Carreau Fluid Model Research Articles

Influences of stenosis and transplantation on behavior of blood flow in the host and grafted vessels using computational fluid dynamics

In this research, the changes of wall shear stress (WSS) of flow blood affected by stenosis and grafted vessels are studied. For the simulation of non-Newtonian fluid, blood in this paper, the Carreau fluid model is used. The severity of the stenosis is considered to reduce the internal cross-sectional area of the host vessel by 30 %. In this paper, simulations are performed on the human body in sports, which are classified into anemia (LHD), normal (NHD) and high blood pressure (HHD). Results are presented in three sections including after stenosis region, transplantation section, and after transplantation region by calculating wall shear stress (WSS). It is reported that wall shear stress is increased after stenosis location due to immediate variation in the cross-section area when blood flows. To explain, Stenosis reduces the cross-section area of the vessel which causes flow contraction. Consequently, this phenomenon increases flow velocity in the central region of blood flow whereas, after passing from stenosis, blood flow is exposed to an abrupt expansion which causes flow back from the central region to wall vicinity in lateral regions of the vessel. Maximum amounts of wall shear stress are achieved at 280 Pa, 350 Pa, and 550 Pa for anemia, normal, and hypertensive individuals in order. However, the consequence of the mentioned phenomenon in hypertensive individuals is more severe than that of anemic ones. Therefore, the geometry of veins is very important in medical surgeries to prevent vessel failure, especially in stressful points of transplantation.

Non-Newtonian blood flow across stenosed elliptical artery: Case study of nanoparticles for brain disabilities with fuzzy logic

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.

Convective heat transfer with Hall current using magnetized non-Newtonian Carreau fluid model on the cilia-attenuated flow

PurposeCilia serves numerous biological functions in the human body. Malfunctioning of nonmotile or motile cilia will have different kinds of consequences for human health. More specifically, the directed and rhythmic beat of motile cilia facilitates the unidirectional flow of fluids that are crucial in both homeostasis and the development of ciliated tissues. In cilia-dependent hydrodynamic flows, tapering geometries look a lot like the structure of biological pathways and vessels, like airways and lymphatic vessels. In this paper, the Carreau fluid model through the cilia-assisted tapered channel (asymmetric) under the influence of induced magnetic field and convective heat transfer is investigated.Design/methodology/approachLubrication theory is a key player in the mathematical formulation of momentum, magnetic field and energy equations. The formulated nonlinear and coupled differential equations are solved with the aid of the homotopy perturbation method (HPM). The graphical results are illustrated with the help of the computational software “Mathematica.”FindingsThe impact of diverse emerging physical parameters on velocity, induced magnetic field, pressure rise, current density and temperature profiles is presented graphically. It is observed that the cilia length parameter supported the velocity and current density profiles, while the Hartman number and Weissenberg number were opposed. A promising effect of emerging parameters on streamlines is also perceived.Originality/valueThe study provides novel aspects of cilia-driven induced magnetohydrodynamics flow of Carreau fluid under the influence of induced magnetic field and convective heat transfer through the asymmetric tapered channel.

Ramification of Hall effects in a non-Newtonian model past an inclined microchannel with slip and convective boundary conditions

Abstract 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.

Integrating the complex rheological Carreau model with the Graetz-Brinkman problem in a horizontal passage

ABSTRACT The current investigation emphasizes the influence of viscous dissipation in laminar forced convection internal flow for horizontal conduit using the non-Newtonian fluid. A Carreau fluid model is taken into account. The hydrodynamically developed velocity profile is obtained by employing a perturbation approach. A classical Graetz approach is utilized to achieve the solution of the developed energy equation while the MATLAB built-in command bvp4c is taken into account for the solution of the Eigenvalue problem. The negligible axial conduction and uniform physical characteristics are presumed. The influence of the viscous dissipation and model parameters on non-dimensional bulk temperature and Nusselt number is deliberated for both cooling and heating situations. The current analysis is valid for small values of Weissenberg number We ≤ 1 . The findings reveal that viscous dissipation has a significant impact on temperature distribution in both developing and fully established regions.

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.

