Carreau Nanofluid Research Articles

Optimizing heat and mass transfer in Carreau nanofluid with mixed nanoparticles in porous media using explicit finite difference method

Optimizing heat and mass transfer in Carreau nanofluid with mixed nanoparticles in porous media using explicit finite difference method

On the thermal performance of a three-dimensional cross-ternary hybrid nanofluid over a wedge using a Bayesian regularization neural network approach

Abstract Significance Studying the flow of ternary nanofluids [Ag, Cu, MoS2] holds significant importance in both science and engineering. Ternary nanofluids are vital in advancing thermal management systems, heat exchangers, aerospace, and materials processing applications. Purpose This study investigates the ternary hybrid Carreau nanofluid numerically for thermal proficiency in the inclined magnetized environment. In this study, three distinct nanoparticles of [Ag, Cu, MoS2] and base fluid water over the wedge are used. The velocity of nanofluids is judged under the influence of an inclined magnetic field, and the thermal performance is scrutinized by incorporating the thermal radiation effect. Methodology The physical problem generates partial differential equations, which are transformed into ordinary differential equations (ODEs) through similarity variables. These ODEs are linearized into a system of ODEs and then passed under the bvp4c Matlab program to get the solution. This solution is again trained by an artificial neural network, and further results are obtained with both schemes and compared. Findings The most rapid heat transport analysis is found for ternary hybrid nanofluids compared to bi-hybrid nanofluids. The thermal radiation parameters and the magnetic environment augment the rate of heat transport.

Variable density and heat generation impact on chemically reactive carreau nanofluid heat-mass transfer over stretching sheet with convective heat condition

The present study focuses on the physical significance of heat generation and chemical reaction on Carreau nanofluid with convective heat conditions. Heat transfer is characterized using convective boundary conditions. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by using well define stream functions and similarity transformations. Using a shooting methodology, the Keller-box method with Newton Raphson scheme is used to elaborate the numerical solutions of physical phenomena. Utilizing a similar technique to find the impact of physical parameter such as the production of heat δ, the rate of reaction Λ, Biot numbers γ, Brownian motion variable Nb, the thermophoresis parameters Nt, the Weissenberg quantity We, Prandtl number Pr, and Lewis number Le on velocity profile, temperature profile and mass transmission profile are determined graphically. The skin-friction coefficient −f″(0), local Nusselt −θ′(0), and Sherwood numbers −ϕ′(0) are analyzed numerically. Increment in fluid velocity and slip temperature are depicted with high Biot number. Maximum magnitude of fluid temperature and fluid concentration function are depicted at high value of temperature dependent density. The magnitude of heat and mass transportation enhanced with maximum choice of Brownian motion.

Numerical simulation of bio‐convection radiative heat transport flow of MHD Carreau nanofluid

Numerical simulation of bio‐convection radiative heat transport flow of MHD Carreau nanofluid

Multilayer deep-learning intelligent computing for the numerical analysis of unsteady heat and mass transfer in MHD Carreau Nanofluid model

The objective of this article is to investigate the mechanism of unsteady heat and mass transfer (HMT) in a magnetohydrodynamics Carreau nanofluid flow (MHD-CNFF). To accomplish this, we utilized a novel artificial intelligence-based (AI) method, deep learning predictive technique combined with Levenberg-Marquardt scheme (DLPT-LMS). The similarity transformation is applied to convert the partial differential equations (PDEs) into a set of non-linear ordinary differential equations (ODEs). We numerically solved these resulting ODEs using the Adam numerical approach in sophisticated “Mathematica” software. The influence of Brownian motion parameter, thermophoresis parameters, Prandtl number, Lewis number, and mass transfer parameters on the temperature, velocity, and concentration profile is analyzed using a synthetic dataset. This evaluation is conducted across different variation of MHD-CNFF by leveraging DLPT-LMS. The absolute error (AE) across various iteration of MHD-CNFF demonstrated a progressive drop, indicating the accuracy of DLPT-LMS. The outcomes of this investigation revealed that the AE ranged from 10-3 to 10-8 which shows a minimum error between actual and predicted value. Additionally, the MSE confirmed the accuracy of proposed DLPT-LMS in predicting the behavior of velocity, temperature, and concentration profiles, with lower values showing better predictions. The model accuracy was reinforced by performance results, including regression analysis and error histograms. Error values gradually decreased during training, validation, and testing phases, exhibiting a robust convergence and indicating the highly reliability of AI-based algorithm for investigating intricate fluid dynamics in MHD-CNFF systems.

