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The paper investigates the effects of the Forchheimer term (form drag) and vertical pressure gradient on the buoyancy‐induced instability of power‐law saturating fluid in a porous plane medium. Two isobaric permeable layers are assumed to sandwich the horizontal porous plane. In the meantime, Dirichlet and Neumann equations are the thermal boundary conditions considered for the lower and upper layers. A base flow developed analytically via the governing equations is just in function of the Péclet number P $P$, with no dependence on the characteristic parameter of the power law fluid. A linear stability analysis consists of substituting a base flow with a small perturbation into the governing equations leads to a four‐order eigenvalue problem. An analytical solution is performed for the asymptotic cases of an infinite wavelength. The Runge–Kutta solver is applied together with the shooting technique to evaluate numerical solutions for the general case of nonnegligible wave numbers. Among the findings is the contribution of the Forchheimer term in the variation of the threshold Péclet number whose value can switch the wave numbers from zero to nonzero and increase the stability of the system. [ABSTRACT FROM AUTHOR]

The mechanics of bile flow in the biliary system plays an important role in studying bile stasis and gallstone formation. Bile duct stricture is an abnormal phenomenon that refers to the bile duct getting smaller or narrower. The main objective of this study is to study the influence of stricture on bile flow dynamics using numerical methods. We employed a numerical Computational Fluid Dynamics model of the bile flow within a strictured hepatic duct. We studied and compared the influence of stricture severity, stricture length, eccentricity, and bile flow property on the bile flow dynamics. The bile flow velocity, pressure distribution, pressure drop, and wall shear stress are provided in detail. The stricture alters the normal bile flow pattern and increases flow resistance. At the location upstream and downstream of the stricture, bile flow slows down. In the area of the stricture throat, bile flow is accelerated, and recirculation forms behind the stricture. The maximum pressure drop of the biliary system increases with the stricture length. The eccentricity makes the flow deflect away from the duct's centerline. The behavior of the deflected flow is significantly altered downstream of the stricture. Such bile flow behavior as deceleration and recirculation may lead to cholestasis. Stricture alters bile flow in the biliary tract, causing changes in biliary hydrodynamic indexes, which could potentially serve as an omen for gallstone formation and other related diseases. The consideration of the bile duct stricture could lead to better patient stratification. [ABSTRACT FROM AUTHOR]

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non‐Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (Lb) of 0.2 ≤ Lb ≤ 0.6 and the outlet hole positions (S) of 0≤S≤0.9 $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, Nuavg $N{u}_{\mathrm{avg}}$ increased by 23.3% at n=0.6 $n=0.6$, and 13.8% at n=1.2 $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer. [ABSTRACT FROM AUTHOR]

In this paper, we show that a weak solution for unsteady flows of 3D shear‐thinning fluids is strong under certain integrability assumptions about two components of the vorticity. In particular, if two components of the vorticity belong to the marginal critical space L1(0,T;BMO)$$ {L}^1\left(0,T; BMO\right) $$, then the solution is strong. [ABSTRACT FROM AUTHOR]

The measurement capabilities of a newly developed in‐situ rheometric device based on a single passive acoustic emission sensor and machine learning algorithms were investigated. Two surfactant structured fluids demonstrating complex non‐Newtonian rheology (Power‐law and Herschel‐Bulkley models) were examined. Furthermore, a static evaluation on the laboratory scale in comparison to dynamic processing on the pilot scale was conducted. The results indicate that the machine learning algorithms of this technology can identify, in > 90 % of scenarios, the correct type of rheology or the manufacturing process step across both scales. This identification is based on solving a classification problem using quadratic support vector machine learning algorithms, which have proven to deliver the most robust predictions across a choice of 24 different algorithms tested. Additionally, a new format of in situ rheology display was introduced, referred to as RRF™ factor. [ABSTRACT FROM AUTHOR]

