Carreau-Yasuda Fluid Research Articles

Entropy-optimized dissipative flow of Carreau–Yasuda fluid with radiative heat flux and chemical reaction

The main propose of this research communication is to explore the collective influence of Ohmic heating, radiative heat flux, and viscous dissipation on the entropy-optimized reactive flow of non-Newtonian fluid toward a stretched surface. The fluid flow is electrically conducted in the presence of applied magnetic field and generated by stretching phenomenon. The effects of heat generation/absorption, radiative heat flux, dissipation, and Ohmic heating are utilized in the mathematical modeling of energy expression. Furthermore, the chemical reaction is considered. The total entropy rate of the Carreau–Yasuda fluid is discussed versus four irreversibilities, i.e., heat transfer irreversibility, fluid friction irreversibility, magnetic or Ohmic heating irreversibility, and chemical reaction irreversibility and is calculated through implementation of the second law of thermodynamics. Series solutions are calculated for the desired flow expressions via homotopy analysis method. Behaviors of sundry flow parameters on the velocity, temperature, concentration, entropy rate, and Bejan number are physically discussed and the results are plotted graphically. The skin friction coefficient (drag force) and Nusselt number (heat transfer rate) are calculated numerically and discussed with the help of magnetic parameter, Weissenberg number, Prandtl number, radiation parameter and Eckert number. The obtained results reveal that entropy enhances for higher values of radiation parameter and Brinkman number.

A comprehensive finite element examination of Carreau Yasuda fluid model in a lid driven cavity and channel with obstacle by way of kinetic energy and drag and lift coefficient measurements

In current pagination the flow problems involving shear rate dependent nonlinear viscosity have been treated successfully in the sense of space discretization and solvers. The stable finite element pair Q2/P1disc is employed to approximate the velocity and pressure spaces independently. Discretized form of non-linear expressions is linearized by implementing Newton’s procedure and the resulting systems are solved using a geometric multigrid approach. The flow generated by way of driven cavity and by an obstacle are very important benchmarks of computational fluid dynamics. In current pagination shear rate reliant viscosity model renowned as Carreau Yasuda fluid is capitalized. The obtained results are demonstrated and analyzed with the help of velocity and viscosity plots. In addition, we have produced new reference data for kinetic energy (K.E) for driven cavity problem and drag and lift coefficients for circular obstacle problem. The obtained results for driven cavity problem reveal the fact that K.E is an increasing function of the relaxation parameter (λ) and power law exponent (n) whereas a decreasing function of the model parameter (a). For the case of flow around obstacle the drag coefficient (CD) and the lift coefficient (CL) show strong dependence on (λ) and (n), however a weak dependence on the parameter (a).

Theoretical and numerical investigation of Carreau–Yasuda fluid flow subject to Soret and Dufour effects

BackgroundNewtonian fluids can be categorized by a single coefficient of viscosity for specific temperature. This viscosity will change with temperature; it doesn’t change with strain rate. Just a small group of liquids show such steady consistency. A fluid whose viscosity changes subject to relative flow velocity is called non-Newtonian liquids. Here we have summarized a result for the flow of Carreau–Yasuda fluid over a porous stretchable surface. Mixed convection is considered. Modeling of energy expression is performed subject to Soret and Dufour effects. MethodThe nonlinear PDE’s are changed to ODE’s through suitable transformations and then solved for numerical solutions via Built-in shooting method (bvp4c). ResultsVariation of important variables is studied on the concentration, temperature and velocity fields. Tabular representation for study of skin friction and heat transfer rate is presented for important variables. Our results show that velocity decreases versus higher estimations of Weissenberg number, porosity parameter, buoyancy ratio and mixed convection parameter. Temperature decays via Weissenberg number and porosity parameter. Increase in concentration is noticed through higher Soret number and porosity parameter. Skin friction and heat transfer rate (Nusselt number) boosts versus larger porosity parameter and Prandtl number respectively while it decays against Weissenberg number and Dufour and Eckert number.

