Flow Of Maxwell Fluid Research Articles

Significance of Cu-Fe3O4 on fractional Maxwell fluid flow over a cone with Newtonian heating

The goal of this research is to investigate fractional Maxwell hybrid nanofluids utilizing partial differential equations in terms of Caputo time fractional derivatives. Specifically, the effect of Newtonian heating on the thermal performance of a fractional Maxwell hybrid nanofluid moving over a permeable cone in the presence of thermal radiation and heat generation is considered. The Crank–Nicolson method and L1 algorithmt of Caputo derivative are used to find numerical solutions to the considered nonlinear problem. The effects of significant flow factors on fluid properties are examined and illustrated in various graphs. According to the results, the thermal performance of the fluid raised by 0.4%, 6.1%, and 3.1% on adding 4% volume fraction of Fe3O4, Cu, and Cu−Fe3O4, respectively, in the base fluid.

A comparative study on the rheological properties of upper convected Maxwell fluid along a permeable stretched sheet

The objective of this paper is to examine the flow of a non-Newtonian Maxwell fluid induced by a permeable stretching sheet in motion within a porous medium. The research incorporates the Cattaneo-Christov heat flux model to study the heat transfer process. The utilization of the Cattaneo-Christov heat flux approach becomes relevant in scenarios involving materials with high thermal conductivity or during short time intervals. Consequently, the current investigation holds significant importance. It is assumed that the viscosity of the Maxwell fluid changes exponentially as the temperature changes. The modeling of the physical phenomena being investigated takes into account the effects of a magnetic field, thermal radiation, velocity, and thermal slip conditions. In this study, the viscous dissipation phenomenon is taken into account because it can have notable impacts on the temperature and viscosity of the fluid, and is known to play a crucial role in fluid flow phenomena. The equations developed to model fluid flow are transformed into nonlinear ordinary differential equations through the use of appropriate similarity transformations. The focus of the research revolves around investigating the numerical solution of ordinary differential equations accompanied by boundary conditions using the shooting technique. The findings are then showcased via tables and graphs and scrutinized in order to arrive at conclusions. Furthermore, the precision of the present findings was evaluated by contrasting the heat transfer rate with outcomes that were previously published. Based on the obtained outcomes, it can be concluded that both the Eckert number and thermal radiation have a comparable enhancing influence, whereas the thermal relaxation parameter and thermal slip parameter exhibit opposing effects.

Impact of charged soft layers on electroosmosis of Maxwell fluids in soft nanochannels

In the present paper, we theoretically study the transient electroosmotic flow of general Maxwell fluids through the polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain the transient electroosmotic flow from the Cauchy momentum equation and the Maxwell constitutive equation. For the nanochannels grafted with polyelectrolyte layers having different layered distributions of charges, we consider the influence of the dimensionless relaxation time, the dimensionless polyelectrolyte layer thickness, and the dimensionless drag coefficient on the transient electroosmotic flow. We present the results for some particular cases. First, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, the total electroosmotic flow is non-zero. In particular, depending on charge distribution within the end part of polyelectrolyte layers, the direction of the electroosmotic flow can be reversed critically. Second, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between the layered charge densities of two polyelectrolyte layers. Increasing ks allows the electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can intentionally control the direction of the flows as well as the strength of electroosmotic flow.

Analysis of physiological pulsating flow of fractional Maxwell fluid in a locally narrow artery

The purpose of this paper is to provide a novel reference for the early diagnosis and treatment of atherosclerosis. Two-dimensional governing equations of fractional-order Maxwell fluid flow in a local stenotic artery are established, taking real physiological pulsating blood flow at inlet into consideration. Drawing support from the finite difference method as well as the L1 formula, vorticity and stream functions are introduced to acquire numerical solutions for velocity, stream function, and pressure. The distribution of blood flow in narrowed arteries within a real physiological pulse cycle is discussed. Furthermore, the influences of the degree of stenosis δ, the stenosis length parameter L0, fractional order parameter α, and relaxation time λ on crucial medical indicators, including the time average of the wall shear stress, oscillatory shear index, relative residence time, and pressure distribution are revealed. The results show that the deceleration and reversal phases of real physiological pulsatile flow critically affect the progression of arterial stenosis, and increasing the fractional order parameter α weakens the development of stenosis, while increasing λ has the opposite effect. This study is expected to serve as a reference for formulating standards of key medical indicators in the early diagnosis of vascular stenosis.

