Carreau Nanofluid Research Articles

Thermal transport and magnetohydrodynamics flow of generalized Newtonian nanofluid with inherent irreversibility between conduit with slip at the walls

This study enlightens the magnetohydrodynamic Jeffery-Hamel flow under an inclined Lorentz force through a non-uniform conduit having slip at walls, which is frequently applied in geothermal applications, electronic cooling devices, and modern energy systems, etc. Therefore, the performance of a two-dimensional purely radial flow inside a converging-diverging channel is explored from the perspective of second law of thermodynamics for Carreau nanofluids. The intersecting walls of conduit are inclined with horizontal plane to construct a converging flow for negative angle (α<0) and a diverging flow for positive angle (α>0). Additionally, second law thermodynamic evaluation offers an effective method for improving thermal performance by reducing entropy production. To accomplish the main objective, rigorous physical theories and assumptions are implemented based on the passive control approach of Buongiorno's model. By applying distinctive modifications, the governing equations are renovated into a system of ordinary differential equations, which are solved numerically by a collocated technique based on finite difference code. Simple shear near the wall influences the flow configurations allow compression in a local flow topology in regions of divergent channel. The temperature profiles increase with sophisticated heat source and Brinkman number. Entropy is minimum and uniform with optimum channel angle and velocity slip.

Radiative transport of MHD stagnation point flow of chemically reacting Carreau nanofluid due to radially stretched sheet

The flow of Carreau nanofluid with generation/absorption and magnetic field can be valuable for modifying solar energy production. In this work, we extended the study of the MHD boundary layer flow of Carreau nanofluid with heat generation/absorption close to a stagnation point over the radially extending plate. Likewise, the features of radiation and magnetic field with convective boundary conditions are considered. Further, keeping in view the importance of chemical reactions, their effect is also incorporated during the modelling process. For motivation, the impact of thermophoresis and Brownian motion has been taken into account. Using appropriate similarity transformation, we converted nonlinear governing partial differential equations of Carreau nanofluid into a couple of nonlinear ODEs. Using a recognized shooting technique and the MATLAB bvp4c solver and Mathematica ND-solve built-in command, we were able to get numerical results for these modeled ODEs. Through graphs and tables, the effects of different physical parameters like magnetic, Weissenberg number, Brownian motion, thermal radiation, thermophoresis, Prandtl number, chemical reaction, and rate of heat generation/absorption on non-dimensional velocity, temperature, and concentration profile are discussed.

Heat transfer aspects in Carreau nanofluid having hybrid nanoparticles through a porous medium

AbstractThe effects of nanofluid radiation and magnetic fields are important in biotechnology and medical treatment. The efficiency of hybrid nanomaterials flow (Carreau fluid) over a porous medium was investigated, and the findings were presented. The partial slip impact was used to thoroughly scrutinize the properties of the nanofluid flow. Using suitable variables, the PDEs in the Carreau model were reduced to ODEs, and the governing PDEs were transformed to ODEs using similarity transformations. The consequent ODEs are numerically investigated using the RKF‐45 Method. Furthermore, the results of the parameters involved in thermal and velocity were discussed. To the finest of the journalists' knowledge, no one has endeavored to depict medical occurrences and medical approaches by watching the flow through a malleable porous medium including blood as a base fluid and hybrid nanostructure materials. Indeed, the endeavors of this study are exceptional, and the obtained simulations have never been published by anyone academic.

Improvement for engineering applications through a dissipative Carreau nanofluid fluid flow due to a nonlinearly stretching sheet with thermal radiation

Due to its important applications in petroleum industries, biomedical engineering and geothermal reservoirs, a numerical analysis is performed to study the cooling process using a model of nanofluid flow and heat transfer due to a surface embedded in a porous medium, taking into account the presence of thermal radiation and viscous dissipation phenomenon. Ordinary differential equations (ODEs) are recovered from boundary flow equations using appropriate similarity transformations. The shooting technique is used to solve these ordinary differential equations numerically. In addition, all parameters influencing the problem that have the potential to improve the efficiency of cooling operations will be investigated. Graphical analysis is used to examine how various variables behave in relation to velocity, temperature, and concentration. Additionally calculated and studied are the numerical values of skin-friction coefficients, the local Nusselt number, and the local Sherwood number. In order to validate the numerical results, comparisons with previously published data in the literature are lastly made. There is wonderful harmony. The main findings indicate that the temperature and the concentration are both enhanced, but the velocity field is reduced by the magnetic and viscosity factors. Also, it is observed that the Nusselt number and skin friction coefficient fall at larger values of the Brownian parameter. Furthermore, it is discovered that the changes in the power-law index parameter have a significant impact on the thickness of the momentum and thermal boundary layers.

