Carreau-Yasuda Fluid Research Articles

Numerical modeling of Carreau–Yasuda fluid with induced magnetic field in a heated curved channel having ciliary walls

Cilia motion is commonly located in mammalian cells of living organisms which continually grow and feature conspicuously. The ciliary apparatus is associated with cell cycle movement and proliferation, and cilia play a dynamic part in human and animal growth and everyday life. The motivation of these applications, this article is to present a metachronal wave analysis for non-Newtonian Carreau–Yasuda fluid inside a curved channel with ciliated walls. Hall effect is encountered in the momentum equations to measure the magnetic field while the viscous dissipation and thermal radiation terms are considered to address the energy analysis. The curvilinear coordinates are used due to the curved nature of flow geometry in the derivation of flow equations. The computations for axial velocity, pressure rise, temperature field, mass concentration, and stream function are carried out under low Reynolds number and long wavelength approximation in the wave frame of reference by utilizing appropriate numerical implicit finite difference method (FDM). The implementation of numerical procedure and graphical representation of the computations are accomplished using MATLAB language. Furthermore, the skin friction and Nusselt number at the channel walls are determined for a variety of critical parameter assessments.

A drag and lift passive control study of Carreau–Yasuda fluid in a channel with a cylinder rooted in a transient flow

A drag and lift passive control study of Carreau–Yasuda fluid in a channel with a cylinder rooted in a transient flow

Scrutiny of MHD impact on Carreau Yasuda (CY) fluid flow over a heated wall of the uniform micro-channel

The Carreau-Yasuda model is a useful rheological tool for describing complex fluid flow behavior, especially those involving non-Newtonian fluids. This is significant because it allows for a more accurate depiction of fluids with non-linear connections between shear stress and shear rate. This research aimed to examine the effects of slip on the peristaltic transport of a magnetized Carreau–Yasuda (CY) fluid in a uniform channel where the fluid characteristics change at a heated wall. Non-dimensionalization of the governing equations was achieved by assuming a large wavelength and a low Reynolds number and then solving the resulting coupled equations with appropriate boundary conditions and mathematical "ND Solve" methods. This research looked into the two extremes of shear rate-dependent fluid behavior: shear-thinning (a decrease in viscosity with increasing shear rate) and shear-thickening (an increase in viscosity with increasing shear rate). The model can also predict Newtonian and Carreau fluid behaviors. Critical parameters such as velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number were displayed visually and tabulated in the study's results. In addition, the study used the stream function method to investigate the peristaltic motion of the bolus, uncovering that magnetic effects can decrease bolus size due to their substantial influence on apparent viscosity, with shear-thinning behavior proving more influential than shear-thickening behavior. The study further clarifies the dynamic fluctuations in fluid viscosity in response to increasing shear stress, which sheds light on the viscoelastic nature of shear-dependent behavior in a uniform microchannel using the Carreau–Yasuda fluid.

Numerical and analytical study of heat transfer in the wire coating process using Carreau–Yasuda fluid model

In this article, we present a non-isothermal study of the wire coating process using the Carreau–Yasuda fluid model. Our aim is to explore how the Carreau–Yasuda fluid model parameters are linked to key operational factors in the wire coating process. These factors encompass the radius of the coated wire, the volumetric flow rate, and the force needed to pull the wire. The equations that depict the flow and heat transfer within the die are solved: (a) analytically using the perturbation method to get the analytical expression for velocity, temperature distribution, and relevant engineering quantities; (b) numerically using shooting method with the “Runge–Kutta–Fehlberg algorithm.” The physical effects of the Weissenberg number (We), power law index (n), pressure gradient (A), and Brinkman number (Br) on the velocity profile, temperature distribution, and engineering quantities are discussed with the help of different graphs. Our findings reveal that, in the case of shear thinning (n < 1) with a constant pressure gradient, as compared to the Newtonian scenario, both the thickness of the coated wire and the force required to pull the wire decrease with an increase in the Weissenberg number (We). Moreover, the force required to pull the wire also decreases with an increase in the values of the pressure gradient parameter.

