Carreau Liquid Research Articles

Flow transitions and effective properties in multiphase Taylor–Couette flow

The properties of multiphase flows are challenging to measure, and yet effective properties are fundamental to modelling and predicting flow behaviour. The current study is motivated by rheometric measurements of a gas-fluidized bed using a coaxial rheometer in which the fluidization rate and the rotational speed can be varied independently. The measured torque displays a range of rheological states: quasistatic, dense granular flow behaviour at low fluidization rates and low-to-moderate shear rates; turbulent toroidal-vortex flow at high shear rates and moderate-to-high fluidization rates; and viscous-like behaviour with rate-dependent torque at high shear rates and low fluidization or at low shear rates and high fluidization. To understand the solid-like to fluid-like transitions, additional experiments were performed in the same rheometer using single-phase liquid and liquid–solid suspensions. The fluidized bed experiments are modelled as a Bingham plastic for low fluidization rates, and as a shear-thinning Carreau liquid at high fluidization rates. The suspensions are modelled using the Krieger–Dougherty effective viscosity. The results demonstrate that, by using the effective properties, the inverse Bingham number marks the transition from solid-like to viscous-flow behaviour; a modified gap Reynolds number based on the thickness of the shear layer specifies the transition from solid-like to turbulent vortical flow; and a gap Reynolds number distinguishes viscous behaviour from turbulent vortical flow. The results further demonstrate that these different multiphase flows undergo analogous flow transitions at similar Bingham or Reynolds numbers and the corresponding dimensionless torques show comparable scaling in response to annular shear.

Novel nanostructural features of heat and mass transfer of radiative Carreau nanoliquid above an extendable rotating disk

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field.

Rheological behaviour of Carreau liquid past a wedge surface with binary chemical reaction

The time-dependent stream of rheological Carreau nanoliquid carrying microbes through a rotating lodge through porous media in addition to irregular heat source or sink characteristics is the subject of this article. Due to the fact that the Carreau liquid can reveal the rheology of liquids with short-chain suspended particles, liquid crystals, surfactants, and human and animal blood, it is helpful to depict a range of physical problems. The influence of infinite shear rate thickness is combined to provide the mathematical formulation. Both the static and moving physical features are covered in great depth. Prior to using the finite element technique to solve revised equations numerically, pertinent similarity transformations are used to get equations in their dimensionless form. According to the findings of our study, the temperature and the thickness of the thermal boundary layer that corresponds to that temperature both improves the function that the thermal radiation factor plays in shear thickening and thinning liquids. Additionally, a moving wedge has a greater velocity than a static wedge. The thermophoresis factor's rising function is the concentration field. Furthermore, by increasing the Piclet number's magnitudes, the profile of microbes is diminished.

Onset about isothermal flow of Carreau liquid over converging channel with Cattaneo-Christov heat and mass fluxes

In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

Applications of variable thermal properties in Carreau material with ion slip and Hall forces towards cone using a non-Fourier approach via FE-method and mesh-free study

This research highlights the utilization of two viscosity models to study the involvement of variable properties in heat and momentum transport in a rotating Carreau fluid past over a cone. The rheology of the Carreau material is assessed by the variable dynamic viscosity over the heating cone. The transport of momentum phenomenon is modeled by considering generalized Ohm’s law in Carreau liquid and thermal transport in derived by considering variable thermal conductivity, heat flux model. The considered model is derived in the form of nonlinear PDEs with boundary layer analysis. The nonlinear PDEs are converted into coupled ODEs by using approximate transformation and converted equations are solved numerically by finite element methodology. The impact of numerous parameters is displayed graphically, and their behavior is discussed in detail.

