Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Advancements in Numerical Solutions:Fractal Runge-Kutta Approach to Model Time-Dependent MHD Newtonian Fluid with Rescaled Viscosity on Riga Plate

Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal time-dependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of space-and temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Numerical Study of Temperature-Dependent Viscosity and Thermal Conductivity of Micropolar Ag–MgO Hybrid Nanofluid over a Rotating Vertical Cone

The present paper examines the temperature-dependent viscosity and thermal conductivity of a micropolar silver(Ag)−Magnesium oxide(MgO)hybrid nanofluid made of silver and magnesium oxide over a rotating vertical cone,with the influence of transverse magnetic field and thermal radiation.The physical flow problem has been modeled with coupled partial differential equations.We apply similarity transformations to the nondimensionalized equations,and the resulting nonlinear differential equations are solved using overlapping grid multidomain spectral quasilinearization method.The flow behavior for the fluid is scrutinized under the impact of diverse physical constraints,which are illustrated graphically.The results of the skin friction coefficient and Nusselt number varying different flow parameters are presented in the form of a table.It is observed that the main flow of the hybrid nanofluid,nano particle fraction of silver and Magnesium/water,enhances compared to the mono-nano fluid MgO as the coupling number increases.The application of studies like this can be found in the atomization process of liquids such as centrifugal pumps,viscometers,rotors,fans.

Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL

In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces.An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow.For different internal viscosities,this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate.This analysis may explain the attenuation of pressure drop in strong flows from a phenomeno...

Residence time distribution of high viscosity fluids falling film flow down outside of industrial-scale vertical wavy wall: Experimental investigation and CFD prediction

The flow behavior of gravity-driven falling film of non-conductive high viscosity polymer fluids on an industrial-scale vertical wavy wall was investigated in terms of film thickness and residence time distribution by numerical simulation and experiment.Falling film flow of high viscosity fluids was found to be steady on a vertical wavy wall in the presence of the large film thickness.The comparison between numerical simulation and experiment for the film thickness both in crest and trough of wavy wall showed good agreement.The simulation results of average residence time of falling film flow with different viscous fluids were also consistent with the experimental results.This work provides the initial insights of how to evaluate and optimize the falling film flow system of polymer fluid.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Effect of Viscosity on Pumping-Up of Newtonian Fluid Driven by a Rotating Cone

Effect of viscosity on flow patterns of pumping-up of liquid generated by a cone rotating at the liquid surface has been experimentally studied with various concentrations of glycerol aqueous solution. We have previously found that the higher viscous non-Newtonian fluid was lifted-up along the conical surface with a radial filament-wise pattern, which is quite different from the monotonic thin film-wise pattern observed for the lower viscous fluid such as water. In order to elucidate the pumping-up mechanism, a transition diagram indicating the critical rotation rate is obtained as a function of viscosity?of Newtonian fluid in this study, varying from the lower value of water (μ?=?0.890 mPa·s) to the higher one of glycerin (μ?= 910?mPa·s). It is found that there are three categories depending on the viscosity classified as?1) film-wise pumping-up region for the viscosity?μ?≤?134?mPa·s,?2) filament-wise pumping-up one for the viscosity?μ?≥?520?mPa·s, and?3) no pumping-up phenomenon occurs?for 134??μ??mPa·s.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Analysis of the Influence of Viscosity and Thermal Conductivity on Heat Transfer by Al2O3-Water Nanofluid

The addition of nanoparticles into liquid,even at low concentrations,leads to an increase in both,dynamic viscosity and thermal conductivity.Furthermore,the increase in temperature causes an increase in thermal conductivity and a decrease in the nanofluid viscosity.In this context,a numerical investigation of the competition between viscosity and thermal conductivity about their effects on heat transfer by Al_(2)O_(3)-water nanofluid was conducted.A numerical study of heat transfer in a square cavity,filled with Al_(2)O_(3)-water nanofluid and heated from the left side,was presented in this paper.Continuity,momentum,and thermal energy equations are solved by the finite volume method.Regarding the pressure-velocity coupling,the SIMPLER algorithm was used.The working conditions,allowing the increase of heat transfer,are established.In addition,two correlations for viscosity and thermal conductivity of Al_(2)O_(3)-water nanofluid as functions of the concentration and diameter size based on experimental measurement are proposed.These correlations were more precisely compared to those given by the theoretical models.Moreover,other models for viscosity and conductivity depending on temperature are used and discussed.The results reveal that heat transfer by Al_(2)O_(3)-water nanofluid is enhanced only when the temperature exceeds 40℃ and the diameter size does not exceed a certain limit of the order of 45-50 nm depending on temperature.