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate the steady two‐dimensional flow of a magnetohydrodynamics Maxwell liquid over a stretched exterior having prescribed exterior hotness in the presence of changeable free stream temperature. Here the Maxwell liquid replica reflects non‐Newtonian liquid behavior. By means of similarity alterations, the leading differential equations which are partial in nature are altered to differential equations that are ordinary in nature and subsequently numerical solutions are received via a shooting scheme. The motion and heat transport characteristics for the leading parameters is scrutinized and talked about elaborately using their graphical demonstration. It is established that the liquid speed reduces with escalating magnetic parameter. The consequences of growing Maxwell parameter are to hold back the speed of liquid. An increment in heat movement speed has been observed for enhancing the temperature ratio and Maxwell parameters. [ABSTRACT FROM AUTHOR]

This study is a study of three‐dimensional couple stress Casson fluid flow with nonlinear thermal radiation and heat source effects. The convective heat and mass transfer analysis is applied to a porous stretching sheet. In fluid flow direction, a uniform magnetic field can be applied. Using the similarity transformations, nondimensional expressions are achieved. The obtained equations are found numerically via the shooting technique as well as Runge‐Kutta‐Fehlberg method in MATLAB software. The contribution of different physical parameters is explored and discussed. Such parameters are porous parameter, couple stress parameter, heat source parameter, nonlinear thermal radiation, temperature parameter, and Lewis number. We found, the decreasing rate of heat transfer in the case of couple stress fluid motion when comparing Casson fluid flow with various values of Γ1 ${\Gamma }_{1}$ and Pr $\text{Pr}$. [ABSTRACT FROM AUTHOR]

Thermal and rheological characteristics of nanomaterials under electromagnetic force are of considerable interest in engineering, mining, biomechanics, and so on. Inspired by the worldwide applications of novel functional nanomaterials, this communication aims to shed light on the thermal gravitational magneto‐convection of a non‐Newtonian hybrid nanoliquid (Graphene oxide [GO]–molybdenum disulfide [MoS2 ${\text{MoS}}_{2}$]/water–ethylene glycol [WEG]) inside a confined channel. GO and MoS2 ${\text{MoS}}_{2}$ are dispersed into a WEG mixture (50%–50%). The physical effects of Hall currents, porous resistance, and thermal radiation are included in the flow system. An analytical approach is chosen to resolve the nondimensional momentum and energy with associated wall conditions. The stipulated graphs and tables are designed to extract and illustrate the effects of critical physical parameters on several dynamical functions or variables. The results obtained reveal that durable acceleration is induced in the fluid motion along the vertical direction with an increase in the Hall parameter, whereas it dampens the magnitude of the fluid velocity in the cross‐flow direction. An increase in frequency leads to an attenuation in the temperature profile and the amplitude of the heat transfer rate at the right wall. Streamlines and heatlines are plotted to envision the flow pattern inside the channel. The current study generalizes previous investigations with a non‐Newtonian hybrid nanoliquid and introduces the novel parameter of an inclined magnetic field. This study may be valuable in chemical engineering, mineral and cleaning oils manufacturing, and so on. [ABSTRACT FROM AUTHOR]

The study of electromagnetohydrodynamics (EMHD) of non‐Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter. The radiation parameter and Prandtl number suppress the temperature profile. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing fracture propagation is the main factor affecting the fracturing effect. In view of the more diversified selection of fracturing fluid, the problem of fracture propagation in non‐Newtonian fluid fracturing is often encountered in fracturing. In this paper, the influencing factors of fracture propagation of non‐Newtonian fluid fracturing fluid are analyzed. Based on PKN model, a three‐dimensional fracture propagation model considering the rheology and filtration of fracturing fluid is established, the better fracture shape simulation results are given, and the effects of fluid properties, rock physical properties, and injection parameters on fracture propagation are analyzed in detail. The research shows that (1) in the process of fracture propagation, the fracture length and width gradually increase, and the corresponding pressure in the fracture also increases. The overall increase trend is that the growth is rapid in the initial stage of fracturing and gradually slows down in the later stage. (2) The greater the consistency coefficient and rheological index, the greater the fracture width and pressure in the fracture, and the easier it is to form wide fracture. The larger the filtration coefficient is, the weaker the fracture forming ability is, and the fracture width, length, and pressure in the fracture are reduced. (3) Rock physical properties have a certain influence on fracture propagation, Young's modulus has a great influence on fracture propagation, while Poisson's ratio has little influence on it. However, the larger the Young's modulus, the more difficult the fracture is to expand, and the smaller the corresponding fracture width. (4) The larger the pump injection rate, the larger the fracture size and the higher the pressure in the fracture. The model can provide a theoretical basis for fracturing design and fracture shape prediction. [ABSTRACT FROM AUTHOR]