Thermal radiative flux and energy of Arrhenius evaluation on stagnating point flowing of Carreau nanofluid: A thermal case study

This research extends to investigate the effects of activation energy and thermal radiation on mixed convection striation point flow of Carreau liquid toward the stretchable sheet. Heat transport assessment is utilized in the existence of activation energy. For flowing formulations, Carreau substance rheological relationships are used. For modelling and simulation, the Buongiorno nanoliquid model with thermophoretic and Brownian diffusion features is used. The obtained partial differential equation is converted to an ordinary differential equation by utilizing appropriate transmission. The mathematical formulation of the outcoming equation is achieved by utilizing the RK-Fehlberg approach with the bvp4c technique. This assessment illustrates several significant empirical features of flow and heat transport. Numerical simulations are taken for various scales of Hartmann number, temperature ratio parameter, and Schmidt number. The assumption is that the velocity estimation reduces the Hartmann number. The opposite result of the thermal ratio parameter remains valid for the Nusselt effect and temperature curve. Furthermore, the influence of Schmidt quantity on the Sherwood amount and solutal contour are extremely opposite.

Quadratic multiple regression model and spectral relaxation approach for carreau nanofluid inclined magnetized dipole along stagnation point geometry

Researchers across the world have tried to explore the impact of non-Newtonian liquid flowing via an extendable surface with the inclusion of various effects due to its industrial and engineering applications like polymer production, paper production, filament extrusion from a dye, etc. This study investigates the behavior of stagnation point flow of Carreau liquid attached with inclined magnetic effect and spectral relaxation approach is utilized here for the numerical outcome. In this study, a few other vital features are attached like the quadratic multiple regression model for Nusselt number evaluation, passive control of nanoparticles, viscus heating thermophoresis, Brownian motion, and mixed convection, etc. Velocity disbursement visibility is analyzed by placing an inclined magnetic field. Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. Further for numerical process, spectral relaxation method is used. Growth in K causes a reduction in velocity because this parameter K creates the impedance to flowing resulting in confines the movement of liquid in restricted the plate. Direct relation is found between Ec and the energy file. In the case of S > 1, physically it is a representation of Joule and viscous dissipations. This article is novel in its sense that the influence of oblique magnetic force and second order velocity slippage on Carreau nano liquid and its numerical computation with help of the spectral relaxation method has never been done before. Furthermore, the quadratic multiple regression model has been employed to find the heat transition rate in the status of the Nusselt number.

A comprehensive physical insight about thermo physical aspects of Carreau fluid flow over a rotated disk of variable thickness by implementing finite difference approach

Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating disk. Mathematical formulation is constructed in view of complex coupled partial differential system. Afterwards, boundary layer approach is executed for comprehensive examination of under consideration phenomenon with in boundary layer region. Karman's transformation is capitalized to convert the attained PDE's into ordinary differential equations system. Solution of attained ODE's system is solved numerically by implementing Keller-Box scheme. Influence of protuberant involved parameters on momentum and thermal distributions is illustrated through sketches. In addition, impact of flow concerning parameters on wall shear stress and thermal flux is also evaluated. The assurance of present finding is done by making agreement with published results and by restricting considered problem to Newtonian case. Here, we observed that radially and tangentially directed wall drag lessen with growing magnitude of power law exponent index. Moreover, the consequence of disk thickness parameter grows stresses along radial direction whereas opposite behavior is depicted in case of tangentially directed friction and heat flux factors.

Passive scalar transfer rate at bubble interface in Carreau liquid in a transition regime

The scalar transfer rate from a bubble to a quiescent fluid with Carreau rheological behavior is studied here with Bond and Galilei number values respectively equal to 30 and 2 and a non-dimensional inelastic time constant (λ) equal to 6. Under these conditions the bubble dynamics regime stays within the steady and oscillatory areas. Navier Stokes equations are solved numerically in a non-stationary three dimensional domain and are coupled to the mass transfer equation of a scalar. The effect of the Peclet number (Pe) and flow index (n) of the quiescent fluid on the Sherwood number is explored within the following range: 10<Pe<1000, and 0.3<n<1.7. We observed that the shear thinning rheology destabilizes the bubble flow dynamics from steady towards an oscillatory regime and increases transfer rates between the bubble and surrounding fluids. This trend became even more prominent as Pe increased. Our results are condensed into an empirical predictive correlation that outperforms previous similar correlations and can be used to estimate the heat and mass transfer rate at the bubble interface in a Carreau liquid in a transition regime at a specific Galilei and Bond numbers.