The impact of Carreau-Yasuda nanofluid flow on ciliated walls of the channel

The peristaltic transport of Carreau-Yasuda fluid model over a sinusoidal medium of non-Newtonian nano flow is examined. In this analysis, the channel walls are considered as ciliated with the higher and lower walls. The formulation of the 2D fluid model depends on the nonlinear (PDEs) that are transformed into simple ordinary (ODEs) by applying the dimensionless parameters and long-wavelength approximation. The numerical solution of the 2D system is taken out by applying the MATHEMATICA solver NDSolve function. The impact of various parameters, such as, flow rate parameterF, wave-length number δ, Brownian motion number Nb, thermophoresis number Nt, and account of eccentricity αon the velocity profile, temperature distribution, and concentration distribution and stream function are addressed with graphs.

Effect of Cattaneo-Christov heat and mass flux in Carreau-Yasuda tri-nanofluid

The Cattaneo-Christov heat and mass flux theory extends classic models to provide more accurate predictions in situations with instantaneous heat and mass transfer. Herein, an enhancement of heat and mass transfer in Carreau-Yasuda (CY) tri-nanofluid (TNF) over a stretched surface is modeled and studied via generalized conservation laws subjected to Cattaneo-Christov heat and mass flux theory. Silicon carbide (SiC), Aluminum Oxide (Al2O3), and Silver (Ag) are recruited as active nanoparticles in ethylene glycol (C2H6O2), and hired as CY fluid. Based on Finite Element Method (FEM), the code is created and validated for the formulated problems by comparing the current results to the published benchmarks. The computational findings showed that the thickness of the thermal and diffusion boundary layer decreases by increasing the thermal (δ) and diffusion relaxation (δc) parameters. The numerical analysis showed that CY-TNF exerts the largest shear stress on the wall compared to CY mono nanofluid (NF), and CY hybrid nanofluid (HNF). If CY-TNF has to flow over the specific surface, then adequate surface strength must be ensured. Moreover, comparing enhancement in thermal properties of CY-NF, CY-HNF, and CY-TNF revealed that the CY-TNF performs better than CY-HNF and CY-NF. Owing to the highest heat and mass flux, CY-TNF has an optimized ability to transport heat and mass, thus proving to be an efficient fluid for all processes requiring optimized heat and mass flux.

On non-Newtonian fluid flow generated via complex metachronal waves of cilia with magnetic, hall, and porous effects

Cilia beating influences bio-fluid flow, and conduits with ciliated surfaces serve numerous purposes. Cilia are hair-like adjuncts that produce liquid drive and cell locomotion. This novel research integrates magnetohydrodynamics, Hall effects, and porous medium with the cilia-driven flow. The developed problem is further simplified by utilizing famous assumptions, i.e., low Reynolds number and large wavelength. The bvp5c function in MATLAB (2023a) is adopted to achieve a convergent solution. The graphical illustrations of streamlines, pressure drop, and axial velocity under the influence of pertinent parameters are thoroughly examined. The findings suggest that when a high magnetic field (Hall current) and porous media are combined with the Carreau–Yasuda fluid, the pumping equipment operates better than the viscous liquid. In addition, fluid movement in biological organs is improved by metachronal ciliary motion. Furthermore, it is predicted that this study will make a significant contribution to biomedical engineering in terms of the upgrading and advancement of various types of drug-delivery technologies.

Analysis of blood flow of unsteady Carreau-Yasuda nanofluid with viscous dissipation and chemical reaction under variable magnetic field

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

Integrating effects of Carreau–Yasuda slime on bacterial hydrodynamics

This work deals with gliding motion of bacteria over a non-Newtonian slime layer attached to a solid substrate. The surface of a glider is approximated with a simple wavy two-dimensional sheet while the sticky slime is modeled as Carreau–Yasuda fluid. The classical Navier–Stokes equations are transformed by using Galilean transformation and dimensionless variables. Flow beneath the organism is creeping and the lubrication assumption is also valid in this scenario, hence the equation is reduced to fourth-order BVP in terms of stream function. The basic purpose is to compute the gliding speed and flow rate of the slime which are present in the boundary conditions. MATLAB built-in bvp5c solver is utilized to calculate the numerical solution of the stream function. Further, unknowns (flow rate and cell speed) are refined by using modified Newton–Raphson method (MNRT). Further, these pairs are employed in the formula of energy expended. Velocity and stream function is also plotted for these computed pairs. This study is motivated by scientific interest and the desire to understand the dynamics of gliding bacteria. The findings of this study are thought to be beneficial in the development of artificial crawlers.