Thermal analysis of mathematical model of heat and mass transfer through bioconvective Carreau nanofluid flow over an inclined stretchable cylinder

In this proceeding the main focus to scrutinize the heat and mass transfer rate increment due to the involvement of motile microorganisms in the Carreau nanofluid flow through an inclined stretchable cylinder under the consequences of activation energy and thermal radiation. This phenomenon has many physical applications in the field of civil, mechanical and seismographic engineering. The research focuses on creating and analyzing new nanocomposites with applications in energy storage, showcasing the transformative impact of nanotechnology on the advancement of high-performance materials. First of all, for the numerical treatment of the above physical model mathematical model is developed in the form of partial differential equations (PDE's) by considering all involving quantities. The resultant model is highly nonlinear and of higher order. Appropriate similarity variables are defined to transform this system of PDE's into first order ordinary differential equations (ODE's). For numerical results we develop a numerical algorithm from nonlinear ODE's and use ‘bvp4c’ built in package of MATLAB. Numerical results are acquired from software in the form of graphical visuals and tabular data as narrated in the results and discussion section. Using this tabular data streamlines are constructed for the better understanding of heat and mass transfer through this phenomenon under the defined constraints. From results, velocity profile increased by the augmentation of values of curvature parameter. Thermal profile is stronger when values of thermophoresis parameter is boosted, Concentration of nanoparticle profile get smoother when temperature coefficient increased, and motile microorganism's density profile is enlarged upon inclining the values of bioconvection lewis number.

Modeling heat‐mass transport for MHD bio‐convection Carreau nanofluid with Joule heating containing both gyrotactic microbes and nanoparticles diffusion

AbstractThe study of a bio‐convection is a natural progression that happens as microbes transport unsystematically in single‐celled or colony‐like environments; as they live ubiquitously, individuals, as in rodents, and plant forms. They're so much denser than liquid, owing to which, microbes develop a basis of bio‐convection. Gyrotactic microbes are individuals that dip up‐stream in contradiction of gravity in motionless liquid, producing the higher portion of the deferment to be thicker than the lesser part. Bioconvection's significance can be realized in a diversity of bio‐microsystems, for instance, bio‐tech allied to mass transport, biofuels, enzyme biosensors and fraternization. Together with nanofluids, a mixture of bioconvective is working to progress the structure's thermal enactment which has uses in diverse scientific structures. Recent study has related the progress of extrusion features, radiative heat progression and biofuel fabrication to the use of nanoparticles. The essential plans of the modern scrutinization are to examine the magneto bioconvection flow of nonlinear radiative Carreau fluid persuades by the nanofluid and Joule heating. Additionally, Convective conditions of heat, mass and motile microorganism with heat sink/source and chemical reaction have been explored. By means of similarity alteration to alter the nonlinear partial differential equations into nonlinear Ordinary differential equations (ODE). The solutions of subjected equations have been attained by exploiting the bvp4c algorithm. Homotopic algorithm has been also executed for comparison of bvp4c results and former studies. The impacts of relatable factors on diverse fields are sketched in graphic form. The study explores temperature field enhancement for thermo Biot and Brownian motion factors. Furthermore, the fluid concentration exaggerates for mass Biot and chemical reaction factor; however, declines for Brownian motion factor. The motile density field decays with the rising values for Peclet number and intensifies for motile density Biot factor. The comparison tables of current work and previous work also have been presented for the authentication of work with two different techniques.

Carreau nanofluid dynamics with activation energy gyrotactic microorganisms in a porous medium: Application to solar energy

This study investigates the magnetohydrodynamic (MHD) flow of Carreau nanofluid through a porous medium with motile microorganisms, focusing on various geometries under shear-thinning and shear-thickening conditions. The aim is to elucidate how factors such as activation energy, Schmidt number, Peclet number, bioconvection, Brownian motion, thermophoresis, and heat generation influence flow dynamics. Using similarity transformations, we nondimensionalize the governing equations and solve them numerically with the Runge–Kutta method and a shooting technique in MATLAB. Our findings indicate that variations in Carreau, magnetic, and suction parameters notably impact velocity, temperature, concentration, diffusion, wall friction, and heat transfer, generally resulting in reduced values. Specifically, the flat plate geometry exhibits lower skin friction, heat transfer, and mass transfer rates, as well as decreased gyrotactic microorganism effects. Increased activation energy enhances concentration fields, signaling slower chemical reactions, while higher Peclet numbers and bioconvection inversely affect flow properties. Additionally, reduced Schmidt numbers lead to lower microorganism concentrations. These results provide valuable insights into the complex interactions between fluid dynamics and microorganism behavior, with implications for optimizing processes in biotechnology and environmental management.

