non-Newtonian Power-law Fluid Research Articles

Lift, drag and torque on a rotating sphere in a stream of non-Newtonian power-law fluid

The flow of a non-Newtonian, power-law fluid, directed normally to a rotating sphere is considered in the present paper. The problem is investigated by means of a three-dimensional numerical simulation with the SIMPLE algorithm. The investigation covers the power-law index from 0.2 up to 2, rotation rate from 0.1 up to 3 and Reynolds number from 0.1 up to 100. The following general rules are valid. The lift coefficient increases with increasing the rotation rate. At high Re numbers the drag coefficient increases with the power-law index. At high Re numbers the torque coefficient increases with the power-law index and with the rotation rate, whereas the torque coefficient reduces as the Reynolds number increases. In addition, there are some special cases which are analyzed in the text.

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

A mesoscopic method based on the lattice Boltzmann method for thermal–solutal incompressible non-Newtonian power-law fluids through porous media is introduced. The macroscopic equations of different representative element volume (REV) models of porous media are presented, and the equations of power-law fluids through porous media for various REV models reported. The general mesoscopic model for two- and three-dimensional cases are presented, and their derivations shown. To demonstrate the ability of the proposed method, natural convection and double-diffusive natural convection of Newtonian and power-law fluids in porous cavities are studied, and the results are validated against previous findings. Finally, double-diffusive natural convection in a porous cubic cavity filled with a non-Newtonian power-law fluid is simulated by the proposed method.

Modeling of a gas slug rising in a cylindrical duct and possible applications to volcanic scenarios

The paper deals with the mathematical modelling of a gas slug rising in a cylindrical duct filled with an incompressible liquid. This research is motivated by a phenomenon commonly observed during Strombolian eruptions at basaltic volcanoes, that is, mildly explosive events driven by a large bubble of magmatic gas (a slug) rising up the conduit and bursting at the surface. The model is compared with the laboratory experiments described in [15] and we prove that the constancy of the slug ascent velocity observed in these experiments is fully justifiable. The model is developed both in the case of a Newtonian fluid and in the case of a non-Newtonian power law fluid, more suitable for magmas, and applied to a volcanic scenario.

Forced convection heat transfer study of a blunt-headed cylinder in non-Newtonian power-law fluids

Abstract In this present work, forced convection heat transfer from a heated blunt-headed cylinder in power-law fluids has been investigated numerically over the range of parameters, namely, Reynolds number (Re): 1–40, Prandtl number (Pr): 10–100 and power-law index (n): 0.3–1.8. The results are expressed in terms of local parameters, like streamline, isotherm, pressure coefficient, and local Nusselt number and global parameters, like wake length, drag coefficient, and average Nusselt number. The length of the recirculation zone on the rear side of the cylinder increases with the increasing value of Re and n. The effect of the total drag coefficient acting on the cylinder is seen to be higher at the low value of Re and its effect significant in shear-thinning fluids (n < 1). On the heat transfer aspect, the rate of heat transfer in fluids is increased by increasing the value of Re and Pr. The effect of heat transfer is enhanced in shear-thinning fluids up to ∼ 40% and it impedes it’s to ∼20% shear-thickening fluids. In the end, the numerical results of the total drag coefficient and average Nusselt number (in terms of J H −factor) have been correlated by simple expression to estimate the intermediate value for the new application.

Shear thickening polishing of the concave surface of high-temperature nickel-based alloy turbine blade

High-temperature nickel-based alloy, which is a valuable crucial material for fabricating functional components, is commonly used to fabricate turbine blades. However, the concave surface of the turbine blade is much difficult to be polished. In this work, shear-thickening polishing (STP), which employed the shear-thickening mechanism of non-Newtonian power-law fluid, was utilized to achieve high efficiency and high-quality polishing of the concave surface of the high-temperature nickel-based alloy turbine blade. The finite element simulation of the pressure and velocity distribution on the concave surface during STP process was carried out by ANSYS, and the effects of different polishing angles, polishing velocities, pH values of polishing slurry and Fenton's reagent on the surface morphology and roughness of the workpiece were investigated by experiment. The comparison between simulation and experimental results indicated that the suitable polishing angle is 45°. The best surface can be obtained with a pH value of 6.5. With the increase of the polishing speed, polishing efficiency improved gradually. The workpiece surface was improved by adding 0.5% hydrogen peroxide (H2O2) and 0.15% FeSO4 in the polishing slurry. In the final, surface roughness of the turbine blade was reduced rapidly from Ra = 72.3 nm to Ra = 4.2 nm after 9 min polishing under the appropriate conditions. The research results provide reference and basis for high-temperature nickel-based alloy turbine blade polishing.