Heat transfer enrichment in magnetohydrodynamic cylindrical flow of Maxwell fluid with thermal radiation and Stefan blowing effects

Energy transfer and boundary layer flow on a stretching cylinder are used in extrusion procedures, fiber technology, the manufacture of polymer sheets, and the creation of plastic films. In view of these applications, this article examines a transport model for a boundary layer flow with magnetohydrodynamics derived from a Maxwell fluid flow under the influence of radiation, Brownian motion, thermo phoresies and Stefan blowing on a stretching cylinder. Using MATLAB bvp4c function, the governing equations are numerically solved after being changed into ordinary differential equations via similarity renovations. Calculations and analyses determined how various emergent parameters affected the flow field, heat transfer and mass transfer. Some characteristics were discovered to affect the width of the boundary layer. The influence on MHD (M), radiation (Rd), the Schmidt number (Stc), Brownian motion (Nb), thermo phoresies (Nt) and the Stefan blowing parameter (Sb) on the velocity, energy and concentration profile have been explored. Excellent assessment is recognized over a tabular explanation to validate the adopted numerical technique. Significantly the Stefan blowing parameter rises the profiles on velocity and temperature. For an increasing value of the Maxwell fluid parameter, the skin friction coefficient decreases compared to the Stefan parameter.

Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects.

Thermal Efficiency of Spherical Nanoparticles Al2O3-Cu Dispersion in Ethylene Glycol via the MHD Non-Newtonian Maxwell Fluid Model Past the Stretching Inclined Sheet with Suction Effects in a Porous Space

The flow of nanoparticles has many dynamic applications in solar systems, the thermal sciences, heating and cooling mechanisms, energy-producing sources, and many other disciplines. Following invaluable applications and inspiration, the current study is carried out by focusing on the thermal efficiency of spherical nanoparticles of Al2O3-Cu in ethylene glycol through the non-Newtonian Maxwell fluid flow model. In the current analysis, the inclined stretching sheet equipped with suction effects is embedded in porous media, including the magnetohydrodynamics effects. The mathematical representation of the proposed problem is given a form in terms of partial differential equations. Then, this system is reduced to a system of ordinary differential equations by using appropriate similarity variable formulations. The obtained model is solved with bvp4c solver for the graphical and tabular aspects of the velocity field, the temperature field along with the skin friction coefficient, and the Nusselt number. The main outcomes of the results indicate that fluid velocity increases with increasing values for the angle of inclination, Maxwell fluid parameter, and suction parameter; however, the reverse process is seen for the porous medium parameter and magnetic field parameter. Moreover, the fluid temperature rises for augmenting values of the magnetic field parameter and porous medium parameter, whereas the opposite behavior is seen against the suction parameter. The present results are compared with the published ones and it is concluded that there is excellent agreement between them, which endorses the validity and accuracy of the current study.

Effectiveness of thermal radiations and homogeneous–heterogeneous reactions in Maxwell flow field across a rotating cylinder

This paper investigates the impact of cubic autocatalysis on energy transport in Maxwell fluid flow induced into a rotating cylinder inspired by a solar radiative surface. The homogeneous-reaction is assumed to be furnished by the kinetics of isothermal cubic autocatalytic and the heterogeneous reaction by kinetics of first order. To prevent induced axial secondary flow, the cylinder's rotation is maintained at a constant rate. The characteristics of thermal radiation are also investigated to regulate the pace of heat transmission. A magnetic beam is projected in the upward radial direction to control the fluid momentum. A suitable flow ansatz is used to convert the entire physical problem of thermal energy transmission and fluid flow from partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). Results obtained numerically with the bvp4c approach are presented graphically and explained physically. It is observed that by flourishing the Reynolds parameter, the penetration depth decreases. Further, when the thermal relaxation period increases, the temperature field degrades. Moreover, when the homogeneous–heterogeneous reaction's strength is increased, a reduction in fluid concentration is shown.

The generalized Fourier’s and Fick laws effects on MHD free convection flows of Maxwell fluids by employing Caputo–Fabrizio time-fractional integral

The relevance of time-dependent magneto-free convection and its consequences for mass and energy transport are being increasingly understood in science. Unfortunately, very little is known about how the fractional generalized technique would affect a complete analysis of Maxwell fluid dynamics over a porous plate. Using the Caputo–Fabrizio time-fractional integral, the Fourier thermal flux law and the fractionally generalized Fick’s equation of mass flow are both generalized. Using the appropriate similarity transformations allows us to characterize the structured governing equations, which are nondimensionalized. The dimensionless energy, concentration, and velocity distribution problem is solved using the Laplace transform method. The graph demonstrates how physical and fractional parameters are affected. Fractional derivatives may be employed to accurately represent the rheology of such fluids. The Maxwell generalized fluid across an oscillating sheet was studied by Zheng et al. 3

Squeeze flow of a Maxwell fluid between two parallel disks or two spheres

In this study, we investigated the squeeze flow of an upper convected Maxwell fluid between two rigid disks or spheres. It has been proved that the velocity field of the Maxwell squeeze flow between two disks is similar to Newtonian at low Deborah numbers. Based on the Newtonian fluid velocity field, we analyze the pressure distribution between two parallel disks and develop a theoretical model of normal squeeze force. We also use the same method to analyze the interaction between two nearly contacting, arbitrary rigid spheres. We obtained the analytical expression of the pressure distribution and normal squeeze force, which can be implemented into the contact model for the discrete element simulation of a wet particle system with the Maxwell fluid.

