Carreau Fluid Model Research Articles

Temperature‐dependent electrical conductivity impact on radiative and dissipative peristaltic transport of boron nitride‐ethylene glycol nanofluid through asymmetric channels

AbstractMathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic pumping within vertical asymmetric channels filled with BN‐EG nanofluid under the influence of temperature‐dependent electrical conductivity and thermal radiation. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non‐Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN‐EG nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. A uniform magnetic field together with nanoparticles and mass concentrations, joule heating, first‐order chemical reaction as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity u, heat transfer rate Z, concentration profile Ω, temperature profile θ, extra stress tensor , pressure gradient , pressure rise and stream function ψ. The major outcomes revealed that the maximizing in electrical conductivity coefficient, variable viscosity coefficient and magnetic field parameter is better to obtain a higher rate of the heat transfer while the increase in thermo‐diffusion effects as well as linear thermal radiation coefficient causes a reduction in the rate of heat transfer.

Second law assessment of injected nanoparticles to blood flow with thermal radiation and magnetic field in conduit artery

BackgroundThe stipulated flow over an artery is optimized by adopting an artery as convergent or divergent channel with an arbitrary cross section. The standard Carreau fluid Model is used in this work to account for viscoelasticity in the whole network. The viscoelastic contribution at borders (inlet, outlet, and core region) is implemented while keeping the mathematical model parabolic character in mind. Due to low toxicity, MgO nanoparticles dispersed in blood having potent antibacterial effects against three major food-borne illnesses. Furthermore, Hypomagnesaemia is produced by a magnesium deficit in the blood, which is an additional stimulation for different diseases such as diarrhea, nausea, and decrease in appetite. To compensate for this shortage, MgO is delivered as a nanoparticle into the blood (base fluid). The mechanics of energy and irreversibility are evaluated with the contribution of viscous dissipation, Ohmic heating, and radiant heat. MethodsSuitable renovations are used to amend the system of complex PDEs into nonlinear ODEs. The numerical solutions to these ODEs are calculated using the fourth order Runge-Kutta scheme and the shooting mechanism. Significant findingAn elevation of radiation parameter contributes significantly to blood velocity, temperature, and entropy. The flow dynamic and energy of the blood stream is higher when nanoparticles are injected in base fluid. Bejan detracts as Brinkman number grows but increases as radiation parameter increases. High Weissenberg numbers dictate thermodynamic behavior relating to pure elastic energy. The system entropy amplifies against Rd. With increase in M, viscous dissipation irreversibility takes precedence overheat transfer irreversibility, while Be deteriorate.

Magneto-Convective Transport of Immiscible Binary Fluids in Inclined Channel

Abstract This work theoretically investigates the interfacial transport of immiscible fluid layers in an inclined fluidic channel in the presence of magnetofluidic actuation. Immiscible binary system consists of both non-Newtonian fluid (top layer) and Newtonian fluid (bottom layer), while the Carreau fluid model is used to describe the rheology of non-Newtonian layer. We develop a theoretical framework consistent with the homotopy analysis method (HAM) to obtain the approximate analytical solutions for the underlying thermofluidic transport features. By depicting the auxiliary parameter curve (ℏ-curve) of flow velocity and temperature distribution, we ascertain the effective reliability of the theoretical method developed here. We demonstrate both velocity and temperature variations in the channel for a set of involving parameters pertinent to this analysis. Albeit the flow configuration considered in this analysis is not complex, yet, the method developed here seems to be efficient in capturing underling transport features, retaining the simultaneously acted implications of fluid rheology and magnetohydrodynamics. Form the consistency observed in predicting the flow velocity for any values of shear-thinning parameter, including nonintegers, our semi-analytical method is deemed pertinent to predict the thermohydrodynamics of immiscible multilayer system even by accurately capturing the intervening effects of fluid rheology and applied fields.

