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This paper studies the similarity of silver-blood-based Carreau–Maxwell, Carreau–Oldroyd-B and Carreau–Jeffrey binary nanofluids on the parabolic trough solar collector. By the energy equations, Joule heating effects and nonlinear thermal radiation were integrated. The velocity slip condition by the solid–liquid interface was again worked out. In this model, magnetic field aspects and viscous dissipation were again taken into account. The converted construction was modeled into ordinary differential methods with the help of appropriate comparison applications. This governing relation on current flow problem was given graphically and determined mathematically by applying made-up MATLAB computational tool with the aid of renowned mathematical shooting methods bvp4c (Lobatto's IIIa Formulae). This mathematical outcomes are given in tabular and graphical models. It was observed that the nonlinear thermal radiation aggregates the temperature profile. This skin friction was improved for greater values of magnetic parameter by 6.16%. Moreover, the local Nusselt number was reduced about developing values of radiation parameter into 71.78%. Moreover, these Casson–Jeffrey and Casson–Maxwell nanofluid models are more efficient than the Casson–Oldroyd-B nanofluid models. [ABSTRACT FROM AUTHOR]

The aim of this study is to perform analysis of nonlinear mixed convection flow of Carreau fluid due to curved stretched surface with slip condition. Furthermore, the effect of Darcy–Forchheimer and MHD is taken into consideration. The energy equation is modified by considering the variable thermal conductivity with Joule heating effect. The governing equations of the problem are highly nonlinear partial differential equations subjected to boundary conditions. Similarity transformations are used to transform nonlinear PDEs into ODEs. The numerical technique is used to solve this problem via bvp4c. The main outcomes of this research are that the impact of Forchheimer and porosity parameter tends to decrease the fluid velocity for shear thickening case. The velocity slip condition increases the fluid velocity only near the surface but the fluid velocity away from the surface does not get affected. The changing thermal conductivity raises the temperature of the fluid near the boundary. Furthermore, the impacts of various parameters on the velocity and temperature profiles are demonstrated. The values of local Nusselt number and skin friction for a different parameter are provided. [ABSTRACT FROM AUTHOR]

This paper presents the numerical study for heat generation and electro-osmotic effects of Carreau model of a fluid in an unsteady channel. This prepared model has many useful applications in microfluidic biological and mechanical research. Modified Darcy's law, viscous dissolution and ciliated walls are also presented. Non-Newtonian fluids play a key role in biological fluids which include the motion of foods within digestive zone, blood circulation, including small bowls and migration of urine. The main findings for the research is to analyze the flow rate change and check the behavior of velocity and temperature by using different parameters. The modeled equations of Carreau fluid flow are depressed into a simple form by employing the long wavelength approximation and small Reynolds number, then the resulting equations are calculated numerically by using MATHEMATICA. Impact of physical factors are graphically figured for velocity, temperature field and streamline distribution. The results show that velocity modifies by applying different values of flow rate and Darcy's number. Temperature profile increases for advanced values of Prandtl number, Eckert number and heat source parameter. For heat source parameter (γ = 0. 5 , 0.6 and 0.7) and Eckert number ( E c = 1. 0 , 1.5 and 2.0) the temperature profile expands at the region (y < 1. 0). [ABSTRACT FROM AUTHOR]

This paper presents the numerical study for heat generation and electro-osmotic effects of Carreau model of a fluid in an unsteady channel. This prepared model has many useful applications in microfluidic biological and mechanical research. Modified Darcy’s law, viscous dissolution and ciliated walls are also presented. Non-Newtonian fluids play a key role in biological fluids which include the motion of foods within digestive zone, blood circulation, including small bowls and migration of urine. The main findings for the research is to analyze the flow rate change and check the behavior of velocity and temperature by using different parameters. The modeled equations of Carreau fluid flow are depressed into a simple form by employing the long wavelength approximation and small Reynolds number, then the resulting equations are calculated numerically by using MATHEMATICA. Impact of physical factors are graphically figured for velocity, temperature field and streamline distribution. The results show that velocity modifies by applying different values of flow rate and Darcy’s number. Temperature profile increases for advanced values of Prandtl number, Eckert number and heat source parameter. For heat source parameter (γ=0.5, 0.6 and 0.7) and Eckert number (Ec=1.0, 1.5 and 2.0) the temperature profile expands at the region (y

The purpose of this article is to study the effect of electromagnetic (EM) stimulation on the pipeline, which has an electrical and thermal effect in addition to the chemical reaction on the crude oil and makes a sinusoidal wave on the wall. Modeling the crude oil as Carreau fluid is done. EM stimulation is an effective and safe technology that can be used to improve fluid movement in a variety of industrial applications. The flow analysis by applying EM may avoid blocking the crude oil pipeline which leads to a loss of production and capital investment. The basic partial differential equations of momentum, temperature and concentration are reduced to a system of nonlinear partial differential equations, which is solved numerically by using the Rung–Kutta–Merson method with Newton iteration in a shooting and matching technique under the assumption of long wavelength and the effect of physical implanted parameters is represented through charts for velocity, temperature, and concentration and numerical application. [ABSTRACT FROM AUTHOR]