Significance of improved heat conduction on unsteady axisymmetric flow of Maxwell fluid with cubic autocatalysis chemical reaction

This paper investigates the effect of chemical reactions on the flow of magnetized Maxwell fluid generated by an unsteady stretching surface. The thermal transport phenomenon is analyzed by using the Cattaneo-Christov theory. By applying the appropriate similarity transformations, the governing equations of motion turn into a set of nonlinear differential equations. For the velocity, temperature, and concentration fields, the resultant equations are then solved as series solutions using the homotopy analysis approach. Using graphical representations, the physical behavior of significant factors is examined in depth. The analysis reveals that higher Maxwell parameter values reduce the flow field while increasing energy transportation in the fluid flow. Further, it is noted that thermal distribution declines for the higher values of the thermal relaxation parameter. Additionally, the solutal distribution bootup for the increasing values of Schmidt number while it shows a decreasing trend for homogeneous and heterogeneous reactions strength. In order to verify our findings, a comparison to earlier research is also included.

Chemotaxis bioconvection in swirling flow of Maxwell fluid with diffusion-thermo and thermal-diffusion effects

The dynamics of the chemotaxis mechanism for the bioconvection in the fluid motion engender by the swirling movement of a flexible heated cylinder is the core concern of the present investigation. The cylinder movement is basically combination of constant rotation and axial dependent stretching. The non-linear viscoelastic fluid is considered here with the time relaxation phenomenon. Moreover, the fluid also contains the gyrotactic micro-species. In energy transportation analysis the impact of thermal and concentration gradients on solutal and thermal transportation of energy, respectively, is analyzed with the help of the Soret-Dufour theory. The magnetic field is applied as an external constraint in the flow present problem. The problem governed by non-linear differential equations is solved with help of bvp5c function. The outcomes of the present problem are expressed in graphical forms and explained in the view of practical implementation. Each result of the study reflects the impact of non-dimensional parameters on flow, energy, and bio-convection phenomena. It is depicted that fluid temperature increases for Soret and Dufour number because these effects prevent the solutal deposition and serve as a coolant for surface boundary.

THE CONVECTIVE FLOW OF MAXWELL FLUID DRIVEN BY TWO ROTATING AND SPINNING DISKS

The present work addresses the axisymmetric flow of Maxwell fluid between two stretchable and rotating disks with porous regime. The influence of velocity slip and convective heat transfer are considered to govern the flow. The energy equation is modeled using Cattaneo-Christov heat flux model. The resulting mass, momentum and energy PDE’s are converted to ODE’s by using the Von Karman similarity transformations. Successive linearization method is implemented for numerical solution. The tangential velocity of the fluid increases with the rotating speed of the disks. The enhancement in the convective heat transfer of lower disc results in the rise of temperature profiles whereas temperature falls with the rise in Biot number of the upper disk.

Numerical investigation of MHD Cattaneo–Christov thermal flux frame work for Maxwell fluid flow over a steady extending surface with thermal generation in a porous medium

This study examines thermal diffusion's impact on thermal transport in magnetohydrodynamic (MHD) mixed convection using the Cattaneo–Christov thermal flux framework. It investigates a fluid with Maxwellian nature over an extending sheet with a magnetic field, thermal dissipation, and suction/injection phenomena. By transforming the governing partial differential equations into interconnected ordinary differential equations, the study employs the RK-Fehlberg technique for computational calculations. The results align with previous research, showcasing velocity and temperature profiles, local skin-friction coefficient, local Nusselt number, and thermal generation for different parameters. The study concludes that porosity and Deborah number notably affect the skin-friction coefficient and Nusselt number, with increased porosity and heat generation enhancing the Nusselt number while reducing the skin-friction coefficient in Maxwell fluids. The work's novelty lies in considering thermal diffusion effects and the combined influence of magnetic field, thermal dissipation, and suction/injection phenomena, offering valuable insights into porosity and heat generation in Maxwell fluids' thermal transport.

