non-Newtonian Power-law Liquids Research Articles

Effects of Heat Generation and Radiation on Darcy Convective Non-Newtonian Power Law Liquid with Yield Stress over a Vertical Plate

The effects of heat flux, and thermal buoyancy on mixed convective flow for a non-Newtonian power law liquid with yield stress via a vertical plate filled with a porous material under the influence of thermal radiation, and heat production are investigated in this topic. For this model, The PDE's that govern the flow are constructed and converted to a set of ODE's using appropriate transformation and the resultant ODEs are quantitatively determined using Shooting technique. The impacts of different flow regulating factors such as index parameter, yield stress, radiation, and heat generation are illustrated through graphical representation for fluid properties. This research shows that the velocity distribution, Nusselt and Sherwood numbers declines as the dimensionless rheological parameter rise, but temperature and concentration profiles exhibit the reverse tendency. Also, the velocity, temperature curves and mass flux grow as the radiation parameter rises, whereas the concentration curves and heat flux fall as the radiation parameter rises. For a specific case, a comparison with Lakshmi Narayana et al.,13 was made, and a great agreement was established.

Second Law Investigation in a Non-Newtonian Liquid Flow in a Porous Channel with Circular Obstacle

The problem of non-Newtonian fluid flow has taken considerable interest and has been the subject of several work in latest years due to its various requests in different fields of engineering, in particular the interest in the problems of heat transfer in non-Newtonian liquids, such as lubrication, hot rolling, cooling problem and drag reduction. Here, mixed convection heat transport and its related entropy production in a porous channel with circular obstacle saturated via non-Newtonian power law liquid has been scrutinized. The influences on entropy production of the power law index, the Reynolds number, the Rayleigh number and the Darcy number are investigated. Being a novelty of this work, an optimization study of the thermodynamic irreversibility as a function of the channel inclination angle and the power law index is undertaken. The governing equations of the problem are solved employing the COMSOL software. Outcomes illustrate that the governing parameters strongly affect the entropy production. The thermal entropy generation is maximal at low value of power law index and high value of Reynolds number. The effect of Reynolds number become insignificant at relatively high power law index. At fixed Reynolds number value, a rise in the power index (n) leads to a reduce in the thermal entropy. This decrease is tiny, at low value of Reynolds number (Re) and turn into increasingly considerable as Re rises. The streamlines show the existence of two recirculation zones just after the circular obstacle, whose existence depends on both Re and power law index. Results show that the greatest variation relating to the inclination angle is for power law index equal to 0.4. Results indicate also that, at low Darcy number and relatively high power law index, the intrinsic effect of the modified Darcy number on Darcy viscous irreversibility become pronounced giving a sharp increase in the total entropy production.

Close-contact melting of phase change materials with a non-Newtonian power-law fluid liquid phase—Modeling and analysis

Close-contact melting of phase change materials with a non-Newtonian power-law fluid liquid phase—Modeling and analysis

Dissipative Power-law fluid flow using spectral quasi linearization method over an exponentially stretchable surface with Hall current and power-law slip velocity

The present article aims to reports laminar, incompressible, electrically conducting two-dimensional non-Newtonian (power-law) liquid flow via exponentially stretching sheet with power-law slip velocity conditions. Transverse magnetic field, Hall current, viscous dissipation and radiative flux effects are incorporated in the formulation. Rosseland's diffusion model is defined for the radiation heat transfer. The non-linear partial derivation formulations satisfying the flow are transformed to the non-linear derivative equations by employing the local similarity quantities and then solved analytically through spectral quasi-linearization method (SQLM). The resultant solution is computed for different parameters in tables and graphical representation for clear understanding of the thermo-physical terms. Extensive visualization of primary and secondary velocities, temperature distributions for various emerging parameters presented for n = 0.7 (pseudo-plastic fluid) and n = 1,3 (dilatant fluid). The results are verified for limiting cases by comparing with various investigations and found excellent accuracy for Newtonian case. It is interesting to note that secondary flow rate is more dominant for both the cases of pseudo plastic and dilatant fluids for Hall parameter and Eckert number. Increasing Hall current leads suppress the fluid temperature but as Eckert number grows it leads grow the fluid temperature. Further, it is observed that as Hall parameter increases local Nusselt number strongly elevates.