Numerical exploration of buoyancy inspired flow of pseudoplastic fluid along a vertical cylinder with viscous dissipation effects

This research presents a numerical investigation for flow around a stagnation point on a vertical stretching cylinder placed in a pseudo-plastic fluid. An important Carreau fluid model is adopted to account for pseudo-plastic effects in the flow field. Buoyancy force term arising due to the vertical boundary is formulated under the well-known Oberbeck-Boussinesq approximation. Conservation equations simplified under boundary layer assumptions are solved for the similarity solutions for full range of parameter A, giving the ratio of free stream velocity to the cylinder surface velocity. The shape of velocity profile is dependent on the choice of the parameter A. Contributions of buoyancy force term and shear-thinning effect in both assisting and opposing flow situations are scrutinized. A striking influence of rheology is such that resisting wall shear declines and cooling rate of the surface drops whenever shear-thinning effect is present. However, cooling rate amplifies as the strength of buoyancy force is enhanced. Special cases of the model including the case of flat surface and Newtonian fluid are presented separately.

FEM Simulations to Analyze Flow and Thermal Characteristics of Carreau Non-Newtonian Fluid in a Square Cavity

Heat transfer aspects induced by natural convection in enclosures have promising utilizations and essence from theoretical as well as practical prospective like in, nuclear and chemical reactors, electronic devices, cooling, polymeric processes, solar power collection and so forth. After viewing aforementioned extensive practical importance present communicatn is addressed to explain the flow attributes of Non-Newtonian Carreau fluid model in a square cavity. For non-elastic Carreau fluid model expressing the stress and strain relations at infinite and zero stress magnitude. Mathematical formulation of problem is conceded by obliging conservation laws of momentum and energy. A square enclosure with unit dimension is assumed by providing no-slip constraints at all extremities whereas bottom wall is uniformly heated. In order to maintain state of thermal equilibrium in which upper wall is adiabatic and lower and left wall is kept heated and right wall is considered as cold.by incorporation above restrictions on formulated problem equation are attained in partial differential dimensional form. Later on, these expressions are transmuted into dimensionless form by executing variables. Numerical simulation, based on infinite element method by utilizing COMSOL multi physics commercial software is computed. For this purpose, firstly preprocessing involving the steps of meshing at different refinement level is carried out. After this influence of involved dimensionless parameters as flow concerning profile is manifested through graphs and tables. Validation of result is also provided by constructing comparison with existing literature. Grid independence test for heat transfer coefficient is also performed. Engineering interest quantities like kinetic energy, local and average Nusselt number is also computed.

On the steady flow of non-newtonian fluid through multi-stenosed elliptical artery: A theoretical model

The study of blood flow through stenotic arteries is more important as the existence and progression of stenosis may lead to severe damage. The current study aims to analyze and understand the non-Newtonian nature of blood flow through the multi-stenosed artery of an elliptical cross-section. The Carreau fluid model accounts for the non-Newtonian nature of blood. The mathematical equations are transformed to dimensionless form, and assumptions of mild stenosis are employed to reduce the non-linearity of the mathematical model. The perturbation method via polynomial technique is utilized to solve the resulting equations by considering We2 as the perturbation parameter. The results of the velocity and wall shear stress are examined graphically. It is found that stenosis severity substantially impacts flow velocity in the narrower portion of the artery. The stenosis growth strongly affects the flow velocity and wall shear stress in the stenotic region. The non-Newtonian effects are found to dominate along the minor axis. This fact assures that the conduit’s narrower cross-section strengthens the fluid’s non-Newtonian behavior. It is observed that the non-Newtonian fluid has a smaller velocity than the Newtonian fluid. Moreover, non-Newtonian fluid has a different nature along the minor and major axes, but Newtonian fluid has the same behavior.

The peristaltic flow for Carreau fluid through an elastic channel

Abstract The purpose of this study is to investigate the effect of an elastic wall on the peristaltic flow of Carreau fluid between two concentric cylinders, where the inner tube is cylindrical with an inelastic wall and the outer wall is a regular elastic sine wave. For this problem, cylindrical coordinates were used, and a short wavelength “relative to channel width for its length,” as well as the governing equations of Carreau fluid in the Navier–Stokes equations. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the fourth-order in dimensionless Weissenberg number ( W e {W}_{{\rm{e}}} ). The performed computations of various parameter values such as velocity, shear stress, and wave frame streamlines are discussed in detail for different values of the Weissenberg number ( W e {W}_{{\rm{e}}} ). The obtained results demonstrate that the fluid velocity increases with the increase in the value of W e {W}_{{\rm{e}}} and some features of the wall, while the opposite behavior is observed with the increase in other features of the wall. Hence, the presented numerical analysis reveals many aspects of the flow by considering a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies. The results were evaluated using the Mathematica software program. The Mathematica program was used by entering various data for the parameters, where the program showed the graphs, then the effect of these parameters became clear and the results were mentioned in the conclusion.