This article investigates the effect of activation energy on Carreau fluid flow in the presence of variable thermal conductivity, inclined magnetic field, melting heat transfer, and Soret and Dufour phenomena. A set of suitable similarity transformations is applied for transforming the governing partial differential equations (PDEs) considered for the physical phenomena into non-linear ordinary differential equations (ODEs). We obtained the results by solving the non-linear ODEs numerically which describe the behavior of the velocity, temperature, and concentration profiles of the fluid against the governing parameters and illustrated these graphically. The velocity distribution decreases for angle of inclination while it is increasing against higher melting parameter. The temperature distribution enhances with higher modified Dufour parameter and Prandtl number while it declines for thermal conductivity, activation energy, and melting parameters. The concentration distribution increases for melting parameter, Soret number, and activation energy parameter while decreasing for temperature difference parameter, Schmidt number, and reaction rate parameter. Skin friction, Nusselt and Sherwood numbers are evaluated numerically against the various governing parameters. Accuracy of the present work is illustrated and established through comparison carried out for skin friction versus magnetic parameter with existing results in the literature. [ABSTRACT FROM AUTHOR]

The current work examines the significant impact of Carreau hybrid nanofluid, particularly in enhancing thermal conductivity and heat transfer efficiency, which is discussed through the integration of aluminium oxide (Al2O3) and titanium dioxide (TiO2) nanoparticles into a base fluid made of 50 % water and 50 % ethylene glycol solution. The study is concentrated on thermal radiation, chemical reactions, thermophoresis, Brownian motion, and viscous dissipation over an exponentially curved Riga surface. The governing partial differential equations are formulated in light of all of these factors. Subsequently, the original partial differential equations are transformed using boundary layer approximations and similarity variables to produce a dimensionless ordinary differential equation. The above equations are solved numerically using the shooting method and the MATLAB function bvp4c. The behaviour of heat and mass transfer in both shear thinning (pseudoplastic) fluids and shear thickening (dilatant) fluids is discussed in detail, and efforts are made to highlight some important parameters such as the Weissenberg number, the curvature radius, the modified Hartmann number, Thermophoresis, Brownian motion, and chemical reaction. The fundamental observation is that a rise in the Weissenberg number results in a reduction of skin friction and Nusselt number in shear thickening scenarios, whereas it leads to an increase in shear thinning scenarios. Increasing the modified Hartmann number results in elevated skin friction and a reduction in the Nusselt number for both shear thickening and shear thinning scenarios. These findings are advantageous for developing strategies applicable to heat control across many industries and biological sectors to enhance energy efficiency and system performance.

In this article, the mixed convection transport of the Carreau fluid in the presence of a magnetic field and a heated circular cylinder within a trapezoidal cavity is examined. Finite element analysis is used via COMSOL Multiphysics software to simulate the two-dimensional flow. The heat equation is formulated by incorporating the effects of viscous dissipation and Joule heating. The upper and lower surfaces of the cavity are adiabatic, while the left and right sides are assumed to be cold. The temperature distribution and flow field within the cavity are visualized through the plotting of isotherms, streamlines, and total entropy generation. The graphical representations are performed to examine the impacts of physical parameters on temperature, flow field, and total entropy generation, including the Reynolds number , Weissenberg number [Formula: see text], Power law index [Formula: see text], Hartman number [Formula: see text], and Richardson number [Formula: see text] and [Formula: see text]. It is found that the Joule heating and Richardson number are the main reasons to increase the thermal performance within the cavity. The r[Formula: see text] ising values of power law index and Weissenberg numbers caused to reduce the velocity field, irreversible effects and circulation within cavity. While the entropy is augmented by elevating the Eckert and Hartmann numbers. Furthermore, heat transfer improved with the increased magnetic field and Eckert number.

Many applications, including micro air vehicles, automotive, aerospace, refrigeration, mechanical–electromechanical systems, electronic device cooling, and micro heat exchanger systems, can be used to determine the heat flow in microchannels. Regarding engineering applications, heat flow optimization discusses the role of entropy production minimization. Therefore, this work explores new facets of entropy production in fully developed Carreau fluid heat transport in an inclined microchannel considering exponential space/temperature dependence, radiative heat flux, and Joule heating. The Carreau fluid model’s rheological properties are taken into account. Additionally, the influence of Hall slip velocity and convective boundary conditions is considered. Using appropriate transformation constraints, the governing equations are transformed into a system of ordinary differential equations, which are then numerically solved using the fourth- and fifth-order Runge–Kutta–Fehlberg method. Graphs illustrate a significant discussion of physical parameters on production of entropy, Bejan number, thermal field, and velocity. Our findings established that there is a dual impact of entropy generation for the exponential space/temperature-dependent, radiation parameter, Hall parameter, Weissenberg number, and velocity slip parameter. The Bejan number decreased with the Hall current and the Weissenberg number, and it enhanced with exponential space/temperature dependent. The convection constraint maximizes the entropy at the channel walls. The results are compared with exact solutions, which show excellent agreement.