Discovering and Modelling the Wave-Like Shapes on the Surface of Metal Deposits, being Electrodeposited under the Force Impact

The further evidence is presented for the phenomenon existence of the electrochemical phase formation of metals and alloys through the stage of the overcooled liquid state. An idea is proposed about the possible occurrence of wave-like shapes on the surface of metal deposits, electrodepositing under weak force impact. First it was predicted and then revealed experimentally, a wave-like vibration of a solidifying surface of the metal being electrodeposited in the form of ripples or choppiness under the weak force impact in parallel to the crystallization front. A mathematical model has been obtained describing the liquid state behaviour of metals being electrodeposited under the impact of centrifugal force on the annular plate. The generalized Maxwell model was used as the basic rheological equation of a state. The difference between the results obtained is testified when considering Newtonian and non-Newtonian (power-law) liquid. The software blocks for solving the obtained mathematical model, based on the MathCAD package, have been developed.

On the terminal velocity of single bubbles rising in non-Newtonian power-law liquids

To describe bubbly flows, an accurate prediction of the bubble rise velocity is crucial. For non-Newtonian fluids, closures for the bubble rise velocity provided in the literature are usually empirical and rather restricted in their applicability. In this work, a Front-Tracking Computational Fluid Dynamics model has been used to investigate the behaviour of a single bubble rising in a power-law fluid, for a very wide range of viscosities covering both shear-thinning and shear-thickening behaviour, where the power-law exponent n was varied between 0.5 and 1.5 and for three different bubble diameters (viz. 0.5 mm, 2 mm and 4 mm). The non-Newtonian behaviour of the continuous phase strongly influences the shape of the single rising bubbles caused by the viscosity profiles that develop in the flow field. As a consequence, large non-spherical bubbles become more spherical in shear-thickening fluids (in comparison to the same bubble in a Newtonian liquid), whereas small spherical bubbles lose their sphericity in shear-thinning fluids. To determine the bubble rise velocity for bubbles in non-Newtonian fluids with a power law behaviour, the drag closure derived for bubbles rising in Newtonian liquids proposed by Dijkhuizen et al. (2010), which combines viscous drag and shape-induced drag in a single correlation, is adapted using a modified Reynolds number. In this work it is shown that this adapted correlation is able to predict the terminal rise velocity of single bubbles rising in non-Newtonian power-law fluids within 20% accuracy for the majority of the investigated cases, provided that the drag regime does not change.

Hydrodynamic and thermal study of a trapezoidal cylinder placed in shear-thinning and shear-thickening non-Newtonian liquid flows

Hydrodynamic and thermal features of two-dimensional, incompressible shear-thinning and shear-thickening non-Newtonian power-law liquids under forced convection across a trapezoidal cylinder are the focus of this study, carried out at Reynolds number Re = 1–40, power-law index n = 0.4–1.8 and Prandtl number Pr = 50 using ANSYS Fluent. In this steady system, the drag coefficient is found to decrease, whereas the wake size and the average Nusselt number increase with the increase in Re. However, with the increase in n value, the average Nusselt number decreases. Similar to a square cylinder, compared to Newtonian liquids, shear-thinning liquids increases heat transfer and shear-thickening reduces it. The maximum increase in heat transfer for shear-thinning liquids compared to Newtonian liquids for a trapezoidal cylinder is approximately 25%, while the average heat transfer is somewhat lower for shear-thickening liquids than for Newtonian. The average Nusselt number is smaller for the trapezoidal cylinder than for a square cylinder in the parameter domain investigated; the largest difference is around 25%. A simple relationship for the average Nusselt number as a function of Re and n has been determined.