Investigation of Entropy Production with Thermal Analysis under Soret and Dufour Effects in MHD Flow between Convergent and Divergent Channels.

Hydromagnetic flow and heat transport have sustainable importance in conventional system design along with high-performance thermal equipment and geothermal energy structures. The current computational study investigates the energy transport and entropy production due to the pressure-driven flow of non-Newtonian fluid filled inside the wedge-shaped channel. The nonlinear radiation flux and uniform magnetic field are incorporated into the flow analysis. To be more precise, non-Newtonian fluid initiates from an inlet with the bound of the parabolic profile and leaves at outlet of a convergent/divergent channel. We assume that the channel flow is adiabatic and influenced by the wall friction. The leading flow equations are modeled via the Carreau fluid model using fundamental conservation laws. The thermodynamical aspect of the system is visualized using a two-phase model and analyses of the entropy equation due to fluid friction, ohmic heating, and diffusion of heat and mass fluxes. The modeled system of equations is normalized using a dimensionless variable mechanism. The system was elevated for the significant variation of controlling parameters. The outcomes obtained from the computational investigation are validated with the theoretical results that are available in the literature. An increasing semivertex angle and Reynolds number increase the converging channel flow. In the core flow zone, an increase in the divergent semiangle causes the flow to decelerate, while near and at the channel wall it causes a slight acceleration. Outcomes designate that the main contribution to the irreversibility is due to ohmic loss, frictional loss, and heat loss. The thermal performance and entropy production is dominant for a diverging flow. The outcomes of this research will assist in comprehending the process of entropy minimization in conjunction with the flow of nanomaterials in a nonuniform channel, which is essential in engineering processes such as the creation of micro machines, supersonic Jets, nozzles, and clean energy.

Theortical study of temperature-dependent flow induced by MW model

A theoretical study is examined by taking the effects of the boundary layer flow over a heated rotating disk for both anisotropic and isotropic surfaces. We used the Carreau fluid model for shear thinning and thickening behaviors and determine the steady flow profiles under the partial slip model. Thermal conductivity and mass diffusivity are adopted to explore the flow phenomena. Numerical solution of the boundary layer equation is then preformed by using a shooting technique. Thermal conductivity and mass diffusivity increase the temperature and concentration profiles. We determine the base flow profiles and give a physical explanation of the problem though figures and tables. This study explores the interesting physical parameters on the base flow, heat and mass transfer profiles. Comparison has been made with the present results of the literature, achieving a good agreement.

Peristaltic pumping of Boron Nitride-Ethylene Glycol nanofluid through a complex wavy micro-channel under the effect of induced magnetic field and double diffusive

The main objective of this work is to present a comprehensive study that scrutinize the influence of DD convection and induced magnetic field on peristaltic pumping of Boron Nitride—Ethylene Glycol nanofluid flow through a vertical complex irregular microchannel. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non-Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN-EG nanofluid. In order to imitate complicated peristaltic wave propagation conditions, sophisticated waveforms are forced at the walls. The essential properties of Brownian motion and thermophoresis phenomena are also included in simulating of heat equation as well as viscous dissipation. Mathematical simulation is performed by utilizing the lubrication approach. The resulting nonlinear coupled differential equation system is solved numerically using the built-in command (ND Solve function) in the Mathematica program. Numerical and pictorial evidence is used to illustrate the importance of various physiological features of flow quantities. The major findings demonstrated that the thermal resistance is observed to rise as the Soret and Dufour numbers increase, while the dissolvent concentration and nanoparticles volume fraction have the opposite effect.