Analysis of nanobiofilm flow of Carreau fluid with the effect of buoyancy forces and activation energy: A numerical approach

In the past few years, many technical strategies, such as molding, condenser heat exchanger, liquefied metal filtration, fusion control and nuclear reactor coolant, that involve hydromagnetic fluxes and thermal intensification in porous media have been observed. This study investigates the Carreau nanofluid of nanobiofilm through stretching/shrinking sheet with a stagnant point flow, nanoparticles and convecting microbes. The orthogonal ([Formula: see text] impinge) coating stagnant point circulation of a medium is considered, although the sheet may be stretched/shrinked as the procedure utilized in industry. The variations in the fluid (dynamic viscosity, thermal conductivity, mass permeability) and microbes are utilized. The similarity transformation factors are used to transform the system of partial differential equations into a nonlinear system of ordinary differential equations. To find the solution of a system of equations, the Runge–Kutta method with shooting technique has been used. The flow rate, temperature and concentration, as well as the heat transfer rate, and the physical quantities have been discussed. The nanoparticle volume fraction increases with the increasing effect of activating energy as well as thermophoresis parameter, but it decreases with the enhancing effect of Lewis number (Le) and Brownian motion parameter (Nb). The graphs and tables display the illustration of the influence of different parameters.

Effects of Nonlinear Thermal Radiation and Heat Generation/Absorption on Magnetohydrodynamic (MHD) Carreau Nanofluid Flow on a Nonlinear Stretching Surface Through a Porous Medium

The present paper introduces a numerical study on the electromagnetic flow of Carreau nanofluid on a nonlinearly surface that stretches in a porous medium under the influence of heat absorption/generation and nonlinear thermal radiation besides the effects of thermophoresis and Brownian motion on the distributions of velocity, temperature, and nanoparticle concentration. The similarity transformations were used in converting the structure of governing partial differential equations into a structure of an ordinary differential equations that subsequently answered numerically by the Runge-Kutta fourth order technique with shooting technique. Also, graphical forms and numerical tables were used to show the results of all effects of physical coefficients that will be presented later in detail. Finally, some results of the study showed a decline in distributing the concentration and temperature of nanoparticles when reinforcing the values of the Lewis number and Prandtl number.

Entropy Minimization for Generalized Newtonian Fluid Flow between Converging and Diverging Channels.

The foremost focus of this article was to investigate the entropy generation in hydromagnetic flow of generalized Newtonian Carreau nanofluid through a converging and diverging channel. In addition, a heat transport analysis was performed for Carreau nanofluid using the Buongiorno model in the presence of viscous dissipation and Joule heating. The second law of thermodynamics was employed to model the governing flow transport along with entropy generation arising within the system. Entropy optimization analysis is accentuated as its minimization is the best measure to enhance the efficiency of thermal systems. This irreversibility computation and optimization were carried out in the dimensional form to obtain a better picture of the system’s entropy generation. With the help of proper dimensionless transformations, the modeled flow equations were converted into a system of non-linear ordinary differential equations. The numerical solutions were derived using an efficient numerical method, the Runge–Kutta Fehlberg method in conjunction with the shooting technique. The computed results were presented graphically through different profiles of velocity, temperature, concentration, entropy production, and Bejan number. From the acquired results, we perceive that entropy generation is augmented with higher Brinkman and Reynolds numbers. It is significant to mention that the system’s entropy production grew near its two walls, where the irreversibility of heat transfer predominates, in contrast to the channel’s center, where the irreversibility of frictional force predominates. These results serve as a valuable guide for designing and optimizing channels with diverging–converging profiles required in several heat-transfer applications.

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

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

Peristaltic Transport of Carreau Coupled Stress Nanofluid with Cattaneo-Christov Heat Flux Model Inside a Symmetric Channel

The current analytical study is concerned with studying the impact of Cattaneo-Christov heat flux of an incompressible flow which obeys Carreau nanofluid inside a symmetric channel in the existence of the porous medium. The impacts of couple stress, heat generation absorption, joule heating, couple stress viscous dissipation with Soret as well as Dufour numbers are all presumed. Long wavelength and law Reynold’s number approximations are utilized for solving the governing system of equations. Furthermore, the traditional perturbation method together with the homotopy perturbation technique (HPM) are applied to obtain the resultant solutions of these equations. The different physical parameters on velocity, temperature and nanoparticles concentration distributions are illustrated through a set of graphs. It is found that the elevate in the slip velocity parameter dwindle the velocity. Meanwhile, the rise in the value of thermal relaxation time parameter led to decay the temperature of the fluid. Over and above, enhancing the nano Biot number value caused an enrichment in the concentration of nanofluid.