Non‐Newtonian fluids flowing in a concentric annulus have been widely observed in industrial chemical processes. In this study, the hydrodynamic characteristics of a non‐Newtonian fluid (polymer solution) in concentric annulus are investigated using computational fluid dynamics (CFD) modeling and numerical simulation methods. First, a simple grid independence analysis is carried out to select appropriate grid parameters. Then the rationality of the proposed CFD model is confirmed by the near‐wall velocity profiles. Based on the validated model, the effects of the fluid properties and radius ratio on the flow structure characteristics are studied at various inlet velocities. According to the simulated flow fields (i.e., velocity, pressure, strain rate, and wall shear stress), the flow pattern, flow resistance, and residence time distribution characteristics are analyzed in the laminar and turbulent regimes. The presented results show that non‐Newtonian fluids have unique flow behaviors in concentric annulus when compared with Newtonian fluids. [ABSTRACT FROM AUTHOR]

The present exploration is based on the contributions of heat and mass transport on the non‐Newtonian viscoelastic liquid motion under the impact of magnetism, Soret and Dufour numbers. The model equations that describe the flow mechanism of heat and mass transport are partial differential equations (PDEs). The PDEs were simplified using suitable similarity functions to obtain coupled nonlinear total ordinary differential equations. The simplified equations are numerically solved utilizing the spectral homotopy analysis method. Findings show that the process of heat transport is because of thermal radiation. The velocity, as well as temperature distributions, enhances due to a higher viscoelastic term. The present analysis is examined closely with past works and was discovered to concord. [ABSTRACT FROM AUTHOR]

In this paper, the analytical investigation of non‐Newtonian fluid flow through a turbine disc with a heat generation effect is considered. The flow mechanics through the turbine disc is modeled using a coupled system of higher‐order partial equations, which are transformed into ordinary order utilizing proper similarity transforms. Governing models are analyzed using the variation iteration and homotopy perturbation analytical methods. As observed from the results, the study shows enhancement of heat generation for non‐Newtonian fluid flow through turbine disc, reveals abating thermal distribution. More so, the graphical expression shows that heat generation improves up till mid‐disc. Thereafter, an increasing trend toward the fluid injection surface is observed. Validation of analytical solutions with numerical analysis boosts confidence in this study, which may be used to provide further insights into the engineering science of non‐Newtonian flow of hydraulic/lube oil in practical applications, such as hydraulic couplings. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamical free convective heat transfer flow of non‐Newtonian power‐law fluids has been analyzed numerically. For numerical simulation, the multiple‐relaxation‐time (MRT) lattice Boltzmann method (LBM) has been employed based on graphics process unit (GPU) computing. The computational domain is a two‐dimensional square cavity with thermally adiabatic upper and base walls, uniformly heated left wall, and sinusoidal heat distribution on the right wall. There is no research on non‐Newtonian fluid using MRT‐LBM using this configuration. Hence it is a new study in this field and novel results have been achieved with the magnetic field effect and sinusoidal wall temperature. The numerical simulations are carried out for different vital parameters such as thermal Rayleigh number (Ra), Hartmann number (Ha), and power‐law index (n) to study the characteristics of heat transport along with the flow physics inside the square enclosure. The streamlines and isotherms elucidate the distribution of fluid flow and energy within the cavity. The energy transfer phenomena are interpreted as the local Nusselt number (Nu) distribution and the average Nusselt number (Nu¯) along the heated wall. Computational results show that the rate of energy transfer is attenuated due to the augmentation of the magnetic field. However, (Nu¯) exhibits direct correspondence with the Rayleigh number and an inverse relation with the power‐law index (n). The elevation of Hartmann number (Ha) results in the diminution of Nu and Nu¯ for pseudoplastic fluid (n<1) by 82.65% and 86.04%, respectively. Moreover, the temperature distribution (θ) of Ra=105 amplifies by 95.83% compared to Ra=104 as the fluid transitions from pseudoplastic to dilation behavior. For GPU computing, the NVIDIA CUDA C programming platform is used in the present study. [ABSTRACT FROM AUTHOR]