Activation energy for the Carreau-Yasuda nanomaterial flow: Analysis of the entropy generation over a porous medium

Here incompressible flow of non-Newtonian fluid (Carreau-Yasuda fluid) is addressed over a stretchable sheet. Porous medium is considered. Chemical reaction is accounted at the surface of sheet with activation energy. Furthermore, thermophoresis, viscous dissipation and Brownian motion effects are considered for mathematical modeling of energy expression. Through implementation of second law of thermodynamics the total entropy rate is obtained. Suitable similarity variables are used to change the nonlinear governing expressions into ordinary ones. Convergence series solutions are developed for velocity, temperature and concentration equations through homotopy analysis method. Flow variables are graphically discussed. Skin friction (surface drag force) and heat transfer rate (Nusselt number) are numerically discussed through various flow variables. Key observations are listed in the conclusions section. Velocity of liquid particles boosts up versus higher values of Weissenberg number. Temperature field in more via higher Brownian and thermophoresis variables.

Influence of Heat Transfer on Magnetohydrodynamics Oscillatory Flow for Carreau-Yasuda Fluid Through a Porous Medium

This paper, we have examined the influence of transfer the heat on the magnetohydrodynamics (MHD) oscillatory flow of Carreau-Yasuda fluid through porous medium for two types of geometries "Poiseuille flow and Couette flow". We have solved the problem by using the perturbation technique in terms of the Weissenberg number (We), discussed and analyzed the numerical and arithmetical results of the effect of several parameters, namely The number of Darcy, the number of Reynold, the number of Peclet, the parameter of magnetic, the number of Grashof, the number of Weissenberg, frequency of the oscillation and radiation parameter for the velocity and temperature that are effective on the fluid movement by using MATHEMATICA program using illustrations.

A general analytical approach to study solute dispersion in non-Newtonian fluid flow

Abstract The homotopy analysis method (HAM), a general analytic technique for non-linear problems, is applied to analyze the solute dispersion process in non-Newtonian Carreau-Yasuda and Carreau fluids flow in a straight tube with the effect of wall absorption/reaction. Unlike the other analytical methods such as perturbation method, the HAM provides a simple way to get the convergent series solution. Any assumptions of small or high physical quantities are not required for the HAM. It provides us a great freedom to choose the so-called convergence control parameter which is used to guarantee the convergence of series solution. The convergent series solution is obtained by choosing the optimal value of convergence control parameter for which the series converges fastest. The optimal value of convergence control parameter is obtained by minimizing the square residual which also provides the convergence region for the series solution. The previous analytical studies on solute dispersion fail to justify the convergence of the series solution, whereas in this investigation, our results are convergent and valid for all physical parameters. In addition, present results are validated by the numerical and some existing results. This study explains elaborately about the advantage of the homotopy analysis method over perturbation and eigenfunction expansion methods for nonlinear problems. Owing to the great potential and flexibility of the homotopy analysis method, it is a more suitable analytical approach to solve the different types of non-linear problems in science and engineering. Besides, this study helps to gain some knowledge on the transportation process of drugs in the blood flow.

Impact of enhancing diffusion on Carreau–Yasuda fluid flow over a rotating disk with slip conditions

The present study is devoted to acquire non-similar solutions for the behavior of slip conditions on the steady MHD Carreau–Yasuda fluid flow over a rotating disk. In order to examine the heat transfer phenomena, superior form of Fourier’s law is used and the conductivity of the fluid is assumed to be changeable. The nonlinear partial differential equations leading the flow and thermal field are written in the non-dimensional ordinary differential form by using suitable transformations. The non-dimensional set of coupled ordinary differential equations is solved using the RK method. The impact of various non-dimensional physical parameters on velocity and temperature fields is explored. The numerical results of resistant force in terms of the skin friction coefficient are revealed graphically for various physical parameters involved in the problem.