Magnetohydrodynamic Impact on Carreau Thin Film Couple Stress Nanofluid Flow over an Unsteady Stretching Sheet

A mathematical model of time-dependent thin-film flow of Carreau liquid over a stretching surface is studied in this investigation in the presence of couple stress and uniform magnetic field. To explain the properties of heat and mass transport phenomena, the influence of both thermophoresis and Brownian motion variables is used. For the conversion of the model framework (momentum, heat, and concentration expression with boundary conditions) into a set of ordinary differential equations, the appropriate transformation technique is followed. By using analytical tool, HomotopyAnalysis Method (HAM), the transformed model expressions are solved. For different estimations of the affected physical factors, the numerical results involving skin-friction coefficient, Nusselt number, Sherwood number, fluid velocity profile, thermal profile, and concentration profile are displayed graphically. Besides, the findings for skin-friction coefficient, Nu x , and ϕ η are given in the table format. In raising the fluid temperature, the effect of thermophoresis and magnetic parameters is beneficial. With the Brownian motion and Schmidt number, the solute concentration is found to reduce.

Numerical treatment of magnetohydrodynamic Carreau liquid with heat and mass transport containing gyrotactic microorganisms

In the current examination, insightful approximations are researched for magnetohydrodynamics Carreau nanofluid having gyrotactic microorganisms over a warmed turning plate. The plate is moving with the steady uniform rakish speed. Administering conditions are gotten by utilizing certain actual presumptions as incomplete differential conditions with limit conditions. These nonlinear types of conditions are changed into coupled standard differential conditions utilizing bunch likeness change. Optimal homotopy investigation strategy (OHAM) is utilized to acquire the graphical outcomes and even qualities for the stream field factors. Graphical portrayal of speeds, temperature, fixation and thickness of gyrotactic microorganisms are examined and clarified. It is tracked down that dimensionless microorganism’s fixation develops for bioconvective Lewis number and focus distinction variable of microorganisms. It is additionally seen that dimensionless speeds diminish because of the attractive impact and Carreau liquid boundary. Contour plots and mathematical outcomes are given for neighbourhood motion boundaries like skin rubbing coefficient, Nusselt number, Sherwood number and thickness number of motile microorganisms.

Significance of double diffusion for unsteady Carreau micropolar nanofluid transportation across an extending sheet with thermo-radiation and uniform heat source

The main objective of this manuscript is to glance into the assets of nanoparticles in the stream of generalized micropolar fluid and Carreau fluid against an intensified elongated surface. In order to assess, the heat and mass diffusion occurrences, the Cattaneo-Christov implications are also experienced in the temperature and concentration computations. In contrast to prior studies, rheological attributes on non-Newtonian fluids are depicted by engaging micropolar fluid and Carreau liquid that reflect a clear difference of transport phenomena. By minimizing the number of independent factors, the regulating equations are transmuted into non-dimensional types, that are then tackled numerically using the RK-4 algorithm along with the shooting strategy. For velocity, micro-rotation, temperature and concentration distributions, a visualization evaluation of the entangled flow parameters is executed. It has been revealed that expanding magnetic and micropolar constraints enhance micro-rotation velocity. The unsteadiness parameter enhances all three physical quantities, surface drag force, Nusselt number, and Sherwood number.

Bioconvection phenomenon for the boundary layer flow of magnetohydrodynamic Carreau liquid over a heated disk

A numerical examination is conducted for the magnetohydrodynamics steady Carreau fluid flow on the transport of thermal energy and mass specie comprising nanoparticles with gyrotactic microorganisms through heated disk. The role of thermophoresis and Brownian motion are added in this flow problem. Governing equations are achieved by using the boundary layer theory in view of a coupled system of PDEs involving boundary conditions. The highly non-linear system of ODEs is generated using the concept of the transformation approach. Since the system of transformed equations is highly nonlinear, so, an approximate solution is estimated via optimal homotopy method. The role of prominent parameters on velocity, thermal energy, mass specie and motile density microorganisms examined graphically. Additionally, graphical observations regarding mass specie, thermal energy and velocities are discussed briefly. It has estimated that the motion of fluid particles is diminished because of the intensity of the magnetic field while mass specie and fluid temperature rise versus enhancement the values of the magnetic field.