The flow feature and local shear rate distribution near the impeller blade in a standard Rushton turbine stirred tank with the aqueous solution of sodium polyacrylate were studied by using particle image velocimetry experiments and computational fluid dynamics simulations. Experimental and simulated results, including average velocity and local shear rate distribution at different rotational speeds, were compared, and good agreement was achieved. On this basis, the numerical methods were used to predict the effects of liquid rheology on the velocity and shear rate distribution. The consistency coefficient affects obviously the velocity fluctuation level but has a limited impact on the flow structure. The power‐law index influences significantly the radial jet structure. In addition, the liquid rheology almost has no effect on the average value of the local shear rate near the impeller region, which is proportional to the rotational speed. [ABSTRACT FROM AUTHOR]

Iron oxide nanoparticles have great importance in future biomedical applications because of their intrinsic properties, such as low toxicity, colloidal stability, and surface engineering capability. So, blood containing iron oxide nanoparticles are used in biomedical sciences as contrast agents following intravenous administration. The current problem deals with an analysis of the melting heat transfer of blood consisting iron nanoparticles in the existence of free convection. The principal equations of the problem are extremely nonlinear partial differential equations which transmute into a set of nonlinear ordinary differential equations by applying proper similarity transformations. The acquired similarity equalities are then solved numerically by Runge‐Kutta Felhsberg 45th‐order method. The results acquired are on the same level with past available results. Some noteworthy findings of the study are: the rate of heat transfer increases as the Casson parameter increases and also found that the temperature of the blood can be controlled by increasing or decreasing the Prandtl number. Hence, we conclude that flow and heat transfer of blood have significant clinical importance during the stages where the blood flow needs to be checked (surgery) and the heat transfer rate must be controlled (therapy). [ABSTRACT FROM AUTHOR]

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time-independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth-order Runge-Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number. [ABSTRACT FROM AUTHOR]

The back extrusion (BE) method is a well‐known translational concentric cylinder viscometry that can analyze viscosity from the force–time curve of a cylindrical plunger pushed into a cylindrical cup filled with a sample fluid. It can analyze Newtonian, power‐law, and Herschel–Bulkley flows. However, the plunger must be moved 100 mm or more from the sample surface toward the cup bottom, any sample fluid adhering to the plunger must be removed. Moreover, given the complexity of the calculation steps, the BE method is not as widely. The short back extrusion (SBE) method proposed in this study is an improved immersed‐type BE method. By setting the measurement position inside the sample, the upflow in the annular space is smooth even over a short distance (5–15 mm). Measurement over a short distance decreases the amount of sample adhered to the plunger, mitigating the need to remove any sample from the plunger after each measurement, thereby facilitating repeated measurements. A program automatically determines flow type and, using novel mathematical formulas, it calculates the measured characteristics of the flow. In addition, the greatest advantage of the SBE method is that it can measure samples containing solids. It can be measured in a state in which a person usually eats, because the larger the stress required for the flow, the wider the gap. Moreover, its measurement accuracy is comparable to cone‐plate analysis, and the linear region of the analysis area is wide with less destructive movement. [ABSTRACT FROM AUTHOR]

Based on experiments with single air bubbles rising in stagnant non‐Newtonian fluids, an innovative model containing the aspect ratio (E) and two parameters (α, β) was proposed and proved to be capable of characterizing the bubble shape from spherical/ellipsoidal to prolate/oblate‐tear with good accuracy. Several impacts on bubble deformation were investigated, involving the rheological properties of the fluids and different forces exerted on the bubble, which were quantified by multiple dimensionless numbers (e.g., Reynolds, Eötvös, and Deborah number). Within a wide range, the empirical correlations were obtained for parameter β, and between α and β. Together with the shape model, a complete system was set up for bubble shape characterization and prediction that will provide new ideas for future studies on bubble hydrodynamics. [ABSTRACT FROM AUTHOR]