Stochastic computing with Levenberg–Marquardt neural networks for the study of radiative transportation phenomena in three-dimensional Carreau nanofluid model subjected to activation energy and porous medium

The objective of this research is to establish the modelling and evaluation of a differential mathematical system for the radiated Carreau nanofluid model (RCNFM) by exploiting the skills of stochastic computing with Levenberg–Marquardt neural networks (SCLMNNs).The reference dataset is created using the Adams technique in the Mathematica software by variation of various physical quantities. The reference data results are trained using a split of seventy percent for training and thirty percent for validation and testing methods. This approach aims to enhance and compare the estimated outcomes with established solutions. The precision and efficacy of the developed stochastic computing with Levenberg–Marquardt neural networks are illustrated by a comparison of the results obtained from the dataset using Adams technique. This comparison includes variations in values of several influential parameters including Magnetic number, Weissenberg Numbers, Porosity parameter, Brownian movement, Prandtl number, Unsteady parameter, Temperature Difference Parameter, Stretching/shrinking parameter, and Lewis Number. The reference data results are trained by assigning 70% for training, 15 % for validation and 15 % for testing. Fitness curves of mean square error, regression studies, error evaluated with histogram plots, and evaluation on absolute errors all authenticate the reliability and precision of stochastic computing with Levenberg–Marquardt neural networks. Performance metrics in terms of mean square error are excellent at the levels 1.19E−10, 1.92E−10, 9.60E−11, 1.02E−10, 7.09E−11, 2.07E−09, 1.66E−10, 8.34E−11, and 1.17E−13against 117, 194, 144, 117, 237, 260, 96, 128, and 74 epochs. The error analysis of the designed and reference datasets suggests that the stochastic computing with Levenberg–Marquardt neural networks is accurate and reliable, with values ranging from E−08 to E−04 across all scenarios. Radiative transport in three dimensional Carreau nanofluids with activation energy in porous media improves the following domains: biomedical engineering, energy systems, chemical process, environmental engineering, thermal management and material science.

Exploring double-diffusive convection in ferromagnetic Carreau nanofluid with magnetic dipole: Insights for solar thermal systems over plate, wedge, and stagnation

The use of ferromagnetic Carreau nanofluid in solar thermal systems enhances heat transfer and magnetic effects, optimizing solar collector design, improving solar power efficiency, and innovating nanofluid-based solar heaters and energy storage. Magnetic nanostructures significantly impact viscosity and thermophysical properties, influencing Ferrofluids' magneto-viscous nature. The investigation illustrates double-diffusive convection in radiative flow past three different geometries of ferromagnetic Carreau nanofluid, emphasizing the novel discussion of diffuse-thermal and thermo-diffusion impacts. Numerical solutions are obtained using the shooting technique with the Runge-Kutta fourth-order approach. Graphs and numerical data in tables depict the impacts of pertinent parameters. The study reveals that the radiation parameter, Soret parameter, and Dufour parameter contribute to temperature improvement as they are enhanced. These findings showcase the potential for advancing solar thermal systems through the utilization of ferromagnetic Carreau nanofluid, offering insights for sustainable solar energy applications. As the thermophoresis parameter increases from 0.001 to 0.005, the percentage change in the Nusselt number decreases for all three locations: Plate (0.90 %–0.66 %), Wedge (0.77 %–0.62 %), and Stagnation Point (0.62 %–0.54 %). This indicates that while the absolute values of the Nusselt numbers increase, the rate of change becomes smaller as increases.

Implementation of artificial neural network using Levenberg Marquardt algorithm for Casson–Carreau nanofluid flow over exponentially stretching curved surface

Implementation of artificial neural network using Levenberg Marquardt algorithm for Casson–Carreau nanofluid flow over exponentially stretching curved surface

Bioconvective variable viscosity flow of Carreau nanofluid with external heat source and nonlinear radiation: Analysis with convective heat and mass constraints

In this study, an unsteady model for Carreau nanofluid with microorganism decomposition is developed. The viscosity and thermal conductivity of the Carreau nanofluid are considered variable. Magnetic and porosity effects are included using a magneto-porosity parameter. An additional heat source is introduced to improve heat transfer. Nonlinear analysis is applied for radiative applications. The flow is modeled using an oscillatory stretching surface. Convective mass and heat constraints are used to analyze the problem. Analytical computations are performed on the developed model. The significance of various parameters for the thermal problem is discussed. The results may enhance the performance of transport problems, heat transmission, energy systems, and thermal devices.