Partial Slip Effects on MHD Peristaltic Flow of Carreau-Yasuda Fluid (CY) Through a Planner Micro-Channel

In modern applied mathematics, engineering, and the physiological world, the concept of peristalsis is of great significance. The present article concentrates on the peristaltic movement of Carreau-Yasuda fluid through planner micro-channel under the influence of applied magnetic field and partial slip conditions. The governing system of equations are nondimensionalized and transformed using basic assumptions such as long wavelength and low Reynolds number. A bulti-in route "ND solve" in Mathematica exercised to solve obtained nonlinear coupled equations with appropriate boundary conditions. Obtained results are elucidated by plotting graphs for different physiological constraints such as velocity, temperature, and concentration. Physical characteristics such as skin friction, Nusselt number and Sherwood number are discussed via table results. The typical character of this work e.g. flow index parameter exhibits that the apparent fluid viscosity becomes high when it has a higher value due to which fluid faces more resistance and the presence of a higher magnetic effect predicts the decreasing behavior on velocity. Additionally, the trapping phenomenon explains bolus movement and are discussed briefly.

Significance of skewness and kurtosis on the solute dispersion in pulsatile Carreau–Yasuda fluid flow in a tube with wall absorption

Solute dispersion in Carreau–Yasuda fluid flow in a tube presented in Rana &amp; Murthy (Proc. R. Soc. Lond.A, vol. 472, 2016, p. 20160294) was limited to a steady-state velocity profile due to the nonlinearity associated with the Yasuda parameter$a$with power-law exponent$n$. This limitation is overcome and the velocity profile is obtained for all values of the Yasuda parameter by using the Lagrange inversion theorem, which admits power series solution for the flow field. An analytical solution for the concentration distribution in the circular tube is obtained for the unsteady and pulsatile flow with$n\leq 1$and$\alpha &lt;&lt;1$and the numerical solution is presented for all values of$\alpha$and$n$. The solute dispersion is analysed analytically using the Sankarasubramanian–Gill generalized dispersion method and also using the Aris–Barton method of moments considering up to fourth-order moments. The solute dispersion is also simulated numerically by using a new class of computationally explicit Runge–Kutta method. The axial mean concentration of the solute is estimated by the exchange, convective and dispersion coefficients. The third- and fourth-order moments give rise to skewness and kurtosis revealing the deviation from the Gaussianity and reduction in the peak of the mean concentration profile at a small time of the solute injection. All time variations of these five moments against flow governing parameters are thoroughly investigated. The flow and dispersion regimes that are derived here for moments provide a good understanding of the solute dispersion in the tube. The increase in the Womersley frequency parameter led to a phase lag at each period. This work is the initiation of estimating the skewness and kurtosis in a non-yield stress fluid flow in a tube.

Magnetohydrodynamic flow of Carreau Yasuda fluid inside a complex wavy passage formed by beating cilia: A finite-difference analysis

Inspired by the prevalence of non-Newtonian liquids in biological flows, our aim in this article is to elaborate on the flow of Carreau-Yasuda fluid generated by wavy cilia inside the micro-channel. The impact of complex wave and magnetic field (magnetohydrodynamics) are also taken into account. The low Reynolds number and large wavelength approximation are employed to simplify the problem. The finite-difference approach (finite-difference method) is utilized to get the convergent solution to the problem in MATLAB (2022b). The impact of emerging parameters on the axial velocity and streamlines is examined through various graphs. Moreover, a comparison among the Carreau-Yasuda fluid, Carreau fluid, and Newtonian fluid is also expounded.