Planar laser‐induced fluorescence (PLIF) and electrical resistance tomography (ERT) were applied simultaneously to monitor the mixing performance of a KM static mixer for the blending of non‐Newtonian fluids of dissimilar rheologies in the laminar regime. The areal distribution method was used to obtain quantitative information from the ERT tomograms and the PLIF images. Comparison of the ERT and PLIF results demonstrates the ability of ERT to detect the mixing performance in cases of poor mixing within the resolution of the measurement, though the accuracy decreases as the condition of perfect mixing is approached. Thus, ERT has the potential to detect poor mixing within the confines of its resolution limit and the required conductivity contrast, providing potential rapid at‐line measurement for industrial practitioners. [ABSTRACT FROM AUTHOR]

In this paper, conjugate heat transfer from a circular cylinder with a heat source to a non‐Newtonian power‐law fluid is studied. Numerical calculations are carried out in an unconfined computational domain for Reynolds numbers (5≤Re≤40), power‐law indices (0.6≤n≤1.4), and Prandtl numbers (1≤Pr≤50) with different heat source values. The pressure coefficient, value, and position of maximum temperature inside the cylinder and the local and average Nusselt number are calculated. Also, the effects of Re, Pr, n, and heat source value on the thermal characteristics in the solid cylinder and the fluid around it are studied and discussed. [ABSTRACT FROM AUTHOR]

Abstract: BACKGROUND: The present study aimed to investigate changes in the fundamental rheological properties of dough prepared from wheat grains stored for 6 months at 20 °C, at ambient temperature (temperature varied with time) and at 4 °C. Stress/shear rate ramp, oscillation and creep‐recovery tests were performed to assess the changes in rheological properties as a result of storage. RESULTS: Samples were observed to be non‐Newtonian; thus, the Bingham model estimated the yield stress, which was maximum for the wheat stored under ambient conditions and minimum for wheat stored at 20 °C. The stress required to break the bonds was maximum for wheat‐dough stored under ambient conditions and minimum for wheat stored at 20 °C. Wheat stored at 20 °C also had the highest maximum creep and recovery strain. The viscoelastic properties of the three wheat‐dough samples were compared. CONCLUSION: The results obtained in the present study show that the wheat‐dough prepared under ambient conditions behaves as a rigid and stiff material. The dough prepared from wheat stored at 20 °C had the maximum elasticity. © 2017 Society of Chemical Industry [ABSTRACT FROM AUTHOR]

We consider the initial-boundary value problem for a model of motion of aqueous polymer solutions in a bounded three-dimensional domain subject to the Navier slip boundary condition. We construct a global (in time) weak solution to this problem. Moreover, we establish some uniqueness results, assuming additional regularity for weak solutions. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the analysis of a nonlinear system modeling unsteady flows of an incompressible non-Newtonian fluid mixed with a reactant. We are interested on generalized second grade fluids, which are chemically reacting and whose viscosity depends both on the shear-rate and the concentration. We prove existence and uniqueness of strong-weak solution for a flow filling in the plane [ABSTRACT FROM AUTHOR]

Landslide-generated impulse waves may have catastrophic consequences. The physical phenomenon is difficult to model because of the uncertainties in the kinematics of the mobilised material and to the intrinsic complexity of the fluid-soil interaction. The particle finite element method (PFEM) is a numerical scheme that has successfully been applied to fluid-structure interaction problems. It uses a Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the latter including soil/rock and structures). A mesh connecting the particles (nodes) is re-generated at every time step, where the governing equations are solved. Various constitutive laws are used for the sliding mass, including rigid solid and the Newtonian and non-Newtonian fluids. Several examples of application are presented, corresponding both to experimental tests and to actual full-scale case studies. The results show that the PFEM can be a useful tool for analysing the risks associated with landslide phenomena, providing a good estimate to the potential hazards even for full-scale events. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the radiation and chemical reaction effects on Casson non-Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non-Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing. [ABSTRACT FROM AUTHOR]

We present a model describing unsteady flows of a heat conducting mixture composed from L constituents in two and three dimensional bounded domain. We assume that the flow of the mixture is described only by the barycentric velocity, and that the fluid is non-Newtonian. In addition, we assume that the diffusion flux depends also on the temperature gradient, describing the Soret effect, and that the heat flux depends also on the chemical potentials gradient, describing the Dufour effect. We briefly show under which assumptions on the constitutive equations the model obeys the first and the second laws of thermodynamics and for a large class of physically well-motivated constitutive relations we establish the existence of a weak solution. For simplicity we restrict ourselves only onto the linear models, i.e., the diffusion and the heat flux depend linearly on the temperature and chemical potentials gradients. [ABSTRACT FROM AUTHOR]

