Carreau-Yasuda Nanofluid Research Articles

Three dimensional heat transfer in the Carreau-Yasuda hybrid nanofluid with Hall and ion slip effects

For enhancement of heat and mass transfer, the use of hybrid nano-particles in shear rate-dependent viscous fluid is of great significance given applications. In this study, we have considered the impacts of Hall and ion-slip currents on the three-dimensional (3D) flow of shear rate-dependent viscous fluid. The shear rate-dependent rheology is characterized by the Carreau-Yasuda model. Ethylene glycol is found in plasma and rheological characteristics are best described by the power-law constitutive model which is a special case of the Carreau-Yasuda rheological model, Therefore, the most generalized model is considered to examine the rheological characteristics. Further, Al 2 O 3 − ethylene glycol and TiC − Al 2 O 3 − ethylene glycol are termed as Carreau-Yasuda nanofluid and Carreau-Yasuda hybrid nanofluids respectively. Specifically, here in the considered problem, Titanium carbide and aluminum oxide (TiC and Al 2 O 3) hybrid nano-particles which are source materials for MXenes, are dispersed in the Ethylene glycol (C 2 H 6 O 2) as a base fluid. The finite element method (FEM) is implemented to find the numerical solution of the boundary value problems. The thermal performance of both types of fluids is analyzed under the influence of related parameters. The thermal performance of both types of fluids is compared. Hall and ion-slip currents are induced to the ion and electron collisions and cause Hall and ion-slip forces which have the opposite direction to the magnetic force induced due to the magnetic field interaction. Thus Hall and ion-slip forces are favorable forces and result in to increase in momentum boundary layer thickness (MBLT). It is also discovered that the Hall and ion-slip forces in TiC − Al 2 O 3 − ethylene glycol flow are greater than those in Al 2 O 3 − ethylene glycol flow. Furthermore, Hall and ion-slip currents play an important role in decreasing Ohmic dissipation, which has a negative impact on the thermal performance of the working fluid. The role of generative chemical reaction on the transport of mass is opposite to the role of the destructive chemical reaction. Joule heating (Ohmic dissipation) directly affects the temperature of fluid particles and their kinetic energy increases and hence thermal boundary layer thickness (TBLT) becomes wider. Thus Ohmic dissipation has adverse effects on thermal performance. Thus fluids with no dissipation behave better as coolants.

Numerical analysis of dual variable of conductivity in bioconvection flow of Carreau–Yasuda nanofluid containing gyrotactic motile microorganisms over a porous medium

The increasing need of the modern era of technology for better ways to increase the heat transfer performance of thermal systems has made nanoliquids much more critical than they have been for the previous two decades. With such demand in mind, the Carreau-Yasuda nanofluid in the presence of motile microorganisms and thermal radiation along with Robin’s boundary conditions has been scrutinized. The controlling PDEs are cracked into ordinary differentials through suitable similarity transformation. The transformed ODEs are solved numerically utilizing bvp4c built-in MATLAB computational software. The graphical results of the main parameters against the velocity profile, temperature profile, and solutal field of nanoparticles and motile microorganisms' concentration are illustrated through graphs. Furthermore, the consequence of the involved parameters on the heat transfer rate is also deliberated and offered through table values. This study analyzed that velocity is a declining function of magnetic parameter and buoyancy ratio parameter. Besides, the additional amount of thermal radiation improves the heat transport rate. The concentration field is an escalating function of the thermophoresis parameter. Furthermore, microorganisms’ profile is boosted up by enlarging the magnitudes of microorganism’s Biot number.