Many scholars performed the analysis by using the non-Newtonian fluids based on the nano and hybrid nano particles in blood arteries to investigate the heat transport for cure in several diseases. These performances are presented to investigate the blood flow behaviour with extended form of the novel tetra hybrid Das and Tiwari nanofluid system attached by the Carreau fluid. The assessment of energy transport has been achieved based on the thermal radiation, heat source/sink, Joule heating, and viscous dissipation. The obtained partial differential equation from physical problem is transformed into ordinary differential equations (ODEs) by using the similarity variables. Furthermore, system of nonlinear ODEs attached with boundary conditions are transported into the system of first-order ODEs with initial conditions. For the numerical solution of obtained ODEs, the numerical solutions have been performed based on the RK method. The numerical results are plotted through figures, tables, and statistical graphs. Magnetic forces and inclined magnetic effects are caused to reduce velocity of blood. Temperature of blood within the arteries is increased by increasing the parameter of thermal radiation.

In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.

A theoretical study is examined to investigate the effects of enthalpy and radioactive heat transfer in generalized Newtonian fluid flow due to an inclined rotating disk. In order to examine the shear thickening phenomenon, Carreau fluid model is utilized. Here for the first time, Carreau fluid model under the enthalpy, thermophoretic effect, binary mixture and solar radiation effects are examined near an inclined rotating disk. In this study, the fluid flow does not give an analytical solution of the Navier–Stokes equations, except for the limit case, that is for high Reynolds number. The flow inside three-dimensional boundary layer flow is determined by the von Kármán transformations. The boundary layer equations are converted into system of ordinary differential equations by using von Kármán inequalities and solved numerically by employing shooting method. The effects of shear thinning and shear thickening fluids show a increase behaviour for base flow profiles. Thermal conductivity and mass diffusivity increases the temperature and concentration distributions. The azimuthal velocities increases by increasing values of $ \lambda _{T} $ λ T and $ \lambda _{C}\ $ λ C parameters. We present the numerical solutions for different physical parameters and discussed them for radial and azimuthal velocities and for heat and mass transfer profiles through graphs and tables. [ABSTRACT FROM AUTHOR]

This analysis aimed to explore the blood-based non-Newtonian hybrid nanofluid flow in elliptical stenosed artery with single- and multi-walled carbon nanotubes as nanoparticles. The Carreau fluid model is incorporated to assess the non-Newtonian rheology of blood-based nanofluid for mild stenosis. In particular, the carotid artery is responsible for delivering blood to the brain. If normal blood circulation is disrupted or in the case of severe stenosis, blockage of the carotid artery can lead to the development of brain disability or stroke, which in turn can lead to death. The idealized mathematical equation is transformed into a nondimensional form and solved analytically via the perturbation method through a novel polynomial technique. These analytical solutions are explored and explained graphically. The system’s disorder and variability are assessed by completing an entropy production analysis. The disruption in blood flow due to the presence of nanoparticles causes uncertainty in the flow nature. This uncertainty is dealt with by fuzzy analysis of temperature distribution by accounting for the nanoparticle volume fractions as triangular fuzzy numbers. It is noticed that stenosis shapes and height greatly impact the flow characteristics. The nanoparticles’ percentage in fluid affected the temperature profile. The non-Newtonian characteristics of blood are found to be more dominant along the minor axis, and an effectively higher disorder is produced in this direction. It is observed that the temperature of nanofluid emerged as a triangular fuzzy number of symmetric shape. [ABSTRACT FROM AUTHOR]

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.

The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyze the melting effect on the flow of Carreau fluid over a stretchable cylinder, with special consideration given to the impact of quadratic thermal radiation. Similarity variables and the homotopy analysis method are used to simplify and determine the semi-analytical homotopic solutions of the governing equations. The present findings reveal that the melting parameter increases the heat transfer rate by more than 10% for both fluids, water (Pr = 0.71), and polymer (Pr = 10). However, as the temperature ratio due to quadratic radiation increases, the local Nusselt number for water has been reduced by 25%, and an even more substantial reduction is observed for the polymer. The present study offers valuable insights into achieving optimal efficiency in electronic devices.