Three-dimensional Lattice Boltzmann simulation on thermosolutal convection and entropy generation of Carreau-Yasuda fluids

In this paper, three-dimensional thermosolutal natural convection and entropy generation in a cubic cavity filled with a non-Newtonian Carreau-Yasuda fluid has been simulated by Lattice Boltzmann Method (LBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 104 and 105), the Buoyancy ratio (N = −1, 0.1, 1), the Lewis number (Le = 0.5, 2.5, 10, 100, and 1000), power-law indexes (n = 0.5, 1, and 1.5), Carreau number (Cu = 0.01, 0.1, 1, 10 and 100), and Carreau-Yasuda parameter (m = 0.1, 0.5, and 1). Results indicate that the rise of Rayleigh number enhances heat and mass transfer for various studied parameters. The increase in power-law index provokes heat and mass transfer to drop gradually. However, the effect of power-law index on heat and mass transfer rises steadily as Rayleigh number rises. The enhancement of Carreau number decreases heat and mass transfer, but; the increases in the Carreau-Yasuda parameter augments heat and mass transfer significantly. The augmentation of the buoyancy ratio number enhances heat and mass transfer. It was found that mass transfer increases as Lewis number augments. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the power-law index provokes various irreversibilities to drop significantly. The enhancement of the buoyancy ratio causes the summation entropy generations to increase considerably. The rise of Carreau number and Carreau-Yasuda parameter decreases and increases the total irreversibilities; respectively.

Mixed convective peristaltic flow of Carreau–Yasuda fluid in an inclined symmetric channel

This investigation has been accomplished to study the mixed convective peristaltic transport of Carreau–Yasuda fluid through in an inclined channel. Magnetic field is also taken into account. Combined effects of heat and mass transfer are characterized in presence of heat generation and Soret effect. Effect of chemical reaction is observed. Analysis is presented when slip effects are considered. Large wavelength and small Reynolds number approximation are utilized. Numerical results for velocity, temperature, concentration and heat transfer rate are computed and analyzed.

Heat transfer analysis for peristaltic flow of Carreau-Yasuda fluid through a curved channel with radial magnetic field

Peristalsis of fluids through curved geometries is widely encountered in several industrial and domestic pumping devices. Keeping this fact in mind, effects of variable magnetic field on peristalsis of Carreau-Yasuda (C-Y) fluid through a curved channel with velocity and thermal slip boundary conditions are studied. Heat transfer analysis has been carried out by considering the Joule heating and viscous dissipation effects. The long wavelength and small Reynolds number assumptions are adopted in mathematical modeling of the problem. Resulting non-linear system of differential equations has been solved numerically. Graphical results for axial velocity, temperature, heat transfer rate and stresses at the walls for the different flow parameters are discussed. It is reported that the radially varying magnetic field decreases velocity and increases the temperature of the fluid. Such magnetic field also enhances the heat transfer rate and stresses at the boundaries.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau–Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Analytical solutions for the free-draining flow of a Carreau-Yasuda fluid on a vertical plate

Free-draining flow is observed in many practical and industrial situations. It is considered as a stage of a batch dip-coating process, where the draining of the fluid will form a liquid film over a substrate by gravity. The objective of this work was to develop a mathematical model and to obtain analytical solutions for the fluid-dynamic variables of a free-draining flow during a dip-coating draining stage of a finite vertical plate using a fluid whose rheological behavior is described by the Carreau-Yasuda model. Mathematical expressions have been obtained assuming a monophasic, isothermal, and nonevaporative system, where the most important forces are viscous and gravitational. The studied phenomena occurred far away from the meniscus formed at the surface of the fluid reservoir. The main operative variables that were estimated are velocity profile, flow rate, local thickness, and average thickness of the film. A validation was performed by using experimental data of average film thickness values of several representative food-grade fluids with coating capacity (emulsions and suspensions) obtained from the literature. The information published in this work will be useful for researchers and technicians to control and predict film characteristics (thickness and uniformity) and operational variables (velocity and flow rate) during laboratory and industrial coating processes where free-draining flow takes place.