Analyzing the impact of induced magnetic flux and Fourier\u2019s and Fick\u2019s theories on the Carreau-Yasuda nanofluid flow

The current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

A Combined Convection Carreau–Yasuda Nanofluid Model over a Convective Heated Surface near a Stagnation Point: A Numerical Study

The focus of this manuscript is on two-dimensional mixed convection non-Newtonian nanofluid flow near stagnation point over a stretched surface with convectively heated boundary conditions. The modeled equation representing nonlinear flow is transformed into a system of ordinary differential equations by implementing appropriate similarity transformations. The generated structure is numerically solved by applying the bvp4c method. Consequences of various involved parameters, e.g., stretching parameter, mixed convection parameter, thermophoresis parameter, Brownian movement parameter, Lewis number, Weissenberg number, Prandtl number, Biot number, buoyancy ratio parameter, mass and heat transport rates on temperature and velocity, the stretched surface, and nanoparticle concentration patterns are analyzed. Outcomes are shown graphically and displayed in tables. Velocity fluctuations are responded to by growing parameters of mixed convection and Weissenberg number. Concentration and thermal fields are also discovered for the Prandtl number. There are also flow line diagrams to analyze the behavior.

Peristaltic Carreau-Yasuda nanofluid flow and mixed heat transfer analysis in an asymmetric vertical and tapered wavy wall channel

In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

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

The present comments are presented to increase the awareness among the readers of Journal of Molecular Liquids. Comments are presented in particular on the paper by Ijaz Khan et al. (2020), where the authors utilized the expression of entropy generation to analyze the Carreau-Yasuda nanofluid flow past a porous medium. The present comments show that the volumetric entropy generation (SG) equation is incorrect in the above paper. Also, the Bejan number (Be) equation is corrected.

Zero mass flux and convection boundary condition effects on Carreau-Yasuda fluid flow over a heated plat

A mathematical study is analyzed to explore the impact of zero normal flux condition on boundary layer flow of Carreau-Yasuda nanofluid flow over a heated surface. In this case the mean flow does not give the analytical solution of the Navier-Stocks, temperature, and concentration equations, hence for high Reynold's number the flow of boundary-layer can be determined by non-similarity transformations. The converted boundary-layer equations along with appropriate boundary conditions are then solved numerically. The solution of the modelled differential equations is calculated by utilizing moderate and well-known numerical technique namely BVP4C method. Carreau-Yasuda fluid model is employed to explore the characteristics of shear thinning and thickening fluids. It is generalized form of Carreau-Yasuda fluid which is applicable for having small and infinite shear rates.

Heat transportation in peristalsis of Carreau-Yasuda nanofluid through a curved geometry with radial magnetic field

The present investigation explores the behavior of peristaltic movement of Carreau-Yasuda nanomaterial in curved channel under the influence of radically changing magnetic field. The slip, Joule heating, Brownian motion, thermophoresis, thermal radiation and viscous heating effects are also be accounted. Heat transfer analysis is carried out to understand the energy transfer process. Problem is formulated by using the assumptions of small Reynolds number and long wavelength. Resulting non-linear coupled equations are solved numerically by using built in NDSOLVE in Mathematica. Physical analysis of different flow parameters is carried out through the aid of graphs. Further, it is observed that the Brownian diffusion Nb and thermophoresis Nt effects intensify the heat transfer rate. The opposing results of Brownian diffusion and thermophoresis are noticed for concentration and temperature. Also, results of the straight channel can be obtained by setting k → ∞.