In this paper, we scrutinize the impacts of multi-slip with multi-stratification on nanoparticles MHD Carreau fluid flow through a time-dependent stretching sheet with thermal radiation. We obtain the solution upon the application of the Keller-box scheme with an implicit finite-difference scheme. The influence of thermal stratification and concentration stratification is also being measured. The differentce parameters' influence on the fluid flow is illustrated in diagrams and the quantitative numerical findings are well-argued. For increasing heavier species, fluid index and the reaction rate parameter with Prandtl number Pr = 5. 0 , 10.0 and 15.0 will decrease the concentration of fluid within its boundary limits. Behavior of Weisenberg number on fluid velocity is studied. Moreover, fluid velocity declines as the unsteady parameter rises, while the temperature and concentration significantly decrease. Higher values of solutal and thermal stratification parameters result in decay of velocity and thermal boundary layer thickness while the fluid temperature reflects the opposite behavior. [ABSTRACT FROM AUTHOR]

AbstractBlood flow through a narrowed artery, such as those caused by plaque buildup, can lead to various cardiovascular diseases. Therefore, studying this phenomenon is essential for developing better treatments and understanding the underlying mechanisms. In this study, a mathematical model is developed to simulate blood flow through stenotic arteries with porous walls. The familiar Navier-Stokes equations are executed to simulate flow, whereas the Carreau fluid model is employed to quantify blood rheology. This model illustrates both Newtonian and non-Newtonian characteristics depending on the shear rate. Other than that, the blood vessel is assumed to have a moderate level of stenosis with porous saturated walls. The solution of the governed partial differential equations is carried out using a finite difference scheme. Our research addresses the impacts of permeability and rheological parameters, stenosis size, Brinkman number, and Prandtl number on blood velocity, flow rate, resistance to flow, wall shear stress, and temperature distribution. The findings demonstrate that while flow resistance reduces, the velocity, shear stress, and flow rate increase with high permeability values. Conversely, as the stenosis amplitude increases, the magnitude of wall shear stresses, velocity, and flow rates decrease. In addition, blood rheology also has the potential to transfigure the aforementioned factors. We also found that the temperature distribution increases with the Brinkman number, stenosis size, permeability, and power law exponent. It drives down, however, by raising the values of Weissenberg number and Prandtl number. Collectively, our findings contribute to a better understanding of the complicated phenomena of blood flow in stenotic vessels with porous saturated walls. The findings of this study may be valuable in establishing improved therapies for cardiovascular disorders and formulating more precise mathematical models to forecast blood flow in vivo. [ABSTRACT FROM AUTHOR]

Advancement in thermodynamical characteristics of non-Newtonian fluid is achieved by induction of gyrotactic microorganisms in order to attain efficient thermal and mechanical engineering setups, such as micromixers, microfluidic instruments, biosensors and microdevices. So, the primer motive to conduct this research is to examine the effectiveness of gyrotactic microorganisms in managing heat transport in Carreau nanofluid flow over a linearly stretched surface under the effectiveness of opposing and assisting buoyancy forces. Physical aspect of magnetic field along with slip boundary constraint also entertained by employing in vertical direction. The governing equations are modelled in the form of dimensional PDE's and latterly transformed into dimensionless ODEs via similarity transformations. Solution of obtained set of differential system is solved by implementing Runge-Kutta of order 4 and shooting procedure. Visualizations about influence of flow concerning parameters on associated distributions are analyzed in comparative manner for opposing and assisting buoyancy parameter. In addition, metrics for quantities of engineering interest, such as heat and mass fluxes for nano and gyrotactic particles along with skin friction coefficient are calculated in a comprehensive manner.

For treating and diagnosing cardiovascular diseases, the field of biomedical engineering is significant because it develops new ways and techniques. Stenosis is the narrowing of an artery, and it leads reduction in the flow rate of blood. This study investigates the blood flow mechanism in an artery using a mathematical model of Carreau nanofluid with four distinct nanoparticles. Tetra nanofluid model produces significant advancement in the simulation of blood flow through the stenosed arteries. The model is capable of predicting the pressure drop and velocity distribution for diagnosing and treating stenosis. The spectral relaxation approach is used to present the model's efficiency and effectiveness, which makes it a suitable method for solving the governing equations of this study. The findings of this study have important implications for the development of new treatments and diagnostic techniques for stenosis and other cardiovascular diseases.