An IFDM analysis of low Reynolds number flow generated in a complex wavy curved passage formed by artificial beating cilia

Mother nature utilizes an assembly of beating cilia to transport liquid in various circumstances. The arrays of these hair-like cellular appendages also aid in propelling microorganisms like spermatozoa and paramecium. In our implicit finite difference analysis, we present a pumping performance of a curved channel comprising mucus flow induced via active cilium. The non-Newtonian mucus is modelled as Carreau fluid model. The undulating cilia attached with curved walls are assumed to be complex wavy. The tips of these cilia form a complex wavy peristaltic curved passage with porous medium effects. Well-known continuity and momentum equations (in curvilinear coordinates) are utilized to model the flow problem. Cilia-driven flow is creeping which is based on low Reynolds number assumption. Moreover, long wavelength assumption is also employed in this analysis. The reduced fourth-order BVP is solved via implicit finite difference method (IFDM). The computed results are plotted by using MATLAB (2021a). The mucus velocity is plotted at three different cross-sections and flow rates. Moreover, velocity of mucus, pressure gradient, pressure rise, and level curves are also expounded for various rheological, porous and cilia-based parameters. A special case of straight passage is also presented in the graphical result section.

Thermohydraulic and irreversibility assessment of Power-law fluid flow within wedge shape channel

Entropy production occurs in all thermohydraulic systems, which results in performance degradation. Entropy production promotes irreversibility in complicated systems, which are commonly found in industrial mechanisms. As a response, this technology is successfully applied in several technological applications involving porous media, propulsion ducts, electronic cooling, turbomachinery, and combustion. In the current computational study, energy transfer and entropy development resulting from pressure-driven flow of a non-Newtonian fluid inside a wedge-shaped expanding channel is evaluated. The direct characterization of the inefficiency mechanisms that cannot be accomplished by the conventional energy analysis. Entropy generation analysis, which precisely quantifies the irreversibility resulting from heat transfer, mass transfer, and viscous heat loss of the Jaffrey-Hamelflow of power-law fluid. The conservation equations are used to develop the governing flow equations for the non-Newtonian Carreau fluid model. For the sake of the current investigation, the equation for entropy generation is modelled using the second law of thermodynamics. The appropriate transformations are implemented in order to convert the governing PDEs into a collection of coupled ODEs. To solve the generated extremely non-linear ODEs, the shooting approach and the fourth, fifth order Runge-Kutta method have been used. The acquired numerical statistics indicate that, while the thermal radiation parameter tends to increase the rate of heat transfer, the Eckert number decreases as it rises. For higher estimation of Weissenberg numbers and power law, the entropy number drops in a divergent channel, but a contrary tendency is revealed for Bejan profile. A growth in the power-law index leads to a significant reduction in several irreversibility. Moreover, entropy generation is lower within divergent channel in comparison to the convergent section. Heat and mass transport are substantially reduced as the power-law index rises.

Numerical analysis of generalized Fourier's and Fick's laws for micropolar Carreaufluid over a vertical stretching Riga sheet

AbstractThe present analysis is considered the Micropolar Carreaufluid model over a vertical Riga sheet. Cattaneo–Christov heat flux theory is utilized rather than classical Fourier's law to scrutinize the heat transfer specification. The scheme of developing partial differential equations is turned into ordinary differential equations (ODEs) by employing specific transformations. The numerical scheme is implemented to solve the present model. This article includes the numerical and graphical description of numerous physical parameters on the velocity profile, microrotation, concentration profile, and temperature distribution. The values of skin friction were found to be bigger, but couple stress values were found to be lesser due to boosting values of (buoyancy ratio term). The velocity function gradually improved due to improvement in M (modified Hartmann number). The velocity function gradually improved due to improvement in K (micropolar parameter). The γ (Dimensionless parameter) slowly augmented as well as the velocity function declined. The temperature function curves and γ1 are found to be the same behavior of amassed increasingly.

Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel

The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

Blade coating analysis of carreau fluid model with Magnetohydrodynamics and slip effects

Coating is a process that improves and enhances life, quality and efficiency of the web. Common industrial adhesive application to board and paper, metal foils polymer coatings, photographic film emulsions, recording films, textile fabrics, paints, coating on food items, medicine, catalogues are common examples. There are many fluids that are used as coatings. This paper analyses blade coating using both plane as well as exponential geometries along with slip and magnetohydrodynamics effects for a Carreau fluid model. To study the blade coating phenomenon, slip is introduced at the blade surface and a magnetic field is applied normal to the fluid flow. The LAT (Lubrication approximation theory) has been introduced to convert governing partial differential equations into a simpler form and a numerical solution is obtained by using shooting method. The significant physical quantities like volumetric flow rate, pressure, velocity, load, coated film thickness and pressure gradient are discussed in detail. The effects of power law index, slip parameter, Weissenberg number and Hartmann number on these physical quantities are presented. The observations are depicted in tabular data and in the graphical form as well. The Weissenberg number and Hartmann number play a very important role in controlling the load and coated film thickness.