Laminar natural convection of non-Newtonian power-law fluid in an eccentric annulus

This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th>Tc). The simulations have been taken for the parameters 103?Ra?105, 10?Pr?103, 0.6?n?1.4, 0???0.9 and an inclination angle ? from 0? up to 90?. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=105 at ?=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=103 at ?=90? which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ? = 0, ?=0.9 among them all. The results have compared with some precedent works and showed good agreement.

CONFINED AND UNCONFINED FLOW PAST A RIGID CUBE ENCLOSED IN A RECTANGULAR CHANNEL FILLED WITH NON-NEWTONIAN POWER-LAW FLUID

CONFINED AND UNCONFINED FLOW PAST A RIGID CUBE ENCLOSED IN A RECTANGULAR CHANNEL FILLED WITH NON-NEWTONIAN POWER-LAW FLUID

Electro-thermo-convection in non-Newtonian power-law fluids within rectangular enclosures

Abstract Electro-thermo-convection is a typical interdisciplinary problem, that has been widely studied in terms of its physical phenomena in Newtonian fluids. As an essential supplement to the study of electrohydrodynamics, electro-thermo-convection in power-law fluids within rectangular enclosures is investigated in this paper. Two geometrical configurations are considered, namely differentially heated vertical and horizontal wall configurations. The governing equations are discretized using the finite volume scheme, and the bifurcations, flow patterns, and heat transfer efficiency under different power-law indexes are studied. A comprehensive comparison between the Newtonian and non-Newtonian cases is presented. The results indicate that electro-thermo-convection in power-law fluids exhibits more complicated hydrodynamic behavior than in Newtonian fluids. The shear-thinning characteristic decreases the criterion of subcritical bifurcation and corresponds to a smaller hysteresis loop, whereas the shear-thickening characteristic has an opposite effect. The bifurcation diagrams exhibit various features under different power-law indexes, and some of which have not been observed in Newtonian fluids. Additionally, the effects of the non-Newtonian behavior on the temporal evolution of the flow are discussed, and the fluid motion is found to be sensitive to the power-law index.

Time-dependent power-law nanofluid with entropy generation

This work studies the time-dependent convective flow of non-Newtonian power-law fluid by vertical plate. Fluid flow is studied in the presence of thermal radiation. The Buongiorno model is employed to describe the features of nanofluid. Entropy generation and Bejan number are calculated. The flow, temperature and concentration are given by the system of partial differential equations (PDE’s). The system of PDE’s is transformed into dimensionless form by transformation and then solve implementing finite difference technique. Special emphasis is given to the outcomes of Prandtl number, Reynolds number, Eckert number, radiation parameter, thermophoresis, Brownian parameter, and Schmidt number. Velocity, temperature, concentration, skin friction, Sherwood and Nusselt numbers are graphically analyzed. Graphical results show that velocity of fluid enhanced for high Grashof number while shows opposite behavior for Reynold number. For the high estimation of the thermophoresis parameter and Brownian motion parameter temperature and concentration increase. For the higher value of the radiation parameter, the irreversibility of fluid particles increases while the Bejan number decreases.

Study of continuous cake pre-baking in a rectangular channel using ohmic heating

An original device dedicated to additive manufacturing was developed to pre-bake cake batter. Its originality lies in the fact that pre-baking is ensured by ohmic heating implemented in a rectangular channel equipped with two parallel electrodes. Experiments and numerical studies were carried out and benchmarked. The rheological properties of the cake batter (non-Newtonian power-law fluid) and the influence of voltage and temperature on electrical conductivity were accommodated in the numerical model. Due to the low velocities of the very viscous products near the solid-liquid interface, it was found that the heterogeneity of the temperature at the nozzle outlet under continuous ohmic heating could lead to nozzle clogging when high temperatures are reached. Hot spots were identified in different areas of the channel, such as corners where the electric field is high and velocity is close to zero. A parametric study was performed on the impact of the thermophysical properties of the batter, showing that specific heat has a much greater impact than thermal conductivity on the accuracy of the temperatures computed. Analysis of the process parameters showed that a stronger electric field leads to a higher temperature gradient in the nozzle section. The temperature gradient decreases with electrode distance (delect) and nozzle width (l). This model could be used to optimize the ohmic heating nozzle configuration, with the objective of obtaining a continuous flow of pre-baked cake batter, while preventing clogging. Such a system could be used as 3D printing head. Industrial relevanceConventional 3D printing of bakery products is based on the deposition of a batter, followed by a baking. This study proposes an innovative approach based on a printing nozzle equipped with ohmic heating, with the objective of achieving a uniform temperature distribution and of obtaining high mass flow rate. Despite a significant temperature gradient in the baked batter at the exit of the nozzle, the obtained results showed that adjusting the nozzle geometry allows a reduction of the gradient. Further investigations are thus needed to reduce the temperature gradient and to accommodate expansion of the batter in the case of formulation using baking powder. The transfer of such concept for industry application may be doable in a close future.

Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

Free convective heat transfer of a non-Newtonian fluid in a cavity containing a thin flexible heater plate: an Eulerian–Lagrangian approach

In the present study, the free convection heat transfer of a power-law non-Newtonian fluid is considered in a cavity containing a flexible hot thin heater. The sidewalls of the square cavity are maintained at cold temperatures, while the hot heater is placed inside the cavity. The top and bottom walls of the cavity are kept insulated. The thin heater plate can undergo large deformations due to the interaction between the fluid flow and the heater. The arbitrary Lagrangian–Eulerian moving mesh method is employed to track the displacement of the heater in the fluid domain. Appropriate non-dimensional parameters are utilized to transform the governing equations into a general non-dimensional form. The equations governing fluid flow and heat transfer are solved using the finite element method with an automatic time-stepping scheme. The effect of control parameters such as the non-Newtonian power index (0.6 1) behavior reduces the fluid circulation and heat transfer rate in the cavity, but it increases the magnitude of the exerted tensions on the element. Moreover, raising Ra from 104 to 106 enhances the average heat transfer the value of Nuav by up to 3.5 times in pseudoplastic fluids and by 1.5 times in dilatant ones. In addition, it is found that shifting the heater upward deteriorates the heat transfer rate by suppressing the convection flow intensity. A 35% rise in the average heater can be obtained when the height of the plate was divided by 4 in the cse of dilatant fluid, and an increase by up to 100% is found for pseudoplastic fluids. Increasing the length of the element is also found to reduce the average Nusselt number and to increase the tensions in the heater. The average Nusselt number can be doubled when the length of the plate is reduced seven times.

Controlling the natural convection of a non-Newtonian fluid using a flexible fin

In the present study, the flow and heat transfer of a power-law non-Newtonian fluid in a cavity are addressed. The top and bottom walls of the cavity are well insulated, the left vertical wall is at a hot temperature, and the right wall is at a low temperature. A flexible elastic fin is mounted at the hot wall of the cavity. The non-Newtonian fluid circulates inside the cavity due to the buoyancy forces. Fluid-Structure Interaction (FSI) and the non-Newtonian flow within the cavity and the hot fin are coupled. The flow interaction with the fin leads to the deformation of the fin, and the change in the shape of the fin changes the flow and heat transfer. Hence, the coupling between the fluid and the structure is two ways. The Arbitrary Lagrangian-Eulerian (ALE) along the moving mesh method is employed to model the deflection of the structure inside the fluid domain. The finite element method is adopted to solve the governing equations. The results show that the deflection of the fin is higher for a dilatant non-Newtonian fluid, compared to the pseudoplastic and Newtonian fluids. The number of flow vortexes and flow hydrodynamic notably change by the variation non-Newtonian index. The variation of the non-Newtonian index produce minimal effects on the heat transfer rate. Moving from pseudoplastic effects to Newtonian and dilatant effects reduces the heat transfer rate and increases the internal stresses in the fin. Moreover, the maximum stress in stiff-fins is higher than soft-fins.

Finite difference method for solving a physical problem in fluid flow

Interaction between nonuniform heat source/sink, magnetic field and thermal radiation with heat flux through the flow of non-Newtonian power-law fluid due to a linearly stretching sheet was studied numerically using an implicit finite difference method (FDM). The heat flux is assumed to depend on both the thermal conductivity and the thermal radiation. Besides, the effects of all governing parameters, such as the magnetic parameter, thermal conductivity parameter, the power-law index parameter, Prandtl number, the space-dependent heat source/sink parameter, the temperature-dependent heat source/sink parameter, and the radiation parameter, on the profiles of velocities and temperature are studied and discussed. In particular, thermal radiation was found to play a key role in the heat transfer characteristics and in the formation of thermal boundary layer. Generally, our numerical results reveal that both the velocity and temperature distributions are marginally influenced by both the magnetic parameter and power-law index. A good agreement is observed between our results via finite difference method and the previously published numerical results for some special case.

Magnetic field effects on natural convection and entropy generation of non-Newtonian fluids using multiple-relaxation-time lattice Boltzmann method

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, [Formula: see text], Rayleigh number, [Formula: see text], PL indices, [Formula: see text]–1.4, Prandtl number, [Formula: see text], to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio [Formula: see text]. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, [Formula: see text] and decreasing the PL index, [Formula: see text]. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, [Formula: see text], fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing [Formula: see text] and [Formula: see text], respectively. In the presence of the magnetic field, [Formula: see text], the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.