On heat and flow characteristics of Carreau nanofluid and tangent hyperbolic nanofluid across a wedge with slip effects and bioconvection

We scrutinized the influence of nonlinear heat radiation on heat transmission evaluation of Carreau nanofluid and tangent hyperbolic nanofluid streams across a wedge with gyrotactic microorganisms by taking slip situations into consideration in this research article. The necessary nonlinear partial differential formulation is transmuted into non-linear ordinary differential equations by employing appropriate similarity variables, and these equations, including the boundary constraints are resolved in Matlab software utilizing Runge-Kutta fourth order via shooting tactic. A definite description of the framework is achieved by fluctuating the inputs of influential variables of the dependent functions and exhibited via graphs. The inhibiting flow velocity is portrayed by the intensifying inputs of buoyancy ratio, magnetic force, Rayleigh number, and eigenvalue. As a consequence of thermophoresis and Brownian motion of nano-particles, the temperature of the liquids initiates to ascend instantly. Because of differentiated viscous effects, the flow velocity for Carreau nanofluid is slower than that of tangent hyperbolic fluid and the temperature behavior is reversed. Further, the magnitude of skin friction factor for tangent hyperbolic nanofluid is almost half ofs that of Carreau nanofluid.

Activation Energy and Inclination Magnetic Dipole Influences on Carreau Nanofluid Flowing via Cylindrical Channel with an Infinite Shearing Rate

Background: The infinite shear viscosity model of Carreau fluid characterizes the attitude of fluid flow at a very high/very low shear rate. This model has the capacity for interpretation of fluid at both extreme levels, and an inclined magnetic dipole in fluid mechanics has its valuable applications such as magnetic drug engineering, cold treatments to destroy tumors, drug targeting, bio preservation, cryosurgery, astrophysics, reaction kinetics, geophysics, machinery efficiency, sensors, material selection and cosmology. Novelty: This study investigates and interprets the infinite shear rate of Carreau nanofluid over the geometry of a cylindrical channel. The velocity is assumed to be investigated through imposing an inclined magnetic field onto cylindrical geometry. Activation energy is utilized because it helps with chemical reactions and mass transport. Furthermore, the effects of thermophoresis, the binary chemical process and the Brownian movement of nanoparticles are included in this attempt. Formulation: The mathematics of the assumed Carreau model is derived from Cauchy stress tensor, and partial differential equations (PDEs) are obtained. Similarity transformation variables converted these PDEs into a system of ordinary differential equations (ODEs). Passing this system under the bvp4c scheme, we reached at numerical results of this research attempt. Findings: Graphical debate and statistical analysis are launched on the basis of the obtained computed numerical results. The infinite shear rate aspect of Carreau nanofluid gives a lower velocity. The inclined magnetic dipole effect shows a lower velocity but high energy. A positive variation in activation energy amplifies the concentration field.

Convective flow of MHD non-Newtonian nanofluids on a chemically reacting porous sheet with Cattaneo-Christov double diffusion

The current study focuses on the MHD flow of Casson and Carreau nanofluids in a porous medium with Cattaneo–Christov double diffusion over a stretching sheet in the presence of thermal radiation, chemical reaction, and suction/injection. Viscous dissipation, Brownian motion, and thermophoresis effects are also considered. The governing PDEs are converted into a system of ODEs by implementing suitable variables. The resulting equations are elucidated via the bvp5c Matlab package. The effects of the dimensionless parameters on the flow, heat, and mass transfer physiognomies are analyzed in detail via figures and tables. It is noticed that an improvement in the thermal relaxation parameter and suction parameter reduces the thermal field. Further, we perceived that the heat exchange rate is dropped for growing values of the Eckert number, the Brownian motion, and thermophoresis parameters. Furthermore, we validated our results with the available results in the literature for some special cases of the problem.