An investigation on flow pattern, pressure drop, and holdup of cocurrent upward two-phase flow in a vertical helical coil tube has been carried out with Newtonian and non-Newtonian fluids. The flow patterns observed in the present study are divided into three main regimes, i.e. plug flow, slug flow, and stratified flow. Lockhart-Martinelli parameter ( X) was used to predict the friction factor and frictional pressure drop of two-phase flow. Correlations for the frictional pressure drop were developed to interpret the observed flow patterns with various operating variables. The effect of geometrical parameters on flow pattern, pressure drop, and holdup are enunciated. Based on the experimental data, a correlation was proposed to predict the flow transitions of flow patterns (i.e. plug-slug flow and slug-stratified flow) by dimensional analysis. Probabilistic neural network model has also been developed to predict the flow patterns of two-phase flow. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper examines thermal-diffusion and diffusion-thermo effects on the fully developed MHD flow of a micropolar fluid through a porous space in a vertical channel with asymmetric wall temperatures and concentrations. The homotopy analysis method ( HAM) is adopted to obtain the approximate analytical solution for the velocity, micro-rotation, temperature, and concentration field. The convergence and the accuracy of the solutions are discussed. The role of pertinent parameters on the heat and mass transfer characteristics of the flow are presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 561-576, 2014; Published online 11 November 2013 in Wiley Online Library (). DOI 10.1002/htj.21100 [ABSTRACT FROM AUTHOR]

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non-Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds ( Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re-number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non-Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation. [ABSTRACT FROM AUTHOR]

Bubble formation from an orifice submerged in quiescent polyacrylamide aqueous solution was investigated numerically with a sharp-interface coupled level-set/volume-of-fluid method based on the rheological characteristics of the fluid. In both non-Newtonian fluids and Newtonian fluids, the numerical approach was able to capture accurately the deformation of the bubble surface, validated by comparison with experimental results. The effects of orifice diameter, solution mass concentration, and gas flow rate on bubble volume and aspect ratio were evaluated. Both the instantaneous and detached volume decrease with the orifice diameter but increase with mass concentration and gas flow rate. The aspect ratio at the departing point tends to rise with the orifice diameter and mass concentration and falls with the gas flow rate. [ABSTRACT FROM AUTHOR]

Models commonly used in literature are evaluated versus 696 data points to predict the pressure drop of gas/non-Newtonian power-law fluids flow in horizontal pipes. Suitable models are recommended. A new correlation is developed by ignoring the pressure drop across the gas slug and adopting the liquid slug holdup of gas/non-Newtonian fluid flow into the homogeneous model. The theoretical curves can capture the test data trends and the overall agreement of predicted values with experimental data is sufficient to be practically applied in industry. [ABSTRACT FROM AUTHOR]

In this paper, we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared with its depth. The mud is treated as a non-Newtonian fluid, and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study investigates the boundary-layer flow and heat transfer characteristics in a second-grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM-Padé. The DTM-Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary-layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge-Kutta with shooting method) illustrates that the DTM-Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030 [ABSTRACT FROM AUTHOR]

In the horizontal drilling process, due to the weight of the drill string, the column may be located at a lower portion of the wellbore, thereby exhibiting an eccentric configuration. It is important to predict the eccentricity effect on the drilling fluids flowing through the annular, a subject not often discussed in the literature. The fluid dynamics of non-Newtonian fluids (xanthan gum solutions) flowing through annuli with the variable eccentricity motion of the inner tube was investigated. The effects of four important operating variables were quantified. The comparison between computational fluid dynamics simulations and the experimental data indicated a very good agreement. [ABSTRACT FROM AUTHOR]