Abstract In this study, we investigate blood flow in a small artery with a constriction using gold nanoparticles (Au) in the presence of microorganisms, mass, and heat transfer. The non-Newtonian behavior of blood fluid in slight arteries is quantitatively inspected by simulating blood flow using the Carreau fluid model. Momentum equations incorporating magnetohydrodynamics (MHD) and Darcy–Forchheimer porous media are used to model the fluid flow. Heat transfer properties, including thermal radiation, joule dissipation, and bio-convective microorganisms, are investigated. Blood serves as the base fluid for the nanofluid, which contains gold nanoparticles. The system's nonlinear partial differential equations are transformed into nonlinear ODEs through suitable transformations. To obtain numerical solutions for these ODEs, the homotopy analysis method is used. The physical implications of flow restrictions are compared with fictitious fluid flow using physical interpretations. Additionally, investigations into the interpretations of blood flow based on drag force and heat transfer are being conducted. ANOVA, or analysis of variance, is a dependable statistical tool used to evaluate regression models and a variety of statistical tests. These investigations include error assessments, total error evaluations, F-values, p-values, and model fit assessments. These statistical investigations were applied to the dataset at hand, with the goal of achieving a robust 95% level of confidence. We investigate the effects of minute adjustments in parameters on both the heat transfer rate and the friction factor rate using these analyses. The study intends to dive deeper into the potential effects of minor changes in one or more factors on the overall effectiveness of surface friction rate and the larger domain of thermal energy transfer. This will be performed by employing sensitivity analysis approaches. This strategy allows us to obtain a better understanding of how minor changes to specific parameters might affect the speed of thermal energy conveyance and fluid flow management. Furthermore, it lays the framework for future studies aimed at optimising system designs. Article highlights We examined blood based MHD Au-nanofluid flow in the presence of microorganisms applying Carreau fluid model. To model the nanofluid flow we used, Darcy-Forchheimer porous media and heat transfer properties. Analysis of variance is a dependable statistical tool is used for the finding of regression models and a variety of statistical tests.

In this review, a quantitative research survey has been carried out on the peristaltic motion of Carreau fluid (CF), one of the most important generalized Newtonian fluids. This work primarily focuses on the fluid's diverse behavior as a result of the application of various methods and the broad overview of peristaltic Carreau fluids in a range of impacts such as Heat and Mass Transfer, Magnetohydrodynamic (MHD), stagnation point, stretching and shrinking sheet, porous medium and boundary layer. The various approaches that have been explored to depict this exquisite physiological transport system, which is frequently seen in nature, are summarized in this paper. The extensive study of biofluid peristaltic pumping pertaining to its importance in various fields, perspectives, and mathematical models is also discussed in depth. This analysis compares the major components and research results over the last 50 years and offers recommendations for future advancement. Researchers can use this analysis as a platform for building peristaltic transport for various applications.

The two-dimensional boundary layer of steady mixed convective magnetohydrodynamic Carreau dusty fluid flow across a stretched sheet was investigated in this study. The primary focus of this study is to examine the impact of Carreau nanofluid on dusty flow dynamics in the presence of the Lorentz force. The partial differential equations governing the fluid flow, temperature, and concentration fields for both the fluid and dust phases are transformed into ordinary differential equations using an appropriate set of similarity transformations. Numerical outcomes are acquired employing the Runge–Kutta technique combined with the shooting method, implemented on the MATLAB platform. The numerical outcomes are compared to previous research and confirmed to be in very good accord. Finally, the impacts of relevant factors of physical and technical importance on flow and thermal transport characteristics are visually and tabulated. The results for the linear density and the quadratic density profile, it is noted that the linear density decreases compared to the quadratic density for velocity, but the opposite behavior is observed for temperature profile. The advancement of dusty nanofluids has resulted in significant enhancements in the heat transfer mechanism, which finds application in manufacturing, industry, and nanotechnology research. Research on dusty flows benefits on is beneficial in air pollution studies, dust entrainment in a cloud formed during a nuclear, vehicle emissions of smoke and other pollutants, crude oil purification, petroleum production, combustion, industrial effluent emissions, capillary blood flow, paint sparing, and, more.

Blood flow analysis plays an essential role in understanding cardiovascular health and disease. An accurate mathematical modeling is necessary in context of representation of arterial domains and blood flow to learn about the intricate blood dynamics. In this paper we concentrate on the mathematical representation of the geometry of the blood artery and find numerical solutions with mild to severe degree of stenosis. Blood dynamics has steady state, in-compressible and laminar nature. The shear thinning non-viscous effects of blood are assumed to obey Carreau model. Fluid flow is based on coupled Navier-Stokes equation in three dimensions and is simulated with finite volume approach over hexahedral elements. Application of a constant mass flow rate at the inlet of the artery results in a number of observations to analyze. It is found that with increasing the severity of stenosis, blood velocity becomes higher in stenotic region, pressure drop along the arterial domain is increased and shear stresses exerted by blood on walls of artery are increased.

The main source of thermal energy is the sun, and with the increase in solar technology, it is now being utilized in many devices such as sun-based panels, photovoltaic cells, batteries and lights, solar fabric, solar water pumping, etc. Nowadays, improvement in flight effectiveness of solar aircraft by utilizing solar energy and nanotechnology is being studied by many scientists. This article is also based on studying the effectiveness of solar aircraft based on solar energy and nanotechnology. For this purpose, few properties of heat transfer among symmetrical wings will be analysed such as porous surface, thermal radiation, convective condition and heat source/sink. It is considered that the ternary hybrid nanofluid moves through the internal side of parabolic trough solar collector. The current study examines the radiative flow of a Carreau tri-hybrid nanoliquid across a convectively heated stretching surface in porous media. Also entropy generation on Carreau fluid is analysed in this work. Energy equation is modelled through heat source/sink and thermal radiation. The well-established numeric technique BVP4c has been used to solve the system of differential equations in the form of concentration, energy and momentum. Several flow variables on fluid velocity, temperature, drag friction, the Nusselt, entropy generation and Bejan number are described in figures and tables. The main outcomes of the current investigation are that the velocity and temperature lowered with augmenting values of Weissenberg number We . Results will prove that THNF is larger in the case of HNF and NF. Further, the drag friction and thermal efficiency of Thnf ( MoS 2 + SiO 2 + Fe 3 O 4 /EG ), Hnf ( MoS 2 + SiO 2 /EG ) and Nf ( MoS 2 /EG ) are computed in percentage with numerous values. The second finding is the addition of entropy due to the increasing magnitude of radiative flow, Carreau fluid variable. When comparing the current results to the reported results, we get a close match. [ABSTRACT FROM AUTHOR]