Entropy generation analysis for axisymmetric flow of carreau nanofluid over a horizontally stretching cylinder

The objective of this work is to scrutinize the entropy production and its effects on Carreau nanofluid flow over a horizontally stretching cylinder. The significant influence of magnetic field, non-linear thermal radiation and Joule heating have been studied to control the heat transfer rate. The importance of nanofluid parameters, Brownian and thermophoresis diffusion, is argued on Carreau nanofluid motion for shear-thinning and thickening behavior. Utilizing convenient transformations, the fundamental equations, devised to a nonlinear system of ordinary differential equations (ODEs), are resolved numerically by Matlab technique bvp4c. The influence of relevant parameters on velocity, Bejan number, temperature, entropy and concentration profiles are examined by virtue of graphs. Furthermore, we determine the repercussion of indistinguishable parameters over skin friction and Sherwood number via tables. From the acquired results, we perceive that entropy generation augments with enhancing magnetic field parameter, Brinkman number, curvature parameter, Eckert number, and power law index while it declines for the Brownian diffusion parameter. Also, skin friction reduces for the magnetic field and curvature parameter whereas it rises for Weissenberg number. Moreover, Sherwood number escalates for the Schmidt number and curvature parameter.

Multiple slip effects on time dependent axisymmetric flow of magnetized Carreau nanofluid and motile microorganisms

This presented work investigate the bio-convections effects of the magnetized time dependent axisymmetric flow of Carreau-nanomaterial performances with multiple slip effects over a stretching sheet. The momentum, heat, concentration and density of motile micro-organism are renovated into the system of equation via using well known similarity revolution. Well known Mathematical computational techniques and software (i.e. bvp4c and MATLAB) are used to draw graphical and tabular results. Velocity profile equation f^{prime}(zeta ), energy equation theta (zeta ), volumetric nanoparticles phi ,(zeta ), density motile microorganism chi (zeta ).The Carreau viscosity model is use to reduce the viscosity of fluid when W_{e} = 0,,, and ,n = 0. Besides we moderate this into power law index with ,n = 0.5 and ,n = 1.5 partial slip condition of velocity is also instigated at the surface. Gravity dependent gyrotactic nanoparticles are utilized for well observing axisymmetric flow with convective boundary layer condition and comparatively better heat transfer rate result and applicable to maximum realistic approach.

The mathematical model for heat transfer optimization of Carreau fluid conveying magnetized nanoparticles over a permeable surface with activation energy using response surface methodology

AbstractThe sensitivity analysis and response surface methodology (RSM) is performed for the key parameters governed by the magneto‐flow and heat transport of the Carreau nanofluids model toward a stretching/shrinking surface in the presences Arrhenius activation energy and chemical reaction. Nanofluid that displayed Brownian motion and thermophoresis was considered with the permeable condition. The effects of different physical parameters were analyzed by employing appropriate similarity transformations in nonlinear partial differential equations and converted to the dimensionless system of ordinary differential equations. The finite difference method in bvp4c code solves the equations numerically. Associated parameters are presented graphically and interpreted against local Nusselt number, Sherwood number, and skin friction coefficient. An increase in the activation energy factor leads to increased concentration in permeable flow. The higher the activation energy lower the temperature and causes the reaction rate constant to decrease. In addition, it slows down the chemical reaction and increases the concentration characteristics. The increase of radiation and Prandtl number leads to an increase in heat transfer for the permeable surface. Furthermore, the Schmidt number and the binary reaction rate parameter increase the mass transfer for suction/injection flow. As a result, the Nusselt number's highest sensitivity is the Eckert number and the lowest to the thermophoresis parameter. The Sherwood number's positive sensitivity is observed for the Eckert number and Brownian motion parameter, whereas negatively sensitive to thermophoresis.

Adaptive Computations to Pressure Profile for Creeping Flow of a Non-Newtonian Fluid With Fluid Nonconstant Density Effects

Abstract The sperm density through the cervical canal plays a dynamic part in promoting the pregnancy progressions of organisms. Therefore, this study aims to probe the combined effects of concentration and temperature-dependent density on the creeping flow of Carreau nanofluid in the cervical canal as the first look in this direction. Chemical reaction and Hall effects are considered. The system of a physical model is simplified/streamlined using appropriate transformation (δ≪1). The system that describes the fluid model is recurrence/rearranged with aid of adaptive shoot techniques (AST) by a computer program using mathematica 13.1.0. Solutions are offered via sketches on the pressure profiles. Besides, graphs of streamlined are achieved in dissimilar values of the nonconstant density of the fluid. To get accurate results and approve the validation of the proposed technique, a comparison with Ibrahim (2022, “Adaptive Simulations to Pressure Distribution for Creeping Motion of Carreau Nanofluid With Variable Fluid Density Effects: Physiological Applications,” Therm. Sci. Eng. Prog., 32, p. 101337) is obtained and seems to be very good. The results indicate that high values of nonconstant density parameters impose a pressure gradient in the cervical canal, which supports the sperm to be more energetic in ovum fertilizing.