This study examined the rheological characteristics of biological treatment sludges originating from secondary stage and sludge treatment unit of a municipal wastewater treatment plant (WWTP), using a rotational viscometer equipped with an ultralow adapter or small cylindrical-shaped spindle. A total of four mathematical approaches were used to investigate the fitting of the dependence of the shear stress to the shear rate, A generalized multi-statistical model was proposed to describe the rheological properties of the sludge. The overall results indicated that Ostwald equations have stronger prediction capabilities of the apparent viscosity of treatment sludges than other rheological modeling approaches and the proposed model. Although the proposed model structure did not exhibit a desirable performance, it may have an application potential to calculate the apparent viscosity tot a particular shear rate and solid content, which can be measured easily in WWTPs. [ABSTRACT FROM AUTHOR]

We conducted an experimental study of the interaction and coalescence of two drops (of the same fluid) or bubbles translating under the action of buoyancy in a cylindrical tube. The close approach of two Newtonian fluid particles of different size in a non-Newtonian continuous phase was examined using image analysis, and measurements of the coalescence time are reported for various particle size ratios, Bond numbers, and particle-to-suspending-fluid viscosity ratios. The flow disturbance behind the leading bubble and the viscoelastic nature of the continuous phase seemed to retard bubble coalescence. The time scale for coalescence of liquid drops in highly elastic continuous phase was influenced by the relative motion of the drops and their coalescence behavior. [ABSTRACT FROM AUTHOR]

The effects of variable viscosity, variable thermal diffusivity and magnetic field on the flow and heat transfer in a laminar liquid film of non-Newtonian fluid on a horizontal stretching sheet through a porous medium are analyzed. Using a similarity transformation, the governing time-dependent boundary-layer equations for momentum and thermal energy are reduced to a set of coupled nonlinear ordinary differential equations. The resulting seven-parameter problem is solved numerically by using Chebyshev pseudospectral method for some representative value of the parameters. The numerical results show that variable viscosity, variable thermal diffusivity, the upper limit of apparent viscosity according to biviscosity model, the unsteadiness parameter, the magnetic parameter, and the permeability parameter have significant influences on the velocity and temperature profiles, shear stress, and Nusselt number. It is observed that the presence as well as the increase in the unsteadiness parameter S, variable viscosity parameter β1, the upper limit of apparent viscosity β, and the magnetic parameter M lead to decrease in the fluid film thickness η∞. Also, as film thickness approaches zero as S comes close to the critical value; then, there is no available solution for the problem. The velocity profiles supported this result, since close to this critical value the velocity of the fluid vanishes. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The transient hydromagnetic flow of an electrically conducting viscous incompressible non-Newtonian Casson fluid bounded by two parallel non-conducting plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a pressure gradient in the axial direction. The lower plate is stationary and the upper plate is suddenly set into motion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term and the parameter describing the non-Newtonian behaviour on both the velocity and temperature distributions are studied. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The radial planar wedge pattern flow with friction and normalized non‐uniform viscosity function will be discussed here. Solving this problem will be done using the flow theory equations for Newtonian and Non‐Newtonian cases with non‐uniform viscosity assumption. General differential equation that connects between the normalized velocity profile and the normalized viscosity has been derived analytically from the flow equations. It was found that for specific wedge semi angle, the radial assumption is no longer valid for the flow velocity. Moreover, it was found that for inlet/outlet conditions the normalized mean hydrostatic pressure for Newtonian fluid is dependent on the geometry, the normalized velocity and the viscosity functions. In addition, it was found that inertia phenomenon can be neglected for small wedge semi angle. A comparison between the axial and the hydrostatic pressure distributions for inlet/outlet conditions was performed for Newtonian and non‐Newtonian flows. Finally, it was found that the axial pressure distribution profile was converged to the hydrostatic profile for critical wedge semi angle. [ABSTRACT FROM AUTHOR]

In this article, we investigate the nonlinear steady-state boundary-layer flow, heat and mass transfer of an incompressible Jeffrey non-Newtonian fluid past a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely, Deborah number ( De), Prandtl number ( Pr), ratio of relaxation to retardation times ( λ), Schmidt number ( Sc), and dimensionless tangential coordinate ( ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the velocity is reduced with increasing Deborah number whereas temperature and concentration are enhanced. Increasing λ enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing Deborah number, De, and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in Deborah number whereas it is elevated with increasing λ. And an increasing Schmidt number decreases the velocity and concentration but increases temperature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (). DOI 10.1002/htj.21111 [ABSTRACT FROM AUTHOR]