This study aims to investigate the impact of suction/injection on a quadratic mixed convection magnetohydrodynamics Carreau fluid over a stretching cylinder. The effects of heat generation, Joule heating, convective boundary conditions, and variable thermal conductivity in the fluid region are considered. The developed partial governing equations are transformed into ordinary differential equations using the similarity transformation technique and then solved using the homotopy analysis method to determine the analytic approximation solutions. Due to the numerous pertinent parameters, the variations of the heat and mass distribution, as well as the physical quantities, such as the local skin friction and the Sherwood and Nusselt number, are analyzed through graphs and tables. Quadratic convection has enhanced the movement of the fluid, heat transport, and mass transfer in a situation without inflow either at the surface of the cylinder or flat plate. The mass transition phenomenon has reduced the impact of quadratic convection. Furthermore, in the suction situation, the concentration and velocity of the fluid field are increased but an opposite tendency in the temperature distribution is observed. The present analysis is essential in controlling the quality of wire coating, pipe coating, or heat exchangers, which depends on the fluid characteristics, as well as its concentration and thermal diffusion. [ABSTRACT FROM AUTHOR]

Present work discusses the effects of channel wall thickness on MHD flow employing permeability effect on porous wall liner. Couette steady Carreau fluid flow in a parallel inclined plate's channel at an inclination λ to the horizontal. We also examined how tilted magnetic fields affect channel flow with slope angle β. We employ slip boundary conditions. Convective boundary conditions affect heat transmission. An incompressible Carreau fluid's governing system equations are in Cartesian coordinates. Low Reynolds number and negligible inertial effects progress the problem formulation. Similarity of nondimensional quantities converts flow controlling equations into conventional differentiation equations. Series solutions for axial velocity are obtained analytically by regular perturbation technique method (RPTM) when Weissenberg number is small, while the energy equation is solved numerically by "Explicit Euler" method with size step of (0.1). Plotting graphs shows the effects of Hartmann number, Darcy number, channel and magnetic field inclination angles, and others on velocity and temperature distributions by using Mathematica program software. [ABSTRACT FROM AUTHOR]

The motivation for this comparative examination is to verify and account for the appropriate source of heat energy needed in production industries, and to expunge the contradictions between Fourier's law and the theory of relativity. In heat management such as in engineering systems, the required heat for effective melting, production rate, etc. dictates the appropriate heat generation/injection module to be deployed. However, the material medium of heat transmission can be a hindering factor for a successful convection process, to this, an investigation of the instantaneous heat propagation paradox is required. An assumption of induced flow due to stretching characteristics is made, and an appropriate similarity transformation is deployed for the governing systems. By means of the Galerkin-weighted residual method, numerical solutions to the system of equations are approximated and validated. In a limited case, the solution compares favourably with existing literature, while the novel comparative investigation predicts the dominance of the Temperature-Dependent Heat Source (TDHS) capable of weakening the fluid cohesive force and upsurging the energy rate in short time in contrast to the Space-Dependent Heat Source (SDHS) module. The material relaxation phenomenon indicated that more time will be needed for prosperous/equal heat energy transfer. Further heat transfer enhancement is called for higher discharge of radiation and boosting of thermal conductivity, while TDHS module is strongly recommended in highly required heat systems. [ABSTRACT FROM AUTHOR]

This paper reports the hydromagnetic mixed convective flow of Carreau nanofluid in the vertical microchannel with slip and convective mechanisms at the boundaries. The main objective of this work is to analyze the conduct of Carreau nanofluid under Buongiorno model as the nano-dimensions of the particle consequently encounters random motion. The novel impression is to retain the outcomes of the flow in regard of Brownian dispersion and thermophoresis. Parameters such as buoyancy ratio, Brownian motion and thermophoresis along with the effect of Weissenberg number are discussed on distribution of flow, temperature and concentration by using graphical demonstration. Surface drag coefficients, transport rates of mass and heat are portrayed by numeric esteems. Boundary layer approximations are made use to tackle nonlinear ordinary differential equations and solved by Runge–Kutta–Fehlberg 4-5th-order method. Results so obtained elaborate that velocity depletes with increased values of buoyancy ratio and viscosity ratio parameter along with power law index. Also, distinct behavior is noticed in the profile of velocity for varying Weissenberg number by boosting and diminishing depending on the power law index. On the other hand, temperature rises by augmentation of thermophoresis and Brownian motion parameter. Elevation in Brownian motion parameter accelerate the concentration panel of the fluid. Skin friction and Nusselt number are in direct proportion with buoyancy ratio parameter and Brownian motion parameter, respectively. [ABSTRACT FROM AUTHOR]