Numerical simulation for peristalsis of Carreau-Yasuda nanofluid in curved channel with mixed convection and porous space.

Main theme of present investigation is to model and analyze the peristaltic activity of Carraeu-Yasuda nanofluid saturating porous space in a curved channel. Unlike the traditional approach, the porous medium effects are characterized by employing modified Darcy’s law for Carreau-Yasuda fluid. To our knowledge this is first attempt in this direction for Carreau-Yasuda fluid. Heat and mass transfer are further considered. Simultaneous effects of heat and mass transfer are examined in presence of mixed convection, viscous dissipation and thermal radiation. The compliant characteristics for channel walls are taken into account. The resulting complex mathematical system has been discussed for small Reynolds number and large wavelength concepts. Numerical approximation to solutions are thus plotted in graphs and the physical description is presented. It is concluded that larger porosity in a medium cause an enhancement in fluid velocity and reduction in concentration.

Hydrodynamics of Newtonian and power-law fluids in microchannel with superhydrophobic wall

The flow peculiarities of the Newtonian and Carreau-Yasuda power-law fluids in a microchannel with the striped superhydrophobic wall is studied numerically. The driving forces leading to deviation of streamlines from the channel axis are analyzed.

Unsteady solute dispersion in Herschel-Bulkley fluid in a tube with wall absorption

The axial dispersion of solute in a pulsatile flow of Herschel-Bulkley fluid through a straight circular tube is investigated considering absorption/reaction at the tube wall. The solute dispersion process is described by adopting the generalized dispersion model suggested by Sankarasubramanian and Gill [“Unsteady convective diffusion with interphase mass transfer,” Proc. R. Soc. A 333, 115–132 (1973)]. Firstly the exchange, convection, and dispersion coefficients are determined for small and large time, and then the axial mean concentration of a solute in the tube is determined. The effect of power-law index l, yield stress of fluid τy, wall absorption parameter β, amplitude of fluctuating pressure component e, and Womersley frequency parameter α on the convection, dispersion, and mean concentration of solute is discussed for a Herschel-Bulkley fluid in the tube. The single frequency period in the oscillation of dispersion coefficient K2 is observed for small values of α while the double frequency period is noticed for large values of α at small time. Only positive dispersion occurs for small values of α. Both positive and negative dispersion is seen for large values of α. Also, the occurrence of negative dispersion is influenced by the parameters l, τy, β, and e for large values of α. A comparative study of the convection, dispersion, and mean concentration of solute among the Newtonian and non-Newtonian Herschel-Bulkley, power-law, Bingham, and Casson [J. Rana and P. V. S. N. Murthy, “Solute dispersion in pulsatile casson fluid flow in a tube with wall absorption,” J. Fluid Mech. 793, 877–914 (2016)] fluid models is presented at small and large time. Also, large time behaviour of non-Newtonian Carreau and Carreau-Yasuda fluid models [J. Rana and P. V. S. N. Murthy, “Unsteady solute dispersion in non-Newtonian fluid flow in a tube with wall absorption,” Proc. R. Soc. A 472, 20160294 (2016)] is considered for comparison with other discussed fluid models. It is noticed that these fluid models exhibit significant differences during the solute dispersion in the presence of wall absorption. These models are applied to study the dispersion process of a solute in blood flow. For a Herschel-Bulkley fluid, the critical value of α at which fluctuations of K2 attain negative magnitude increases as l increases. The critical value of α for a Herschel-Bulkley fluid (l = 0.9 with τy = 0.05) is 2.9 but it is equal to 3 for a Casson fluid (τy = 0.05) [J. Rana and P. V. S. N. Murthy, “Solute dispersion in pulsatile casson fluid flow in a tube with wall absorption,” J. Fluid Mech. 793, 877–914 (2016)] with non-zero β. It is noticed that the amplitude of fluctuations of both negative convection coefficient −K1 and dispersion coefficient K2 for a Casson fluid is lying below that of Herschel-Bulkley fluid at all times. Therefore, the peak of mean concentration Cm for the Casson model is higher than that of the Herschel-Bulkley model. The present study may be useful to know the transportation process of drugs in blood flow through the blood vessels.