Hall current, viscous and Joule heating effects on steady radiative 2-D magneto-power-law polymer dynamics from an exponentially stretching sheet with power-law slip velocity: A numerical study

A mathematical model is developed for 2-D laminar, incompressible, electrically conducting non-Newtonian (Power-law) fluid boundary layer flow along an exponentially stretching sheet with power-law slip velocity conditions in the presence of Hall currents, transverse magnetic field and radiative flux. The secondary flow has been induced with appliance of Hall current. The distinguish features of Joule heating and viscous dissipation are included in the model since they are known to arise in thermal magnetic polymeric processing. Rosseland’s diffusion model is employed for radiation heat transfer. The non-linear partial differential equations describing the flow (mass, primary momentum, secondary momentum and energy conservation) are transformed into non-linear ordinary differential equations by employing local similarity transformations. The non-dimensional nonlinear formulated set of equations is numerically evaluated with famous shooting algorithm by using MATLAB software. The validation of simulated numerical results has been completed with generalized differential quadrature (GDQ). Extensive visualization of primary and secondary velocities and temperature distributions for the effects of the emerging parameters is presented for both pseudo-plastic fluids (n = 0.8) and dilatant fluids (n = 1.2). The study is relevant to the manufacturing transport phenomena in electro-conductive polymers (ECPs).

Investigation of the mixed convection of power-law fluids between two horizontal concentric cylinders: Effect of various operating conditions

The purpose of this paper is to study numerically the mixed convection between two rotating circular cylinders under horizontal arrangement. The cylinders have a concentric position with a blockage ratio of d/D = 2.5. The annular space is completely filled with non-Newtonian power-law fluid. The surface of the inner cylinder is hot whereas the surface of the outer one is cold. Three cases are studied: in the first one, the inner cylinder has a constant rotational speed, while the outer cylinder is completely fixed; the second case: both cylinders are rotating in the same direction and at the same rotational speed; in the last case, both cylinders are rotating in opposite directions at a similar rotational speed. All studied cases are examined for various values of Reynolds number (Re = 1–10), Richardson number (Ri = 0–3), and power-law index (n = 0.6–1.6) at Prandtl number Pr = 50.

A study on the effect of magnetic field and the sinusoidal boundary condition on free convective heat transfer of non-Newtonian power-law fluid in a square enclosure with two constant-temperature obstacles using lattice Boltzmann method

In this paper, the flow pattern and thermal characteristics of free convection of a Newtonian magnetohydrodynamic fluid flow inside a square enclosure are compared against two different non-Newtonian power-law (PL) fluids. The enclosure with horizontal insulated walls has two constant-temperature obstacles, while two sidewalls are differentially heated with sinusoidal pattern. Boussinesq approximation is used to consider the effect of hydrodynamic field on the thermal field. The problem is grounded using lattice Boltzmann method, and D2Q9 function is used to describe distribution of the density and energy. The effects of Rayleigh number, PL index, the aspect ratio of constant-temperature obstacles, Hartmann number, and periodicity of sinusoidal boundary condition on the hydrodynamic and thermal characteristics are investigated. The results showed that with increasing Rayleigh number, the Nusselt number increases but with increasing power-law index and Hartmann number, the Nusselt number decreases for shear thinning, Newtonian and shear thickening fluids. In addition, it was shown that increasing the aspect ratio of obstacles increases the Nusselt number. Also, it was reported that the Nusselt number of Newtonian and shear thinning fluids increases with increasing the periodicity of the sinusoidal boundary condition from 2π to 4π, while it reduces by further increase in periodicity.

Couette creeping flow past a sphere in non-Newtonian power-law fluids

The flow past a sphere, rigidly held between two parallel plates (Couette flow), was studied in a non-Newtonian, power-law fluid, numerically. The three momentum equations have been solved under the following conditions: creeping flow with Re < 1; power-law index 0.2–1; distance of sphere center from the plates 1.15–10; sphere position between the plates 0.1–0.9. Diagrams have been produced for the direct calculation of the force acting on the sphere. The numerical forecast shows a significant disparity between Newtonian and non-Newtonian fluids. All in all, the wall effect in power law fluids is less extreme than in Newtonian fluids. Furthermore, in non-Newtonian fluids, the force changes linearly when the sphere approaches the upper plate.

Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid (blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model. The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function (UDF). Numerical solutions are obtained by the finite volume method based on a nonuniform grid structure. The accuracy and efficiency of the solver are verified through a comparison with the literature. The results are presented graphically for different parameter values, and the effects of the magnetic number, the magnetic source position, the vascular obstruction ratio, the slip parameter, and the power-law index on the flow and temperature fields are illustrated.