Energy transfer in Carreau Yasuda liquid influenced by engine oil with Magnetic dipole using tri-hybrid nanoparticles

The aim of the current analysis is to evaluate the significances of magnetic dipole and heat transmission through ternary hybrid Carreau Yasuda nanoliquid flow across a vertical stretching sheet. The ternary compositions of Al2O3, SiO2, and TiO2 nanoparticles (nps) in the Carreau Yasuda fluid are used to prepare the ternary hybrid nanofluid (Thnf). The heat transfer and velocity are observed in context of heat source/sink and Darcy Forchhemier effect. Mathematically, the flow scenario has been expressed in form of the nonlinear system of PDEs for fluid velocity and energy propagation. The obtained set of PDEs are transform into ODEs through suitable replacements. The obtained dimensionless equations are computationally solved with the help of the parametric continuation method. It has been observed that the accumulation of Al2O3, SiO2 and TiO2-nps to the engine oil, improves the energy and momentum profiles. Furthermore, as compared to nanofluid and hybrid nanofluid, ternary hybrid nanofluid have a greater tendency to boost the thermal energy transfer. The fluid velocity lowers with the outcome of the ferrohydrodynamic interaction term, while enhances with the inclusion of nano particulates (Al2O3, SiO2 and TiO2).

Energy transmission through carreau yasuda fluid influenced by ethylene glycol with activation energy and ternary hybrid nanocomposites by using a mathematical model

The current study aims to assess the augmentation of energy transmission in the presence of magnetic dipole through trihybrid Carreau Yasuda nanofluid flow across a vertical sheet. The rheological properties and thermal conductivity of the based fluids are improved by framing an accurate combination of nanoparticles (NPs). The trihybrid nanofluid (Thnf) has been synthesized by the addition of ternary nanocomposites (MWCNTs, Zn, Cu) to the ethylene glycol. The energy and velocity conveyance has been observed in the context of the Darcy Forchhemier effect, chemical reaction, heat source/sink, and activation energy. The trihybrid nanofluid flow across a vertical sheet has been accurately calculated for velocity, concentration, and thermal energy in the form of a system of nonlinear PDEs. The set of PDEs is reduced to dimensionless ODEs by using suitable similarity replacements. The obtained set of non-dimensional differential equations is numerically computed through the Matlab package bvp4c. It has been perceived that the energy curve enhances by the influence of heat generation factor and viscous dissipation. It is also noted that the magnetic dipole has a momentous contribution to raising the transmission of thermal energy of trihybrid nanofluid and declines the velocity curve. The inclusion of multi-wall carbon nanotubes (MWCNTs), zinc (Zn), and copper (Cu) nano particulates to the base fluid “ethylene glycol”, augments the energy and velocity outlines.

Exploring the Impact of Nanomaterials on Heat- and Mass-Transfer Properties of Carreau-Yasuda Fluid with Gyrotactic Bioconvection Peristaltic Phenomena

This research aims to investigate the impact of nanomaterials on the heat and mass transfer properties of fluids, with a particular focus on exploring the bioconvection phenomena. To achieve this, the study considers Carreau-Yasuda (CY) fluid, which is known for its shear thickening and thinning nature. The effects of a porous medium, radiation, and viscous dissipation are also considered to analyze heat-transfer rates. Velocity and thermal slip constraints are applied to the wall, while zero-mass flux conditions explain the concentration behavior of nanomaterials at the wall. The governing equations and conditions are simplified using a lubrication approach, and a numerical approach is used to solve the final equations with the help of constraints. The velocity, temperature, and concentration of nanomaterials and gyrotactic microorganisms are analyzed through graphs. The study finds that increasing the thermophoresis parameter leads to an increase in the concentration of nanomaterials. However, the opposite trend is noticed for the concentration of motile microorganisms. The results suggest that the addition of nanomaterials to fluids can significantly impact heat- and mass-transfer properties, and may have implications for biological processes.