On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip

Several non-Newtonian fluids are of practical interest, and it is fascinating to examine the rheology of such fluids with various flow features. In this study, the flow of Carreau–Yasuda nanofluid has been analyzed in the presence of gyrotactic microorganisms. The impressive features of nanofluid are displayed by abiding the thermophoresis and Brownian motion aspects. The second-order velocity slip effects are decomposed in the mathematical simulations. Further, the governing flow problem governed the impact of thermal radiation, chemical reaction and convective Nield boundary conditions. Although some attempts are available in the literature which examines the rheological features of Carreau–Yasuda nanofluid, whereas the analysis for bioconvection of flow of this non-Newtonian fluid model in the presence of second-order slip features is not proposed yet. Further, it has been noticed that many investigators used first-order or partial slip effects associated with their flow problems. The flow problem becomes more realistic due to the interaction of second-order slip constrains and subsequently develops a more stable boundary layer. The governing equations for the formulated flow problem are partial differential equations. Standard dimensionless quantities are recommended to alter the flow equations in dimensionless forms. The solution of the locally similar problem has been computed numerically via shooting technique. All the computations are performed by using bvp4c with the help of MATLAB software. Following the iterative procedure, the solution is accurate up to convincing accuracy of $$ 10^{ - 4} . $$ The step size for the present simulation is taken as $$ \Delta \eta = 1 \times 10^{ - 4} . $$ The results are also verified by comparing with already reported numerical computation and found a convincible accuracy. The implication of each parameter is executed for velocity, temperature, concentration and microorganisms’ distributions. Moreover, the substantial quantities, namely skin friction coefficient, motile density number, local Nusselt number, and local Sherwood number numerically evaluated and are overviewed for various parameters. The study reveals that velocity distribution decays with the presence of first-order slip parameter and Rayleigh number, while an enhanced velocity profile has been noted for variation of Weissenberg number. An improved nanoparticle temperature and concentration distributions have been found with the utilization of the second-order slip factor and combine parameter. It is further observed that the density of motile microorganisms declined with Peclet number and bioconvection Lewis number. In recent days, a growing interest has been developed from scientists toward the significance of nanoparticles because of their diverse engineering, industrial and commercial applications. The proposed observations can be useful in extrusion systems applications, biomolecules, biomimetic systems, energy production improvement and enhancement of manufacturing processes.

Temperature-dependent viscosity and thermal conductivity effects on peristaltic flow of Carreau–Yasuda nanofluid in a 2D tapered asymmetric channel: applications of solar collectors

This paper aims to investigate the influences of variable viscosity and thermal conductivity on peristaltic flow of Carreau–Yasuda nanofluid in a 2D tapered asymmetric channel. Viscosity is considered as a function on the temperature of the fluid. Consequently, all dimension parameters that are functions of viscosity such as, thermophoresis and Brownian motion, and Prandtl, local temperature, and local nanoparticle Grashof numbers has also been performed as variable within the flow. For the pertinent problem, the flow equations are first established, and then reformulated under the assumption of low Reynolds number and long wavelength. Numerical results have been obtained for the pressure gradient as well as the velocity, temperature, and nanoparticle concentration distributions. Moreover, numerical integration has also been performed to assess the expressions for the pressure rise. It is worth mentioning that increases in the variable viscosity parameter cause diminishes in temperature. Hence, the use of nanofluids with high viscosity is favorable in application of solar energy to get higher performance (by acting as a cooling system for solar cells) and lower operating costs. Increases in Brownian motion and thermophoresis parameters cause better transport of heat, and highly absorption in the solar range.

Implementation of Darcy–Forchheimer effect on magnetohydrodynamic Carreau–Yasuda nanofluid flow: Application of Von Kármán

Transient MHD flow in Carreau–Yasuda nanofluid produced by impulsively started rotating disk is examined in the occurrence of Darcy–Forchheimer and chemical reactive species considering conventional Fourier’s and Fick’s laws. Appropriate transformations are used to transform the constitutive equations into nonlinear ordinary differential equations and then solve by using improved form of RK-4 Fehlberg scheme (Cash and Karp). The deviation in flow field due to velocity, friction factor, temperature, heat diffusion rate, nanoparticle concentration, and mass transfer rate is analyzed subsequent to various ambient parameters appearing in the problem. The results of the study reveal that Weissenberg number appearing in the equations leads to deceleration of the radial and tangential velocities while the power law index tends to accelerate the radial and tangential velocities.

Numerical investigation for peristaltic flow of Carreau–Yasuda magneto-nanofluid with modified Darcy and radiation

This paper reports numerical study for peristalsis of Carreau–Yasuda nanofluid in a symmetric channel. Constant magnetic field is applied. Modified Darcy’s law and nonlinear thermal radiation effects are considered. Viscous dissipation and Ohmic heating effects are also present. Long wavelength and small Reynolds number are considered. Resulting nonlinear problems are solved numerically. Graphical illustrations depict that temperature increases for larger Hartmann number and it decays for thermophoresis parameter.