Computational study of Carreau nanofluid across a stretching cylinder by homogeneous-heterogeneous responses: A frame work of modified Buongiorno's nanofluid model

This paper studies the Carreau nanofluid employed by modified Buongiorno's model to theoretically analyze a homogeneous-heterogeneous process-influenced numerical solution of a Carreau nanofluid flowing through a stretched cylinder. In steady of Carreau nanofluid model proposed by Buongiorno's flow across a linearly extending cylinder influenced by homogeneous/heterogeneous responses are examined and express the changes of moment, energy, and concentration in both graphical and numerical. The following impact factors are consequences of the result, the stretching limiting factor, the curvature limiting factor and other limiting factors. The effects of both convection and heat generation are seen in flow field analysis. In comparison to ambient fluid, the stipulated exterior temperature and concentration are hypothetically increased. For the regulating equations of velocity, energy, and concentration profiles are permuting from a set of partial differential equations stand to ordinary differential equations manipulating an equivalent conversion. The resulting sequence of equations was solved at the boundary value problem in the fifth-order method. The velocity, temperature, concentration, skin friction coefficient, local Nusselt number, and local Sherwood number fields are studied, and then the outputs are illustrated in graphs and tables.

Cattaneo-Christov heat flux effect on Darcy-Forchheimer dual-phase dusty shear-thickening carreau hybrid nanofluid flow along a stretched vertical cylinder

This research ventures into the convoluted behavior of dusty Copper - Titanium Dioxide and Water shear-thickening Carreau hybrid nanofluid flow within a porous vertical cylinder, incorporating the effects of viscous dissipation and the Cattaneo-Christov heat flux model. By applying the Runge-Kutta-Fehlberg fourth-order method alongside the shooting technique, we address the nonlinear coupled ordinary differential equations governing this flow. The study systematically investigates the impact of various dimensionless parameters on critical flow characteristics such as velocity and thermal profiles, skin friction coefficient, and thermal transfer rate. Our findings indicate that increasing local Weissenberg numbers and power law indices for the Carreau fluid model enhances velocity distribution while reducing the temperature profile. Higher Weissenberg numbers correlate with a decreased skin friction coefficient and an elevated Nusselt number. Initially, the curvature parameter shows a gradual increase in the fluid phase of the velocity profile, but it experiences a significant surge near the boundary. The heat transfer rate diminishes with rising values of the porosity and Forchheimer parameters. Notably, the study reveals the remarkable benefits of the dusty Carreau hybrid nanofluid, demonstrating a 39% increase in absolute shear stress compared to the dusty Carreau nanofluid, highlighting its potential for improved momentum transfer. Additionally, a 20% enhancement in heat transfer rate underscores its suitability for high-performance engineering and heat transfer systems. These results offer promising advancements for industries requiring efficient heat and momentum transfer, contributing to superior performance and energy efficiency.

Numerical simulation of unsteady blood based Carreau nanofluid flow in an inclined porous saturated artery having overlapping stenosis with electro-osmosis

The present paper focuses on the computational modeling of the unsteady non-Newtonian electro-magnetohydrodynamic flow of nano-blood through the inclined and tapered saturated porous artery with overlapping stenosis. The Carreau fluid model is adopted to simulate the non-Newtonian behavior of the blood. This study also uses a modified form of Darcy’s law applied to the Carreau model. Blood is doped with a suspension of homogeneous biocompatible nanoparticles of different shapes. In addition, a combination of a magnetic field and an electric field has also been taken into account. The significance of this work rests in the ability to enhance comprehension of the complicated behavior of hemodynamic flow when exposed to external fields and porous media with the addition of nanoparticles, which has substantial implications for the regulation and treatment of cardiovascular diseases. The finite-difference method is used to obtain the solution of the resulting equations. The simulations are applicable to targeted magnetic therapy for stenotic artery disease and the delivery of nanomedicines.

Entropy generation and Arrhenius activation energy mechanisms in EMHD radiative Carreau nanofluid flow due to Brownian motion and thermophoresis with infinite shear rate viscosity: solar energy application and regression analysis