Nonsimilar modeling and numerical convective transport analysis of forced flow of radiative Carreau nanofluid with zero mass flux boundary condition

AbstractPresent research focuses on nonsimilar analysis of the flow of a non‐Newtonian Carreau nanofluid against different geometrical configurations affected by thermal radiations. The flow is induced by stretchable surface with the implementation of zero‐net mass‐flux conditions on the surface. This considered model is commonly known as Kuznetsov and Nield's proposed updated model for nanoparticles. The derived flow equations are first nondimensionalized by employing appropriate nonsimilar transformations. The transformed system is analytically tackled by employing the local nonsimilarity (LNS) approach up to the second‐truncation level in association with the numerical algorithm bvp4c. The consequences of appropriate parameters, such as the suction parameter, wedge angle parameter, Weissenberg number, Prandtl number, constant velocity parameter, temperature ratio, Brownian motion, Lewis number, thermophoresis and radiation parameters, on fluid velocity, thermal, and concentration profiles are calculated and graphed. Drag coefficient, Nusselt, and Sherwood numbers are also computed and presented in tabular form. It is observed that intensification in the suction parameter shows augmentation in the local skin friction coefficient. Enhancement in the wedge angle parameter increases both the Sherwood and Nusselt numbers. Enhancement in velocity profile of the nanofluids is noticed with the increasing estimations of suction parameter. Thermophoresis parameter enhances both thermal and concentration profiles, however increasing Lewis number leads to a decline in the concentration boundary layer. With judgment, a comparative assessment is made of the present and previous results. This research may be helpful for the researchers that are interested in studying prospective industrial and engineering nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, and many others.

Entropy generation on EMHD Darcy-Forchheimer flow of Carreau hybrid nanofluid over a permeable rotating disk with radiation and heat generation: Homotopy perturbation solution

The intention of this article is to explore the entropy generation of the Carreau hybrid nanofluid in a permeable rotating disk in the presence of thermal radiation, heat generation, and viscous dissipation. By applying the self-similarity variables, the partial differential equations are converted into ordinary differential equations and then the homotopy perturbation method is performed. Graphene oxide (Go) and Silver (Ag) are nanoparticles and kerosene oil as a base fluid is considered. Compared to the numerical technique (Runge-Kutta method), the homotopy perturbation method generates more precise and dependable results. The influence of sundry parameters is exhibited graphically for velocity, temperature, entropy generation, Bejan number, skin friction coefficient, and Nusselt number. The higher values of the Weissenberg number enhance the velocity profile and the opposite nature is observed in the porosity parameter. The entropy generation increases for larger values of the thermal radiation and electric field parameters. Carreau nanofluid expands under higher stress on the surface of the wall than Newtonian fluid. This type of problem would be used for electric devices and solar thermal systems. Moreover, the selected nanoparticles Graphene oxide and Silver play an important role in the biofunctionalization of protein, antibacterial, and anticancer therapy.

A design of soft computing intelligent networks for MHD Carreau nanofluid model with thermal radiation

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values’ accuracy is upto [Formula: see text] which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms.

Irregular heat source impact on carreau nanofluid flowing via exponential expanding cylinder: A thermal case study

In the Carreau nanofluid (CNF) flow, the transmission of heat through the stretching cylinder is observed in two terms, one is non-linear stretching and other is irregular heat sink/source. In this study we observed thermal radiation and thermal conductivity which depends on temperature. We use similar variables to translate the complex partial differential equations into the ordinary differential equations. By using shooting method (SM), we can find the series solution of the highly order nonlinear ODEs. For some particular results we can compare the series solution with some published results. Two different classes of nanofluids, Aluminum Alloys- Engine Oil (AA7075-EO) and Graphene Oxide -Engine oil (GO-EO) are considered for our analysis. We used some graphs and tables to determine the influence of irregular heat sink/source on heat transformation and movement of fluid for the linear and non-linear stretching rate. From this research we find that non-linear stretching rate and source of heat are causing a disruption of temperature distribution in fluid region. We can improve the velocity and heat profile in the nonlinear situations in all conditions, but not in an internal heat sink. Also, in comparison to the GO-EO, AA7075-EO is the ideal source of heat transfer.