Analysis of the Influence of Viscosity and Thermal Conductivity on Heat Transfer By Al_(2)O_(3)-Water Nanofluid

The addition of nanoparticles into liquid,even at low concentrations,leads to an increase in both,dynamic viscosity and thermal conductivity.Furthermore,the increase in temperature causes an increase in thermal conductivity and a decrease in the nanofluid viscosity.In this context,a numerical investigation of the competition between viscosity and thermal conductivity about their effects on heat transfer by Al_(2)O_(3)-water nanofluid was conducted.A numerical study of heat transfer in a square cavity,filled with Al_(2)O_(3)-water nanofluid and heated from the left side,was presented in this paper.Continuity,momentum,and thermal energy equations are solved by the finite volume method.Regarding the pressure-velocity coupling,the SIMPLER algorithm was used.The working conditions,allowing the increase of heat transfer,are established.In addition,two correlations for viscosity and thermal conductivity of Al_(2)O_(3)-water nanofluid as functions of the concentration and diameter size based on experimental measurement are proposed.These correlations were more precisely compared to those given by the theoretical models.Moreover,other models for viscosity and conductivity depending on temperature are used and discussed.The results reveal that heat transfer by Al_(2)O_(3)-water nanofluid is enhanced only when the temperature exceeds 40℃ and the diameter size does not exceed a certain limit of the order of 45-50 nm depending on temperature.

Measurement of thermal conductivity,viscosity and density of ionic liquid [EMIM][DEP]-based nanofluids

This article studied experimentally the effect of multi-wall carbon nanotubes （MWCNTs） on the thermo physical properties of ionic liquid-based nanofluids. The nanofluids were composed of ionic liquid, 1-ethyl-3- methylimidazolium diethylphosphate [EMIM][DEP], or its aqueous solution[EMIM][DEP]（1） ＋ H20（2） and MWCNTs without any surfactants. The thermal conductivity, viscosity and density of the nanofluids were mea- sured experimentally. The effects of the mass fraction of MWCNTs, temperature and the mole fraction of water on the thermo physical properties of nanofluids were studied. Results show that the thermal conductivity of nanofluids increases within the range of 1.3%-9.7% compared to their base liquids, and have a well linear depen- dence on temperature. The viscosity and density of the nanofluids exhibit a remarkable increase compared with those of the base liquids. Finally, the correlation of the effective thermal conductivity and viscosity of the nanofluids was made using the models in the literatures.

Lie Group Analysis for the Effects of Variable Fluid Viscosity and Thermal Radiation on Free Convective Heat and Mass Transfer with Variable Stream Condition

Natural convective boundary layer flow and heat and mass transfer of a fluid with variable viscosity and thermal radiation over a vertical stretching surface in the presence of suction/injection is investigated by Lie group analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. The effects of fluid viscosity and thermal radiation on the dimensionless velocity, temperature and concentration profiles are shown graphically. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by these parameters.

Correlation of Shear Viscosity of Nanofluids Using the Local Composition Theory

In this study,a new method is presented to correlate the shear viscosity of nanofluids by local composition theory.The Eyring theory and nonrandom two-liquid(NRTL)equation are used for this purpose.The effects of temperature and particle volume concentration on the viscosity are investigated.The adjustable parameters of NRTL equation are obtained by fitting with experimental data.The calculated shear viscosities for nanofluids of CuO/water with 29 nm particle size,Al2O3/water with two different particle diameters,36 nm and 47 nm,and CuO/(ethylene glycol,water)are compared with experimental data and the average absolute deviation(AAD)is 1.2%,while the results from some conventional models yield an AAD of 190%.The results of this study are in excellent agreement with experimental data.

Viscosity of Nanofluids. Why It Is Not Described by the Classical Theories

Transport properties of nanofluids are extensively studied last decade. This has been motivated by the use of nanosized systems in various applications. The viscosity of nanofluids is of great significance as the application of nanofluids is always associated with their flow. However, despite the fairly large amount of available experimental information, there is a lack of systematic data on this issue and experimental results are often contradictory. The purpose of this review is to identify the typical parameters determining the viscosity of nanofluids. The dependence of the nanofluid viscosity on the particles concentration, their size and temperature is analyzed. It is explained why the viscosity of nanofluid does not described by the classical theories. It was shown that size of nanoparticles is the key characteristics of nanofluids. In addition the nanofluid is more structural liquid than the base one.

Dynamic analysis of polymeric fluid in shear flow for dumbbell model with internal viscosity

The dynamic analysis of semi-flexible polymers,such as DNA molecules,is an important multiscale problem with a wide range of applications in science and bioengineering.In this contribution,a dumbbell model with internal viscosity was studied in steady shear flows of polymeric fluid.The tensors with moments other than second moment were approximated in the terms of second moment tensor.Then,the nonlinear algebraic equation of the second moment conformation tensor was calculated in closed form.Finally,substituting the resulting conformation tensor into the Kramers equation of Hookean spring force,the constitutive equations were obtained.The shear material properties were discussed for different internal viscosities and compared with the results of Brownian dynamics simulation.

STEADY-SHEAR VISCOSITY AND TRANSIENT STRESS RESPONSE FOR ELASTO-THIXOTROPIC FLUIDS

A phenomenological model for dispersed systems which exhibit complex theological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to differ- ent kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus function G of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic orders n = m = 2.

Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.