Evaluation of entropy generation with thermal radiation on MHD Carreau fluid stream past a wedge

This article keeps an eye out for an entropy age with radiation for unsurprising laminar 2D stream of non-Newtonian Carreau liquid past a moving wedge. The stream is influenced by uniform transverse charming field. The standard conditions and their seeing breaking point conditions are changed into the normal differential conditions by utilizing appropriate likeness changes and solve numerically utilizing the Runge-Kutta Fehlberg strategy together with a shooting structure. The impacts of two or three controlling parameters on speed and temperature arrangements likewise as the granulating coefficient and the Nusselt number are settled. In like manner, the entropy age number and Bejan number are additionally examined for different physical parameters. The outcomes are appeared in graphically likewise as in illicit structure. The present work uncovers that the liquid speed thusly lifted by the precariousness parameter, engaging parameter, Weissenberg number and wedge point parameter while temperature are decelerated. It is additionally dismembered that the entropy profile increments for some physical parameters and Began number increases from the beginning, yet its beginnings changing its direct after unequivocal estimations of η.

Entropy analysis of non-linear radiative flow of Carreau liquid over curved stretching sheet

The objective of the present article is to inquire about the entropy generation in the two-dimensional steady incompressible flow of Carreau liquid over a curved stretching sheet. The heat transfer is characterized by the process of non-linear thermal radiation. The equations were governed through the curvilinear coordinates system which is describing the flow model. The acquired set of equations was converted into non-linear coupled ordinary differential equations utilizing similarity transformation. The governed system was solved via the shooting method employing Runge Kutta Fehlberg (RKF) technique. The interest lies in analyzing the physical quantities like flow velocity, temperature distribution, surface friction, heat flux at wall, and generation of entropy for several involved parameters. The study stated that higher curvature and Carreau liquid parameter enhances temperature distribution and slowdowns the flow. Moreover, the entropy generation enhances fluid parameters and thermal radiation.

Double diffusion in Carreau liquid suspended with hybrid nanoparticles in the presence of heat generation and chemical reaction

Double diffusion models with Carreau rheology strain-relations and correlations for thermal physical properties are used to model double diffusion phenomenon in Carreau liquid passing a wedge-shaped body. Normalized conservation equations are solved numerically using finite element method (FEM). Linear shaped functions are used in weak forms of models under Galerikin approximations. Convergence and mesh free analysis are performed and results are validated. The numerical simulations against parametric analysis are also observed. Suspension of hybrid nano-structures has significantly increased the effectiveness of thermal conductivity and an enhance in thermal and mass transport is observed. An increase in thermal radiations causes a remarkable decrease in temperature. Weissenberg parameter decreases velocity of Carreau liquid in the presence of magnetic field and hybrid nano-structures. The chemical reaction has an impact on the diffusion of specie from wedge into fluid increases for the case of generative chemical reaction whereas opposite trend is noted in case of destructive chemical reaction.

Numerical computing for axisymmetric transport phenomenon in Carreau liquid using variable conductance models

Conservation laws and variable conductance (viscosity, thermal conductivity and mass diffusion coefficient) models are used to develop mathematical problems describing transport mechanism in Carreau fluid over a non-uniformly moving surface. Boundary conditions are developed by no-slip theory. Mathematical models are transformed into suitable residual integrals which are approximated by Galerkin approximations. The obtained residuals are used for solving problems numerically using finite element method. Numerical investigation of variable viscosity, thermal conductivity and mass diffusion coefficients is carried out to examine the impact of parameters. The heat dissipated as a result of friction among the particles of the fluid of constant viscosity is greater than the heat dissipated due to friction force in the fluid of temperature-dependent viscosity. It is also found that ohmic phenomenon in the fluid of variable viscosity is prominent than that in the fluid of constant viscosity. Therefore, this fact must be in mind while using the fluids of variable viscosity in engineering applications. The transport of mass in fluid of constant viscosity is greater than that in fluid of variable viscosity. The Lorentz force is observed to oppose the flow. Hence, flow is decelerated by an increase in the intensity of magnetic field. The rate of transportation of mass has shown increasing trend when mass diffusion coefficient increases due to temperature.