A comparative study of Newtonian and non-Newtonian blood flow through Bi-Leaflet Mechanical Heart Valve

The present study examines flow through Bi-Leaflet Mechanical Heart Valves (BMHV) at physiological conditions considering both Newtonian and non-Newtonian fluid models for blood rheology. It is well known that the non-Newtonian effects of blood are pronounced in small diameter arteries. Most of the earlier works on Mechanical Heart Valves (MHV) have considered blood as a Newtonian fluid as the flow involves large-diameter artery such as the aorta. In this work, we have reported the predicted parameters, such as leaflet kinematics, vortex structures, wall shear stress, and blood damage index for both blood models. It is found that the leaflet attributes smaller asynchronous motion in the case of non-Newtonian Carreau fluid model with slightly reduced angular velocity compared to the Newtonian assumption. Predictions on the blood damage index suggest a 21% higher damage while using non-Newtonian model than Newtonian model, which may be attributed to higher levels of mechanical stress within the fluid. However, vortex structures, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) are found to be similar in predictions using both the fluid models. We have used an in-house sharp interface immersed boundary method with fluid–structure interaction to simulate the coupled action of moving valves and pulsatile blood flow. Our findings suggest that the general consensus of using Newtonian model in large arteries may not be appropriate for prediction of leaflet kinematics and blood damage index in Mechanical heart valves.

Multifaceted simulation: Finite volume and finite element modeling of blood flow in multiple stenosed arteries

Cardiovascular illnesses are a primary global health concern because they are frequently brought on by arterial stenosis. The complicated hemodynamics of blood flow via elliptically shaped arteries with numerous stenotic lesions along their top and bottom walls are examined in this paper. Carreau fluid model is used with Navier–Stokes equations in this study. The complete comparative study is done by using the Finite Element and Finite Volume Methods. This study uses commercial software to examine blood flow velocity, pressure and temperature distributions under various physiological situations at Reynolds number 30. Our results illuminate the interaction between flow dynamics, stenosis characteristics, and arterial geometry. The novelty of the work is to investigate how stenosis size, shape, and location affect pressure gradients, and flow disturbances. These observations provide helpful direction for understanding disease progression, designing treatments, and possibly new stent designs. The future direction of this research may involve further exploration of the interplay between hemodynamics and arterial stenosis by incorporating advanced computational models. Additionally, studies focusing on in vivo validation and clinical applications could enhance the translational impact of the findings. Collaborations between researchers, clinicians, and engineers may pave the way for personalized treatment strategies and innovations in cardiovascular care based on a deeper understanding of the intricate dynamics within diseased arteries.

Exploring the role of nanoparticles in enhancing thermal performance of fractional Carreau fluid flow under magnetic field and hall current

Nanofluids garner significant scientific interest due to their exceptional heat-conducting abilities and potential to enhance heat transfer efficiency. This manuscript investigates the behavior of a two-dimensional fractional Carreau fluid model on a stretched sheet over time, incorporating convection, magnetic fields, nanoparticles, diffusion, and thermal radiations. The model elucidates viscoelastic nanofluids’ memory and inheritance properties, employing non-integer Caputo fractional derivatives innovatively. Fundamental equations are transformed into dimensionless form and solved using an explicit finite difference approach. Essential parameters like Skin friction coefficient, Nusselt number, and Sherwood number are accurately determined. Rigorous stability and convergence criteria ensure effective solution convergence. Visual representations demonstrate the significant impact of each parameter on fluid flow. It is noted that temperature gradient increases 49.38% with the increase of fractional exponent α while it decreases 13.39% with the increase of magnetic parameter M. Moreover, concentration gradient increases 66.48% with the increase of thermophoresis parameter Nt and 94.71% with the increase of pedesis parameter Nb.

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.

Numerical study of binary mixture and thermophoretic analysis near a solar radiative heat transfer

The main focus of the current article is to investigate the two-dimensional boundary layer flow of non-Newtonian fluid induced by a linear stretching surface in the streamwise direction. The flow features of non-Newtonian fluid (i.e. shear-thinning and thickening nature of the fluids) are explored with Carreau fluid model. In addition, thermophoresis, Brownian motion, thermal radiation (with Rosseland approximation), binary mixture and activation enthalpy are also incorporated in fluid model for better analysis of thermal and solutal properties. The mathematical modelling of under consider physical problem yields nonlinear partial differential system. The governing mathematical system is first simplified with scaling transformations for the high Reynolds number and then transformed into non-dimensional ordinary differential system by using the similarity variables. Since the governing mathematical system comprised on nonlinear boundary value problem, thus shooting method is utilized for the numerical solution of the fluid flow governing equations. The obtained results followed the qualitative manners of the previously reported data. The computed results for important physical quantities (i.e. velocity, temperature, and concentration) are presented through graphs and then interpreted physically. It is observed that the boundary layer thickness increased for shear thickening fluids (n>1) while it is reduced for shear thinning fluids (n<1). Also, the temperature of shear thinning fluid is higher than shear thickening fluid. In addition, heat generation and thermal radiations enhance the thermal boundary layer. Thermophoretic viscosity effect reduces the concentration profile significantly in the flow domain.