This research is devoted to analyzing the radiative electro-magnetohydrodynamic (EMHD) Carreau nanofluid flow, emphasising entropy generation and activation energy under unique conditions, specifically, with infinite shear rate viscosity and binary chemical reactions occurring over a nonlinear stretching sheet. Also, this innovative nanofluid model explicitly includes the vital role of Brownian motion and thermophoresis phenomenon, which are significant factors governing the movement and distribution of nanoparticles in the base fluid. A binary chemical reaction has also been taken in this study since it affects the mass transfer rates between different species present in the nanofluid. The ODEs were solved by using the bvp4c routine to effectively tackle momentum, temperature, and concentration equations. It is noted that velocity distribution increases with enhancement in the Weissenberg parameter, whereas the reverse trend is seen on the temperature profile. With an escalation of the viscosity ratio parameter, the velocity profile increases. Further, multiple linear regression has been utilised to statistically scrutinised the effect of pertinent parameters on skin friction coefficient, heat transfer rate, and Sherwood number by considering 64 sets of values of Nr in the range [0.3,0.6]. Nb & Nt in the range [0.1, 0.4] & [0.2, 0.3], respectively, to obtain the regression model.

A Stochastic Numerical Approach to Study Stagnation Point Carreau Nanofluid Flow Impacted by Thermal Radiation and Activation Energy

A Stochastic Numerical Approach to Study Stagnation Point Carreau Nanofluid Flow Impacted by Thermal Radiation and Activation Energy

Viscous dissipation and Joule heating effects of Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk

In this piece of communication, a theoretical investigation of two dimensional boundary layer flow of Magnetohydrodynamics (MHD) Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk is made. The investigation includes the effects of viscous dissipation, Joule heating, thermal radiation, suction/injection, Darcy–Forchheimer porosity model and binary chemical reaction with activation energy, etc. To examine the impacts of the aforementioned effects, the conservation laws are formulated with strongly nonlinear partial differential equations (PDEs), which are then transformed into a system of initial value problems (IVPs) using appropriate similarity transformations and techniques. The 5th order Runge–Kutta with the shooting technique is used to find numerical solutions aided by Python programming with built in program “fsolve”. The method is validated with other published articles under common assumptions and it agrees nicely. The impacts of the pertinent parameters on velocity, temperature, concentration, skin friction coefficient and the rates of mass and heat transfers with in the flow regime are displayed using graphs and tables. The main outcomes include the motivation of local Nusselt and Sherwood numbers for shear thickening (n=1.5) than shear thinning (n=0.5) cases of the Carreau nanofluid. The momentum boundary layer of the Carreau nanofluid gets thinner with an increase in Forchheimer number, unsteady and suction parameters. A dual nature is observed for concentration of the Carreau nanofluid with a rise in Eckert number, i.e increasing in concentration around the wall and decreasing far away from the wall. The rise in destructive and constructive chemical reaction parameters disperse and accumulate the concentration of the system, respectively.

Comparative study of Hiemenz flow in hybrid Carreau nanofluid (Fe3O4-Cu/kerosene-engine oil): nonlinear effects, Newtonian heating and viscous dissipation

ABSTRACT This study is important because it helps us understand how different factors affect the flow of a special liquid with nanoparticles, giving us useful insights for real-world applications in engineering and technology. This research endeavours to explore and contrast the distinctive characteristics of steady, 2-D magnetohydrodynamic (MHD) and stagnation point (Hiemenz) flow in Carreau hybrid nanofluid {Fe3O4-Cu/kerosene-engine Oil} over a nonlinear stretching-shrinking surface with its counterpart, Carreau nanofluid. Employing the laws of conservation encompassing mass, momentum, energy, and concentration, our methodology probes into the multifaceted effects induced by factors like the suction-injection, viscous dissipation, Newtonian heating, Hiemenz flow, thermophoresis, and Brownian motion. This exploration involves the transformation of governing partial differential equations (PDEs) into a system of ordinary differential equations (ODEs) through similarity transformations. Subsequently, the intricate non-linear ODEs are meticulously solved using the bvp4c technique, an adept MATLAB built-in function, facilitating a comprehensive understanding of the intricate dynamics within the system. In addition, the study considers the Newtonian heating effect and a numerical comparison is performed to verify the results. Using two different types of nanoparticles dispersed in kerosene-engine oil, it was demonstrated that increasing Weissenberg parameter values resulted in significant improvements in thermal conductivity and thermal velocity. A comparison of Carreau nanofluid thermal and concentration velocities with Carreau hybrid nanofluid showed that Carreau nanofluid values are lower (Weissenberg parameter). Higher Biot numbers are associated with reduced temperature velocity and elevated concentration velocity.

A comparative study on entropy and thermal performance of Cu/CuO/Fe3O4-based engine oil Carreau nanofluids in PTSCs: a theoretical model for solar-powered aircraft applications

A comparative study on entropy and thermal performance of Cu/CuO/Fe3O4-based engine oil Carreau nanofluids in PTSCs: a theoretical model for solar-powered aircraft applications