Lattice Boltzmann model of gas-liquid two-phase flow of incomprssible power-law fluid and its application in the displacement problem of porous media

A new incompressible gas-liquid two-phase flow model for non-Newtonian power-law fluid is proposed based on an incompressible lattice Boltzmann model. And the fundamental physical mechanism of Newtonian fluid displacing non-Newtonian power-law fluid liquid in porous medium is studied by using the proposed model. The effects of capillary number <i>Ca</i>, dynamic viscosity ratio <i>M</i>, surface wettability <i>θ</i>, porous medium geometry, and power law index <i>n</i> on the displacement process are investigated. The comprehensive results show that with the increase of capillary number, the displacement process turns faster, the fingering phenomenon becomes more obvious and the displacement efficiency decreases. However, for different values of power-law index <i>n</i>, the effects of the <i>Ca</i> on the displacement process have some differences. Specially, the decrease rate of displacement efficiency becomes slow if the displaced fluid is shear thickening fluid as compared with that if the displaced fluid is shear thinning fluid. On the other hand, the displacement efficiency decreases as dynamic viscosity ratio <i>M</i> increases. And the effect of the viscosity ratio on the displacement process becomes more obvious for the low value of the power-law index <i>n</i>. Moreover, the effect of the surface wettability of the porous medium on the displacement process is also related to the size of the power-law index. With the increase of the contact angle of the porous medium, the fingering phenomenon turns less obvious, and the displacement efficiency increases. However, with the increase of power-law index <i>n</i>, the influence of the contact angle on the displacement process decreases. Besides, the displacement processes with different geometric types of the porous media are also studied in the work. The results show that comparing with the case of porous medium denoted by circle shape and square shape, the fingering phenomenon obtained by the case of triangular shape is most obvious, and the displacement efficiency is lowest.

Four stages of droplet spreading on a spherical substrate and in a spherical cavity: Surface tension versus line tension and viscous dissipation versus frictional dissipation

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a completely wettable spherical substrate is theoretically studied. Both convex spherical substrates and concave spherical cavities with smooth or rough surfaces are considered. The droplet on a rough substrate is modeled by either the Wenzel or the Cassie-Baxter model. The two sources of driving force of spreading by the surface-tension and the line tension are considered. Also, the two channels of energy dissipation by the viscous dissipation within the bulk and the frictional dissipation at the contact line are considered. A combined theory of spreading on a spherical substrate is constructed by including those four factors. The spreading process is divided into four stages, each of which is governed by one of two driving forces and one of two dissipations. It is found that the dynamic contact angle $\theta$ has a characteristic time ($t$) dependence at each stage. It does not necessarily follow the standard power law $\theta \sim t^{-\alpha}$. Instead, the relaxation can be a power-law with the exponent $\alpha$ different from that on a flat substrate, or it can be exponential or it can finish within a finite time. Therefore, various spreading scenarios on a spherical substrate and in a spherical cavity are predicted.

Convective hydromagnetic instabilities of a power-law liquid saturating a porous medium: Flux conditions

We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.

Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power-law decay θ∼t^{-α} except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

Spreading law of non-Newtonian power-law liquids on a spherical substrate by an energy-balance approach.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θ∼t^{-α} with the spreading exponent α, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

Analysis of single phase Newtonian and non-Newtonian velocity distribution in periodic packed beds

A three dimensional computational fluid dynamics (CFD) model based on unit cell concept is presented to analyze the hydrodynamics of periodic operation in packed bed reactors (PBRs). Flow profiles, mass flux distribution, and pressure drop results are studied for various split ratios with Newtonian and non-Newtonian power law liquids. Two different structured packing arrangements are considered to understand the effect of particle orientation on the flow maldistribution during fast mode of min–max periodic operation. For a fixed operating condition, better radial liquid distribution is observed for periodic operation with higher split ratio in face centered cubic (FCC) geometry, however, at lower split ratio, well irrigation of the bed is obtained for modified simple cubic (SC) geometry. For both the geometries, shear thinning liquid imparts least maldistribution. Comparison of periodic operation results against continuous flow advocate benefits of the former in terms of liquid distribution in the bed irrespective of splits. This fundamental study essentially sets the foundation of modeling multiphase flow modulation in periodic PBRs.