The influence of radiation, convective heating, second-order velocity slip condition, and activating energy on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer are depicted in this study. A mathematical model of the Carreau nanofluid is carried out with the effects of thermophoresis and Brownian motion. The governing equations are transformed into a system of nonlinear coupled differential equations. Solutions of the transformed equations are derived by the Matlab BVP4c solver. Efficiency of the solver is verified by the comparison with the previous literature. Moreover, the impacts of the dimensionless velocity, temperature, and nanoparticle concentration profile are elucidated graphically. [ABSTRACT FROM AUTHOR]

In this article, the mixed convection transport of the Carreau fluid in the presence of a magnetic field and a heated circular cylinder within a trapezoidal cavity is examined. Finite element analysis is used via COMSOL Multiphysics software to simulate the two-dimensional flow. The heat equation is formulated by incorporating the effects of viscous dissipation and Joule heating. The upper and lower surfaces of the cavity are adiabatic, while the left and right sides are assumed to be cold. The temperature distribution and flow field within the cavity are visualized through the plotting of isotherms, streamlines, and total entropy generation. The graphical representations are performed to examine the impacts of physical parameters on temperature, flow field, and total entropy generation, including the Reynolds number , Weissenberg number $ ({1.0 \le We \le 6.0}) $ (1.0 ≤ We ≤ 6.0) , Power law index $ ({0.1 \le n \le 5.0}) $ (0.1 ≤ n ≤ 5.0) , Hartman number $ ({1.0 \le M \le 50}) $ (1.0 ≤ M ≤ 50) , and Richardson number $ ({0.2 \le Ri \le 5.0}) $ (0.2 ≤ Ri ≤ 5.0) and $ ({0.2 \le Rc \le 0.8}) $ (0.2 ≤ Rc ≤ 0.8). It is found that the Joule heating and Richardson number are the main reasons to increase the thermal performance within the cavity. The r $ ({100 \le Re \le 500}) $ (100 ≤ Re ≤ 500) ising values of power law index and Weissenberg numbers caused to reduce the velocity field, irreversible effects and circulation within cavity. While the entropy is augmented by elevating the Eckert and Hartmann numbers. Furthermore, heat transfer improved with the increased magnetic field and Eckert number. [ABSTRACT FROM AUTHOR]

The primary objective of this article is on examining the impacts of mixed convection flow of Carreau fluid past a permeable stretched surface with Soret and Dufour effects occurring. For the flow analysis, the Darcy–Forchheimer porosity medium is taken into account. In order to explore the transference analysis of heat and mass rate, the impressions of thermal radiation, viscous dissipation, heat generation, Arrhenius activation energy, convective heat, and mass conditions impacts are taken into consideration. The flow equations initially exist as PDEs, and we then employ appropriate similarity transformations to change them into ODEs. The R–K 4th order strategy based on the shooting approach is used to numerically solve these ODEs. Through various emergent variables, the numerical results for the velocity, temperature, and concentration fields are shown. For a variety of distinct variables, the physical quantities such as friction factor, local Nusselt number, and local Sherwood numbers are shown. It is noted that the velocity field is reduced by the magnetic field, but the Weissenberg number buoyancy ratio parameter exhibits the opposite tendency. Further, it is noticed that temperature and concentration distributions have an improving tendency for the Soret and Dufour parameter. [ABSTRACT FROM AUTHOR]

The characteristics of dual solutions of the flow of Casson or Carreau fluids mixed with microorganisms over a permeable shrinking surface are investigated considering the effects of the magnetic field, heat dissipation, Dufour, and thermophoretic diffusivity. By using similarity transformations, the governing equations are converted into a set of ordinary differential equations. These reduced equations are then solved by the well-known shooting technique along with the fourthorder Runge-Kutta method. A comparison is provided and the present solutions hold a good agreement with available published results. The local skin friction coefficient, local Nusselt number, local Sherwood number, and local density number of the microorganisms are found to increase with the increase of non-Newtonian Casson parameter, Dufour, and thermophoretic diffusivity number, however, it decreases with Weissenberg number. The remarkable finding which is not revealed yet is that dual solutions exist in the flow of Casson or Carreau fluids with microorganisms over a permeable shrinking sheet subject to a certain combination of parameters. Moreover, the domain of the occurrence of dual solutions broadens on account of higher values of all physical parameters of the problem except the Eckert number. [ABSTRACT FROM AUTHOR]