Thermal transport exploration of ternary hybrid nanofluid flow in a non-Newtonian model with homogeneous-heterogeneous chemical reactions induced by vertical cylinder

Studying the combination of convection and chemical processes in blood flow can have significant applications like understanding physiological processes, drug delivery, biomedical devices, and cardiovascular diseases, and implications for various fields can lead to developing new treatments, devices, and models. This research paper investigates the combined effect of convection, heterogeneous-homogeneous chemical processes, and shear rate on the flow behavior of a ternary hybrid Carreau bio-nanofluid passing through a stenosed artery. The ternary hybrid Carreau bio-nanofluid consists of three different types of nanoparticles dispersed in a Carreau fluid model, miming the non-Newtonian behavior of blood. This assumed study generates a system of PDEs that are processed with similarity transformation and converted into ODEs. Furthermore, these ODEs are solved with bvp4c. The results show that the convection, heterogeneous-homogeneous chemical processes, and shear rate significantly impact the bio-nano fluid’s flow behavior and the stenosed artery’s heat transfer characteristics.

Numerical comparison of nonlinear thermal radiation and chemically reactive bio-convection flow of Casson-Carreau nano-liquid with gyro-tactic microorganisms: Lie group theoretic approach

The current research presents a mathematical model to study the flow of a non-Newtonian magnetohydrodynamics (MHD) Casson-Carreau nanofluid (CCNF) over a stretching porous surface, considering mass and heat transport rates with Stefan blowing, non-linear thermal radiation, heat source-sink, chemical reaction, thermophoretic and Brownian motions, convective heating, Joule heating, motile microorganisms, and bio-convection. The presence of microorganisms is utilized to control the suspension of nanomaterials within the nanofluid. The current flow model has been rendered by the boundary layer approximation and we get the highly nonlinear partial differential equations (PDEs). These nonlinear PDEs are simplified by the novel Lie group theoretic method. The one-parameter Lie scaling method simplified the PDEs and convert it into the ordinary differential equations (ODEs). Numerical solutions for these ODEs are obtained using the bvp4c scheme built-in function in MATLAB, ensuring reliable outcomes for temperature, velocity, concentration, and motile microorganism density profiles. The numerical results are presented through graphs and compared with available data, showing good agreement. These numerical outcomes reveal several important flow characteristics. Rates of change for Nr are 0.0007 and 0.0005, and for Ω, they are −0.0754 and −0.0536, respectively. Similarly, the rate of change for Rb in both models is −0.002 and −0.0002. Analysis shows a positive impact of the bioconvection Rayleigh number in both models, notably higher for the Casson fluid compared to the Carreau fluid model. Buoyancy ratio parameter exhibits consistent rates of change, while the reduction in impact is more pronounced for the Casson fluid model in the case of the mixed bioconvection parameter. The mixed bio-convection parameter reduces momentum velocity for both Casson and Carreau fluids, whereas the Darcy parameter boosts fluid velocity. As the Newtonian heating parameter increases, the temperature velocity distribution of both fluids also increases. The concentration profile of both Casson-Carreau fluid phases declines as the heat source-sink parameter and Schmidt number increase. Microbial velocity shows a decrease with increasing R values, whereas the opposite trend is observed for the Peclet number Pe.

An extended model to assess Jeffery–Hamel blood flow through arteries with iron-oxide (Fe2O3) nanoparticles and melting effects: Entropy optimization analysis

Abstract Nanofluids are utilized in cancer therapy to boost therapeutic effectiveness and prevent adverse reactions. These nanoparticles are delivered to the cancerous tissues under the influence of radiation through the blood vessels. In the current study, the propagation of nanoparticles within the blood in a divergent/convergent vertical channel with flexible boundaries is elaborated computationally. The base fluid (Carreau fluid model) is speculated to be blood, whereas nanofluid is believed to be an iron oxide–blood mixture. Because of its shear thinning or shear thickening features, the Carreau fluid model more precisely depicts the rheological characteristics of blood. The arterial section is considered a convergent or divergent channel based on its topological configuration (non-uniform cross section). An iron oxide ( F e 2 O 3 {\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3} ) nanoparticle is injected into the blood (base fluid). To eliminate the viscous effect in the region of the artery wall, a slip boundary condition is applied. An analysis of the transport phenomena is preferred using the melting heat transfer phenomena, which can work in melting plaques or fats at the vessel walls. The effects of thermal radiation, which is advantageous in cancer therapy, biomedical imaging, hyperthermia, and tumor therapy, are incorporated in heat transport mechanisms. The governing equation for the flow model with realistic boundary conditions is numerically tickled using the RK45 mechanism. The findings reveal that the flow dynamism and thermal behavior are significantly influenced by melting effects. Higher Re \mathrm{Re} can produce spots in which the track of the wall shear stress fluctuates. The melting effects can produce agitation and increase the flow through viscous head losses, causing melting of the blockage. The maximum heat transfer of 5 % 5 \% is achieved with We {\rm{We}} when the volume friction is kept at 1 % 1 \% . With higher estimation of inertial forces Re \mathrm{Re}\hspace{1em} and same volume friction, the skin drag coefficient augmented to 34 % 34 \% . The overall temperature is greater for the divergent flow scenario.