MHD Flow and Heat Transfer in a Power-Law Liquid Film at a Porous Surface in the Presence of Thermal Radiation

In this paper, the effects of variable thermal conductivity and thermal radiation on the MHD flow and heat transfer of a non-Newtonian power-law liquid film at a horizontal porous sheet in the presence of viscous dissipation is studied. The governing time dependent boundary layer equations are transformed to coupled, non-linear ordinary differential equations with power-law index, unsteady parameter, film thickness, magnetic parameter, injection parameter, variable thermal conductivity parameter, thermal radiation parameter, the Prandtl number and the Eckert number. These coupled non-linear equations are solved numerically by an implicit, finite difference scheme known as the Keller box method. The obtained numerical results for velocity and temperature profiles are presented graphically. Also, the obtained results of our study for some special cases are compared with the previously published results, and the results are found to be in very good agreement. The effects of unsteady parameter on the skin friction, walltemperature gradient and the film thickness are explored for different values of the power-law index and the magnetic parameter. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.

Soret Effect on the Natural Convection From a Vertical Plate in a Thermally Stratified Porous Medium Saturated With Non-Newtonian Liquid

The paper highlights the application of a recent seminumerical successive linearization method (SLM) in solving highly coupled, nonlinear boundary value problem. The method is presented in detail by solving the problem of free convection flow due to a vertical plate embedded in a non-Darcy thermally stratified porous medium saturated with a non-Newtonian power-law liquid. Thermal-diffusion (Soret) and variable viscosity effects are taken into consideration. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian behavior of the fluid. The governing partial differential equations are transformed into a system of ordinary differential equations and solved by SLM. The accuracy of the SLM has been tested by comparing the results with those obtained using the shooting technique. The effect of various physical parameters such as power-law index, Soret number, variable viscosity parameter, and thermal stratification parameter on the dynamics of the fluid is analyzed through computed results. Heat and mass transfer coefficients are also shown graphically for different values of the parameters.

Finite double layer and non-Newtonian power-law effects on electrokinetic diffusioosmotic flows in parallel plate microchannels

Diffusioosmotic flows of electrolytic non-Newtonian power-law liquids in parallel plate microchannels are theoretically investigated by considering the finite thickness of the interfacial electrical double layers. Semi-analytical or numerical solutions to the shear stress, flow velocity, effective viscosity, and volume flow rate are obtained as functions of the spatial coordinate, half channel width to Debye length ratio, interfacial zeta potential, diffusivity difference parameter, and the power-law flow behavior index. The border curves of zero flow rate obtained herein delineating the parametric regimes in which the non-Newtonian diffusioosmotic flow rate is directed towards downstream or upstream are distributed differently on the zeta potential versus diffusivity difference parameter map as compared to those obtained using thin double layer theory. As compared to Newtonian liquids, the rheology of dilatant and pseudoplastic liquids respectively enlarges and reduces the parametric regimes in which flow rate towards downstream occurs, which is a result exactly opposite to that obtained based on the thin double layer theory reported in recent literature.

Prediction of terminal velocity of solid spheres falling through Newtonian and non-Newtonian pseudoplastic power law fluid using artificial neural network

Prediction of the terminal velocity of solid spheres falling through Newtonian and non-Newtonian fluids is required in several applications like mineral processing, oil well drilling, geothermal drilling and transportation of non-Newtonian slurries. An artificial neural network (ANN) is proposed which predicts directly the terminal velocity of solid spheres falling through Newtonian and non-Newtonian power law liquids from the knowledge of the properties of the spherical particle (density and diameter) and of the surrounding liquid (density and rheological parameters). With a combination of non-Newtonian data with Newtonian data taken from published data giving a database of 88 sets, an artificial neural network is designed. Analysis of the predictions shows that the artificial neural network could be used with good engineering accuracy to directly predict the terminal velocity of solid spheres falling through Newtonian and non-Newtonian power law liquids covering an extended range of power law values from 1.0 down to 0.06.