Numerical analysis of unsteady Carreau nanofluid flow with variable conductivity

In thoughtfulness of researchers and technologists in the arena of nanoscience and nanotechnology owing to reduced thermal properties of the usual base fluids, a new-fangled sort of fluids acknowledged as nanofluids have been established, which contains nanoparticles deferred in a hostfluid. For instance, nanofluids have superior heat transport enactment, because deferred nanoparticles have better thermal conductivity allied with base liquid. Here elaborated 3D flow of a Carreau nanoliquid is influenced by a bidirectional stretched surface. To visualize the properties of Brownian motion and thermophoresis on the Carreau nanoliquid, the Buongiorno's relation is exploited in a more proficient tactic. Variable thermal conductivity with the possessions of heat source/sink is pondered for heat transfer mechanisms. Suitable conversion is used to change the PDEs into non-linear ODEs. Numerically, bvp4c scheme is prompted to crack the resulting ODEs. The discrete behaviors for shear thinning/thickening of nanoliquid temperature and concentration field are described and deliberated in aspect for somatic parameters. It is exposed that the Carreau liquid temperature declines for Prandtl number and conflicting trends are being noted for Brownian and thermophoresis parameters. Moreover, heat transfer amount diminishes for higher Brownian and thermophoresis parameters. An assessment between two different approaches namely, bvp4c and homotopy analysis method, is also presented in tabular form which ensure that our outcomes are more precise.

Magnetohydrodynamic flow of Carreau liquid over a stretchable sheet with a variable thickness

PurposeThe magnetohydrodynamic (MHD) flow problems are important in the field of biomedical applications such as magnetic resonance imaging, inductive heat treatment of tumours, MHD-derived biomedical sensors, micropumps for drug delivery, MHD micromixers, magnetorelaxometry and actuators. Therefore, there is the impact of the magnetic field on the transport of non-Newtonian Carreau fluid in the presence of binary chemical reaction and activation energy over an extendable surface having a variable thickness. The significance of irregular heat source/sink and cross-diffusion effects is also explored.Design/methodology/approachThe leading governing equations are constructed by retaining the effects of binary chemical reaction and activation energy. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. Subsequent nonlinear two-point boundary value problem is treated numerically by using the shooting method based on Runge–Kutta–Fehlberg. Graphical results are presented to analyze the behaviour of effective parameters involved in the problem. The numerical values of the mass transfer rate (Sherwood number) and heat transfer rate (Nusselt number) are also calculated. Furthermore, the slope of the linear regression line through the data points is determined in order to quantify the outcome.FindingsIt is established that the external magnetic field restricts the flow strongly and serves as a potential control mechanism. It can be concluded that an applied magnetic field will play a major role in applications like micropumps, actuators and biomedical sensors. The heat transfer rate is enhanced due to Arrhenius activation energy mechanism. The boundary layer thickness is suppressed by strengthening the thickness of the sheet, resulting in higher values of Nusselt and Sherwood numbers.Originality/valueThe effects of magnetic field, binary chemical reaction and activation energy on heat and mass transfer of non-Newtonian Carreau liquid over an extendable surface with variable thickness are investigated for the first time.

A shear-rate-dependent flow generated via magnetically controlled metachronal motion of artificial cilia.

Cilia beating is a naturally occurring phenomenon that can be utilized in fluid transport in designing several biomechanical devices. Inspired by the ubiquity of bio-fluids (which are non-Newtonian), we report the characteristics of shear-rate-dependent viscosities on fluid flow generated by the wavy propulsion of magnetic cilia. We assume that the metachronal waves of these cilia form a two-dimensional wavy channel, which is filled with generalized Newtonian Carreau liquid. Galilean transformation is employed to relate fixed and moving frames. The constitutive equations are reduced under the classical lubrication assumption. The resulting fourth-order nonlinear differential equations are solved via a perturbation approach using the stream function. The effects of four dominant fluid parameters (shear thinning/thickening, power-law index, and zero- and infinite-shear-rate viscosity), magnetic parameter (Hartmann number), and metachronal wave parameters on fluid velocity, pressure rise per wavelength, and trapping phenomenon are shown in graphical results and explained thoroughly. This study could play an advisory role in designing a magnetic micro-bot useful in the biomedical industry.