Chemical reaction for Carreau-Yasuda nanofluid flow past a nonlinear stretching sheet considering Joule heating

Abstract Current analysis has been made to scrutinize the consequences of chemical response against magneto-hydrodynamic Carreau-Yasuda nanofluid flow induced by a non-linear stretching surface considering zero normal flux, slip and convective boundary conditions. Joule heating effect is also considered. Appropriate similarity approach is used to convert leading system of PDE’s for Carreau-Yasuda nanofluid into nonlinear ODE’s. Well known mathematical scheme namely shooting method is utilized to solve the system numerically. Physical parameters, namely Weissenberg number We , thermal slip parameter δ , thermophoresis number NT, non-linear stretching parameter n, magnetic field parameter M, velocity slip parameter k , Lewis number Le, Brownian motion parameter NB, Prandtl number Pr, Eckert number Ec and chemical reaction parameter γ upon temperature, velocity and concentration profiles are visualized through graphs and tables. Numerical influence of mass and heat transfer rates and friction factor are also represented in tabular as well as graphical form respectively. Skin friction coefficient reduces when Weissenberg number We is incremented. Rate of heat transfer enhances for large values of Brownian motion constraint NB. By increasing Lewis quantity Le rate of mass transfer declines.

Numerical study for peristalsis of Carreau-Yasuda nanomaterial with convective and zero mass flux condition

Abstract The present communication investigates flow of Carreau-Yasuda nanofluid in presence of mixed convection and Hall current. Effects of viscous dissipation, Ohmic heating and convective conditions are addressed. In addition zero nanoparticle mass flux condition is imposed. Wave frame analysis is carried out. Coupled differential systems after long wavelength and low Reynolds number are numerically solved. Effects of different parameters on velocity, temperature and concentration are studied. Heat and mass transfer rates are analyzed through tabular values. It is observed that concentration for thermophoresis and Brownian motion parameters has opposite effect. Further heat and mass transfer rates at the upper wall enhances significantly when Hartman number increases and reverse situation is noticed for Hall parameter.

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.

Numerical analysis for peristalsis of Carreau–Yasuda nanofluid in an asymmetric channel with slip and Joule heating effects

This study investigates the peristaltic transport of magnetohydrodynamic (MHD) Carreau–Yasuda nanofluid through an asymmetric channel. Viscous dissipation, Joule heating and Hall effects are also included in the analysis. Velocity, thermal and concentration slip conditions are considered. The problem is modeled subject to long wavelength and low Reynolds number assumptions. Resulting nonlinear equations are numerically solved. Impact of embedded parameters on the fluid velocity, temperature, concentration of nanoparticles and heat and mass transfer rates at the wall are examined. Graphical results show that an escalation in the strength of appliedmagnetic field and increase in the value of Hall parameter reduce the velocity of nanofluid. Brownian motion and thermophoresis effects increase the temperature of the nanofluid. The present study shows an excellent agreement with the previously available studies in the limiting case.

Mixed convective peristaltic transport of Carreau-Yasuda nanofluid in a tapered asymmetric channel

Here modeling and analysis for mixed convective peristaltic flow of Carreau-Yasuda nanofluid have been carried out. The asymmetric channel walls are tapered. Effects of Brownian motion and thermophoresis are taken into consideration. The flow equations for the relevant problem are first constructed and then non-dimensionalized. The resulting non-linear coupled systems subject to lubrication approach are solved. Graphs reflecting the variations of pertinent parameters on the velocity, temperature, nanoparticle volume fraction are examined. Shear stress distribution and pumping and trapping phenomena are discussed. Results indicate that amplitude of shear stress decreases for larger Weissenberg number and power-law index whereas it enhances through viscosity ratio parameter.