Pulsatile pressure-driven non-Newtonian blood flow through a porous stenotic artery: A computational analysis

Blood 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.

Neural networking-based analysis of heat transfer in MHD thermally slip Carreau fluid flow with heat generation

The formulation of heat transfer in non-Newtonian fluid models remains a topic of great interest for researchers. The ultimate flow differential equations in this direction are non-linear and hence difficult to solve analytically. Therefore, we offer state of the art determination of film effectiveness (heat transfer coefficient) by using artificial intelligence (AI). To be more specific, the Carreau fluid model is formulated at a flat surface along with thermal slip, heat generation, velocity slip, chemical reaction, and magnetohydrodynamics (MHD) effects. The developed equations are reduced by the application of the Lie symmetry approach and solved by the shooting method. The artificial neural networking model is built by using 132 sample values of the Nusselt number (NN) as an output. Porosity parameter, Prandtl number, magnetic field parameter, and heat production parameter are all inputs. 92 (70 %) is designated for training, whereas 20 (15 %) is designated for validation and testing. The Levenberg-Marquardt algorithm is used to train the neural network. The constructed artificial neural networking (ANN) is best to predict the NN at a flat surface. It is observed that for large Prandtl numbers, the magnitude of the Nusselt number is greater for porous surface, but the converse is true for magnetic field parameter.

Numerical Computational of Blood Flow and Mass Transport in Stenosed Bifurcated Artery

Stenosis refers to the narrowing of blood vessels caused by atherosclerosis, which can lead to serious circulatory problems by obstructing blood flow and mass transfer to other organs and tissues in the body. The objective of this investigation is to numerically examine the mass transfer of blood flow in a stenosed bifurcated artery using COMSOL Multiphysics, based on the finite element method. The study takes into account the geometry of a bifurcated artery with stenosis present at the mother and daughter arteries. The blood vessel is modeled as a two-dimensional (2D) rigid wall, and the blood flow is assumed to follow a non-Newtonian Carreau fluid model, being incompressible, laminar, and steady. The continuity equation, momentum equation, and mass transfer equation, along with boundary conditions, will be solved using COMSOL Multiphysics based on the finite element method. The simulation results show that the formation of recirculation zones, as indicated by streamline patterns and mass concentration, can significantly impact the severity of stenosis and Reynolds numbers. Thus, individuals exposed to such recirculation zones may be at risk of developing cardiovascular diseases.

Response surface optimization and sensitive analysis on biomagnetic blood Carreau nanofluid flow in stenotic artery with motile gyrotactic microorganisms

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 highlightsWe 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.

Electromagnetohydrodynamic (EMHD) convective transport of a reactive dissipative carreau fluid with thermal ignition in a non-Darcian vertical duct

A mathematical model is developed to simulate the steady, laminar exothermic reactive electromagneto-hydrodynamic combustible non-Newtonian natural convective transport in a vertical duct. Static uniform axial electrical field and transverse magnetic field are imposed. The Frank-Kamenetskii thermal explosion theory is utilized and also the Carreau fluid model, the latter due to its ability to simulate shear-thinning, Newtonian and shear-thickening behaviour. The duct contains a homogenous, isotropic porous medium and to accomodate Forchheimer inertial drag effects, a non-Darcian model is deployed. The duct walls are permeable enabling suction and injection effects to be studied. Viscous and Joule heating (Ohmic dissipation) are also featured in the model. Following a scaling transformation, the dimensionless emerging non-linear ordinary differential boundary value problem is solved with a robust numerical method (Mathematica shooting algorithm). Validation with an Adomian decomposition method (ADM) is included.

Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study

BackgroundThe roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. MethodBy taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. ResultsThe graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life.