Buongiorno model analysis on Carreau fluid flow in a microchannel with Non-linear thermal radiation impact and irreversibility

ABSTRACT The main focus of the current work is to explore the thermal energy and mass transfer process in conducting non-Newtonian fluid flows through a horizontal microchannel along with irreversibility analysis and to investigate the upshot of nonlinear radiation, convective boundary conditions, and magnetic field. Slip regime and temperature jump conditions are used at the boundaries of the microchannel. The rheological characteristics of the Carreau fluid model are also considered. The Buongiorno model was used in this study, which emphasizes the light on Brownian motion and thermophoresis phenomena that occur during the fluid flow. Runge-Kutta Fehlberg’s fourth-fifth order was used to solve governing equations numerically. The significant influence of effective parameters on entropy generation, Bejan number, velocity, temperature and concentration profile have been discussed with the aid of graphs. Entropy generation rises by 40% at the left wall of the channel and is depleted by 36% at the right wall when the thermophoresis parameter augments by 200%. Amplified concentration profile with an escalation of Brownian parameter. The temperature field diminishes with inflation of the radiation parameter.

Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel

The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

Electroosmotically modulated peristaltic propulsion of TiO2/10W40 nanofluid in curved microchannel

The present investigation emphasizes the fluid flow analysis and the heat transfer characteristics of 10 W40-based titanium dioxide nanofluid subject to electroosmotic forces and the peristaltic propulsion in a curved microchannel. The Carreau fluid model is employed to predict the shear-thinning behavior of nanofluid. The effect of Brownian and thermophoretic movements of the nanoparticles and the thermophysical attributes are included in the problem with the modified Buongiorno model. The uniqueness here is the inclusion of variable thermophoretic and diffusion parameters in the Buongiorno model. Moreover, the non-Newtonian fluid model is used with experimentally fitted values of the parameters for the considered fluid. The resulting system of equations is highly nonlinear and coupled and therefore executed numerically through the built-in package in Maple 17. The results of the said investigation indicate that for maintaining a larger temperature difference, buoyancy forces are strengthened and fluid motion is facilitated. However, the magnitude of the Nusselt number drops for the larger temperature difference. It is also revealed that the temperature of the nanofluid drops for a larger curvature parameter which physically corresponds to a less curved channel. Further, the electroosmotic flow parameters have a progressive impact on the velocity and the convective heat transfer process.

Calculating the isotropic and anisotropic roughness by using MW model: A variable thermal conductivity study

In this paper, we analyze the mathematical and theoretical studies of flow over a heated rough rotating disk. By using the Carreau fluid model we examine the dilatant and pesudoplastic behavior along with mean flow under the partial slip conditions. The variable fluid property is considered for heat phenomena. This study has stimulated a great deal of interest in applied engineering due to its enhanced theoretical and mathematical advantages. We analyzed the isotropic and anisotropic solutions for Carreau fluid model with variable fluid property. The similarity transformations used here for the Carreau fluid was initially presented by von Kàrmàn, it reduces the boundary layer equations into ordinary differential equations. Shooting method is used to solve the dimensionless ordinary differential equations. All of the obtained outcomes are analyzed for the mean flow velocity and temperature profiles and physical characteristics are shown in the form of graphs and table.

Magneto Casson-Carreau Fluid Flow through a Circular Porous Cylinder with Partial Slip

In the current study, a comparative analysis of two-dimensional heat transfer by the free convective flow of non-Newtonian Casson and Carreau fluid in electro-conductive polymer on the outside surface of a horizontal circular cylinder under slip and radial magnetic field effects is regarded. The Casson and Carreau fluid model formulation were first developed for the problem of the boundary layer of the horizontal circular cylinder and by using non-similarity transformations, the combined governing partial differential equations are translated into ordinary differential equations. The differential equations obtained are resolved by the Keller Box Method (KBM). The impact of the key parameters, the rate of heat transfer and skin friction is evaluated through graphs and tables. The result reveals that an increase in magnetic number decreases the velocity field of both Casson and Carreau fluid also Casson fluid is higher values when compared to Carreau fluid in variation of magnetic number.