Transient heat transfer and electro-osmotic flow of Carreau–Yasuda non-Newtonian fluid through a rectangular microchannel

PurposeThe purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states.Design/methodology/approachThe Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC).FindingsThe impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < r < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy.Originality/valueThis study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

Potential impacts of Cattaneo–Christov model of heat flux on the flow of Carreau–Yasuda fluid with mixed convection over a vertical stationary flat plate

Heat transfer in Carreau–Yasuda fluid with mixed convection, effect of Cattaneo–Christov model of heat flux past a vertical flat plate has been studied in this paper. Using appropriate transformations, governing PDEs are reduced to higher order non-linear non-dimensional ODEs and subsequently these are solved using “bvp4c” package of MATLAB. The Carreau–Yasuda fluid is used to explore the behaviour of fluids having shear-thinning and shear-thickening characters for several values of the parameter called power law exponent involved in the fluid model. The effects of different physical parameters, such as Weissenberg number(We), thermal relaxation parameter(α), Carreau–Yasuda fluid parameter(d), mixed convection parameter(λ) and Prandtl number(Pr) on velocity and temperature has been investigated and depicted through graphs. Results reveals that for lower value of Pr velocity of fluid enhances with higher value of λ and reverse effect is witnessed for larger Pr. Also, velocity rises for shear-thinning fluid(STNF) and decreases for shear-thickening fluid(STKF) with We and d. Temperature exhibits growing behaviour for Cattaneo–Christov model of heat flux near the plate in comparison with Fourier's model, whereas velocity exhibits growing behaviour with α. For larger We, temperature in Carreau–Yasuda model upsurges for STKF and falls for STNF. The surface drag-force displays higher values for both STNF and STKF with growth in λ. The cooling rate rises/declines with We for STNFs/STKFs.

Inertial lift on a particle in a straight microchannel of Newtonian, power-law and Carreau-Yasuda fluids: A simulation study toward optimized particle separation

Inertial lift on a particle in a straight microchannel of Newtonian, power-law and Carreau-Yasuda fluids: A simulation study toward optimized particle separation

Carreau–Yasuda fluid flow generated via metachronal waves of cilia in a micro-channel

The accretion of excessive bio-fluid in human tissues is triggered due to several reasons, such as pregnancy, local injuries, and allergic reactions or by using certain therapeutic drugs. Motivated by such numerous biomedical applications, this article aims to elaborate on the shear-dependent peristaltic flow of Carreau–Yasuda fluid inside the micro-channel by incorporating the ciliary walls. The long wavelength and the low Reynold's number approximation simplify the problem. Furthermore, the MATLAB-based algorithm known as the bvp5c is adopted for the problem's numerical solution. The impact of emerging parameters on the velocity, pressure gradient, and streamlines is examined through various graphs. The results reveal that while using Carreau–Yasuda fluid, the pumping apparatus performs better than Newtonian or Carreau fluid. The findings could aid our understanding of biofluid movement in the human body. Furthermore, it is believed that this solution has an important contribution in the biomedical industry for the advancement and improvement of several kinds of drug delivery devices.

Analytical Procedure for the Flow of a Carreau-Yasuda Fluid Through the Diseased Tapered Inclined Artery Subject to Heat Transfer and Chemical Reactions

This paper demonstrates the implications of heat transfer and chemical reactions by considering the flow of a Carreau-Yasuda fluid through the diseased tapered inclined artery. The analysis has performed on the artery with mild stenosis. The analytical solution has been obtained using the perturbation method due to its low Weissenberg number to get the blood velocity, the wall shear stress distribution, the temperature, the concentration, the resistance impedance and the stream function. The critical results in this study have depicted that the blood velocity for dilatant fluid is higher than that in viscous and pseudoplastic fluids in the core region of the artery. The value of blood velocity through a Newtonian fluid is extraordinarily lower than that through a Carreau-Yasuda fluid at the core region of the artery. The magnitude of blood velocity across the vertical artery is higher than those in the inclined and horizontal arteries inside the core region of the artery. The wall shear stress distributions are higher in the case of stenosis (diseased artery) than in no stenosis (healthy artery). The temperature transmission for the Carreau fluid is higher than that for the Carreau-Yasuda fluid. The flow resistance progressively increases as the depth of the stenosis increases. The size of the trapping bolus gradually increases, shifting toward the right at the diverging tapering artery, and it gradually increases, moving toward the left at the converging tapering artery. Finally, the streamlines are noticeably more comprehensive along the vertical artery and are higher than those in the inclined and horizontal arteries.