MHD squeezed flow of Carreau-Yasuda fluid over a sensor surface

An attempt has been made to examine the two dimensional free stream squeezed flow through a horizontal sensor surface of an electrically conducting Carreau-Yasuda fluid subject to transverse magnetic field. The governing nonlinear partial differential equations are modeled and then simplified with the aid of suitable similarity transformations. Well known numerical scheme Runge–Kutta–Fehlberg method is utilized to solve the system. Concrete graphical analysis is carried out to investigate the behavior of different pertinent parameters on velocity profile with inclusive discussion. Numerical influence of friction factor is also discussed.

Numerical simulation and experimental validation of liquid‐film‐flow characteristics in dip coating for non‐Newtonian fluids

The film‐flow problem in dip coating is simulated numerically for non‐Newtonian fluids based on Carreau–Yasuda (CY) and Herschel–Bulkley (HB) constitutive equations, with particular focus on coating‐film‐thickening phenomena and on the evolution of free surface and flow field under different sets of conditions. Finite element method (FEM) is combined with remeshing technique using a commercial code (Polyflow). Numerical predictions of the final film thickness and free surface for HB and CY fluids are successfully compared with experiments under the given conditions. Results show that the combination of FEM‐remeshing technique could be useful for dip‐coating design and optimization. Effects of coating fluid properties and withdrawal speed on film thickening and free surface shape and location are also discussed. Flow fields under different conditions are presented to analyze the evolution of the entire flow field and flow characteristics in detail. POLYM. ENG. SCI. 56:1070–1078, 2016. © 2016 Society of Plastics Engineers

Hall and radial magnetic field effects on radiative peristaltic flow of Carreau–Yasuda fluid in a channel with convective heat and mass transfer

The purpose of present investigation is to study the Hall and MHD effects on peristaltic flow of Carreau–Yasuda fluid in a convectively curved configuration. Thermal radiation, Soret and Dufour effects are also accounted. The channel walls comprised the no slip and compliant properties. Constitutive equations for mass, momentum, energy and concentration are first modeled in view of considered assumptions and then simplified under long wavelength and low Reynolds number approximation. Solution of the resulting system of equations is carried out via a regular perturbation technique. Physical behaviors of velocity, temperature, concentration and streamlines are discussed with the help of graphical representation.

Mixed convective peristaltic flow of Carreau–Yasuda fluid with thermal deposition and chemical reaction

The presented article addresses the mixed convective peristaltic flow of Carreau–Yasuda fluid bounded in a compliant wall channel. The thermal deposition and chemical reaction effects are employed simultaneously in the flow analysis. Governing equation comprised the viscous dissipation and thermal radiation effects. Heat and mass transfer have been studied under large wavelength and small Reynolds number. The resulting nonlinear systems are solved numerically. The graphical illustrations show increasing impact of temperature through mixed convection and decreasing behavior of concentration with thermal deposition and constructive chemical reaction.

Simultaneous effects of radial magnetic field and wall properties on peristaltic flow of Carreau-Yasuda fluid in curved flow configuration

The objective of present article is to address the magnetohydrodynamic (MHD) peristaltic flow of Carreau-Yasuda fluid in a curved geometry. The channel boundaries satisfy wall slip and compliant properties. The fluid is electrically conducting through an applied magnetic field in the radial direction. Heat transfer is also studied. Governing equation comprised the viscous dissipation effects. The non-linear expressions are first obtained and then approximated using long wavelength and low Reynolds number considerations. The resulting systems are solved for the series solutions. The expressions of velocity, temperature, heat transfer coefficient and stream function are obtained and analyzed via graphical illustrations.