The main focus of the current work is to explore the thermal energy and mass transfer process in conducting non-Newtonian fluid flows through a horizontal microchannel along with irreversibility analysis and to investigate the upshot of nonlinear radiation, convective boundary conditions, and magnetic field. Slip regime and temperature jump conditions are used at the boundaries of the microchannel. The rheological characteristics of the Carreau fluid model are also considered. The Buongiorno model was used in this study, which emphasizes the light on Brownian motion and thermophoresis phenomena that occur during the fluid flow. Runge-Kutta Fehlberg's fourth-fifth order was used to solve governing equations numerically. The significant influence of effective parameters on entropy generation, Bejan number, velocity, temperature and concentration profile have been discussed with the aid of graphs. Entropy generation rises by 40% at the left wall of the channel and is depleted by 36% at the right wall when the thermophoresis parameter augments by 200%. Amplified concentration profile with an escalation of Brownian parameter. The temperature field diminishes with inflation of the radiation parameter. [ABSTRACT FROM AUTHOR]

In this study, we investigate blood flow in a small artery with a constriction using gold nanoparticles (Au) in the presence of microorganisms, mass, and heat transfer. The non-Newtonian behavior of blood fluid in slight arteries is quantitatively inspected by simulating blood flow using the Carreau fluid model. Momentum equations incorporating magnetohydrodynamics (MHD) and Darcy–Forchheimer porous media are used to model the fluid flow. Heat transfer properties, including thermal radiation, joule dissipation, and bio-convective microorganisms, are investigated. Blood serves as the base fluid for the nanofluid, which contains gold nanoparticles. The system's nonlinear partial differential equations are transformed into nonlinear ODEs through suitable transformations. To obtain numerical solutions for these ODEs, the homotopy analysis method is used. The physical implications of flow restrictions are compared with fictitious fluid flow using physical interpretations. Additionally, investigations into the interpretations of blood flow based on drag force and heat transfer are being conducted. ANOVA, or analysis of variance, is a dependable statistical tool used to evaluate regression models and a variety of statistical tests. These investigations include error assessments, total error evaluations, F-values, p-values, and model fit assessments. These statistical investigations were applied to the dataset at hand, with the goal of achieving a robust 95% level of confidence. We investigate the effects of minute adjustments in parameters on both the heat transfer rate and the friction factor rate using these analyses. The study intends to dive deeper into the potential effects of minor changes in one or more factors on the overall effectiveness of surface friction rate and the larger domain of thermal energy transfer. This will be performed by employing sensitivity analysis approaches. This strategy allows us to obtain a better understanding of how minor changes to specific parameters might affect the speed of thermal energy conveyance and fluid flow management. Furthermore, it lays the framework for future studies aimed at optimising system designs. Article highlights: We examined blood based MHD Au-nanofluid flow in the presence of microorganisms applying Carreau fluid model. To model the nanofluid flow we used, Darcy-Forchheimer porous media and heat transfer properties. Analysis of variance is a dependable statistical tool is used for the finding of regression models and a variety of statistical tests. [ABSTRACT FROM AUTHOR]

This research presents a numerical investigation for flow around a stagnation point on a vertical stretching cylinder placed in a pseudo-plastic fluid. An important Carreau fluid model is adopted to account for pseudo-plastic effects in the flow field. Buoyancy force term arising due to the vertical boundary is formulated under the well-known Oberbeck-Boussinesq approximation. Conservation equations simplified under boundary layer assumptions are solved for the similarity solutions for full range of parameter A, giving the ratio of free stream velocity to the cylinder surface velocity. The shape of velocity profile is dependent on the choice of the parameter A. Contributions of buoyancy force term and shear-thinning effect in both assisting and opposing flow situations are scrutinized. A striking influence of rheology is such that resisting wall shear declines and cooling rate of the surface drops whenever shear-thinning effect is present. However, cooling rate amplifies as the strength of buoyancy force is enhanced. Special cases of the model including the case of flat surface and Newtonian fluid are presented separately.

The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls. Thermal and concentration characteristics due to enthalpy change, activation energy, and non-linear thermal radiation have been examined in the presence of buoyancy forces. The channel walls for both temperature and volumetric fraction are assumed to be isothermal. The instability mechanism of nanofluids is reported using a two-phase nanofluid model, which works reasonably well for nanoparticle concentrations below a certain threshold. A Jeffery-Hamel (J-H) flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation. Using the suitable non-dimensional variables, the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations. The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c, on the template form of commercial software MATLAB. The impacts of material, geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated. Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure, while a slight reduction is perceived in opposing forces. A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter. For endorsing this communication, a comparison analysis is established with existing research and noticed a remarkable agreement. Practically, the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies, high heat-flux condensed heat exchangers, high-performance micro-electronic cooling systems, jets, rockets nozzles, and jet propulsion inlet.