Breakup of a power-law liquid sheet formed by an impinging jet injector

Gel propellant is promising for future aerospace application, but because it behaves as the non-Newtonian power-law liquid, it is difficult to atomize. Impinging jet injectors are often used for atomization of gelled propellant. To understand the atomization mechanism of gelled propellant, a linear instability analysis method was used to investigate the instability and breakup characteristics of the sheet formed by a gelled propellant impinging-jet injector. The maximum disturbance wave growth rate and dominant wave number were determined by solving the dispersion equation of a power-law liquid sheet. It was found that the maximum disturbances growth rate and the dominant wave number both increase as Weber number of the liquid sheet increases. Consistency coefficient and flow index were tested for their influence on the stability of the power-law liquid sheet. A modified model, to predict the breakup length and critical wavelength of the power-law liquid sheet, was adopted. To validate the power-law liquid sheet breakup model, experiments were performed with injectors of different configurations and a high speed camera was used to show detailed information of the liquid sheet breakup process. The rheology of the power-law fluid used in the present study was also investigated. Comparison between the theoretical and experimental results shows that the linear instability analysis method can be applied to predict breakup length and wavelength of the power-law liquid sheet.

Spreading of a non-Newtonian liquid drop over a horizontal plane

The spreading of a drop of non-Newtonian (power-law) liquid over a horizontal solid substrate is analyzed theoretically through energy approach method in the case of complete wetting. In this approach we have used the physical and geometrical reasoning and finally obtained a relation between the rate of spreading and bottom radius of the drop. It is shown that spreading rate of shear thickening liquid is more than that of a Newtonian liquid while shear thinning liquid is having slower rate than the latter one.

Heat Transfer at Convective Solid Melting in Fixed Bed

Abstract — A method to determine experimentally the melting rate, r m , and the heat transfer coefficients, α v (W/(m 3 K)), at convective melting in a fixed bed of particles under adiabatic regime is established in this paper. The method lies in the determining of the melting rate by measuring the fixed bed height in time. Experimental values of r m , α and α v were determined using cylindrical particles of ice (d = 6.8 mm, h = 5.5 mm) and, as a melting agent, aqueous NaCl solution with a temperature of 283 K at different values of the liquid flow rate (11.63·10 -6 , 28.83·10 , 38.83·10 -6 m 3 /s). Our experimental results were compared with those existing in literature being noticed a good agreement for Re values higher than 50. Keywords —C onvective melting, fixed bed, packed bed, heat transfer, ice melting. I. I NTRODUCTION EAT transfer in liquid-solid systems with and without phase change is frequently meet in chemical, food, siderurgic and other industries. From this reason, the literature contains a great number of papers related to this subject. Some of them [1÷12] approach the study of heat and mass transfer in fixed bed of particles without phase change. A few works [13, 14] refer to the heat transfer accompanied by melting in grain-fixed bed. In these papers [1÷14] are presented the results of experimental and theoretical investigations on heat transfer in fixed bed of spherical, cylindrical, pellet and other kind of particles. Newtonian and non-newtonian power law liquids are used as a melting agent. Thus, Pfeffer and Happel [5] in their theoretical study assume the fixed bad as an ensemble of isolated spherical particles, the distance among them being a function of the porosity. Le Clair [6] compares the cell model and the experimental results of heat and mass transfer in fixed and fluidized bed with a Newtonian liquid as melting agent. Kawase and Ulbrecht [8] developed a model for heat and mass transfer from a non-newtonian power-law fluid to particles in fixed-grain bed. The model was obtained on the basis of Blake-Kozeny equation for porous medium and the