissipation rate, which, in contrast to its behavior at the wall, shows similar orders of magnitude for all power-law indexes.

In this paper, a numerical investigation on the effects of variable viscosity, slip velocity and heat generation or absorption on power-law fluids with heat and mass transfer over a moving permeable surface is carried out. The transformation of the governing boundary layer equations into ordinary differential equations has been performed by applying similarity transformations. The transformed governing equations are numerically solved by using MATLAB BVP solver bvp4c. The obtained results are presented graphically and discussed for various values of the viscosity parameter, the slip parameter, the heat generation or absorption parameter, the Eckert number and Lewis number. The result shows that, the variable viscosity parameter , it is confirmed that the local skin-friction coefficient decreases while heat and mass transfer rates increases. The heat and mass transfer rates increases rapidly on increasing the Prandtl number. The rate of mass transfer is rapidly increased when the Lewis number increased.