A modern study on peristaltically induced flow of Maxwell fluid considering modified Darcy’s law and Hall effect with slip condition

The current investigation is designed to scrutinize the Peristalsis of Magneto-hydrodynamics viscous-elastic (Maxwell) fluid with slip condition. The present article is beneficial in a way to understand the Hemodynamics through the arteries, and capillaries by considering the Hall current characteristics. Since the wall shear stress of Maxwell fluid is less as compared to Newtonian fluid hence it exhibits blood flow characteristics. Moreover, modified Darcy’s law is also taken into consideration. The phenomena of heat and mass transport are developed in the light of the thermal conduction mechanism given by Fourier along with viscous-dissipation. The governing system of ODEs is found to be non-linear. To achieve the series solution for considered flow problem, perturbation scheme is used by considering small wavenumber. The graphical impact of influential parameters is discussed exhaustively and graphically. The key outcome of this study is that the Hall current and slip both alter the flow fields. Additionally, it has been observed that temperature and velocity profiles show comparable behaviours for various parameters. The slip parameter has an increasing effect on fluid motion and temperature. The bolus’s size gradually becomes larger as we increase the values of both velocity slip and hall parameter. According to the author's knowledge, no research had previously been done in the literature that specifically addressed the peristalsis of viscoelastic fluid considering the Hall and porosity effect with slip conditions. The current investigation fills the breach in this area of research.

Mathematical Modeling on Magnetohydrodynamics Upper Convected Maxwell Fluid Flow Past a Flat Plate Using Spectral Relaxation Approach

The focus of this treatise is on the scrutiny of MHD heat and mass transfer motion of upper convection Maxwell (UCM) fluid in a thermally radiated flat plate. The models of the flow equations were considered when there is a temperature difference: the Cattaneo-Christov model and the Soret-Dufour mechanisms. A magnetic field of firmness was inflicted in opposition to the flow. The flow inspection is controlled by partial differential equations (PDEs). Suitable similarity variables were utilised on the PDEs to obtain a set of nonlinear ordinary differential equations (ODEs). The simplified set of ODEs shall be answered by exploiting the spectral relaxation method (SRM). The SRM is a numerical technique that solves differential equations by utilising the repetition of a sequence of operations that is iterated iteratively by first decoupling the coupled systems of equations. The magnetism was found to decline the velocity and hydrodynamic boundary layer due to the Lorentz force. The Deborah number was found to enhance the velocity contour. The Eckert number was discovered to improve the temperature profile due to the production of heat energy within the boundary layer. An increase in Prandtl number was found to enhance the hydrodynamic and thermal boundary layer thickness. The local skin friction and Nusselt number were found to be elevated by the increase in the Dufour parameter.

Pipeline flow of double fractional Maxwell fluids based on the rheological experiment of xanthan gum

The purpose of this paper is to investigate the pipeline flow of fractional Maxwell fluids based on the rheological experiment of xanthan gum solutions. The rheological properties of xanthan gum solutions at different concentrations are measured. Based on the experimental data, a grid-search method is used to determine the optimal parameters. The fitting results show that the double fractional Maxwell model is suitable to describe the flow constitutive relationship of xanthan gum solutions. Moreover, the governing equation of the pipeline flow of fractional Maxwell fluids is solved by the numerical difference method. The effects of fractional stress, fractional strain and relaxation parameter on the pipeline flow are discussed. The increase in fractional stress parameter and relaxation parameter has a negative effect on the flow process, while the increase in strain parameter enhances the flow of solutions in the pipeline.

Numerical study of nanoparticles aggregation on radiative 3D flow of maxwell fluid over a permeable stretching surface with thermal radiation and heat source/sink

The flow of fluid past a stretching sheet under heat and mass transfer analysis is significant because it has numerous applications in engineering and technology, including metal spinning, polymer extrusion, the manufacture of glass fibres, and metal casting etc. The current article investigates the effects of thermal radiation and heat source/sink on 3D nanofluid flow over an elongated surface embedded in a porous medium with nanoparticles aggregation. Further, the significance of variable magnetic field is one of the striking features of the present study. We have considered copper (metallic) and titania (metallic oxide) as nanoparticles and water as base fluid. The effective thermal conductivity of nanofluid is predicted by using a modified Maxwell model. Applying similarity transformations, the governing PDEs are transformed into nonlinear ODEs and solved numerically by MATLAB software using bvp4c and the shooting method. Graphs and tables are plotted to depict the significance of the effective parameters on velocity and temperature profiles as well as skin friction coefficient and Nusselt number. The existence of radiative parameter effects is more advantageous for improving heat transmission. The temperature distribution is enhanced due to presence of nanoparticles aggregation. Thus, the impact of nanoparticles aggregation is supportive theoretical tool in future bioengineering and industrial applications.

Significance of heat generation and impact of suction/injection on Maxwell fluid over a horizontal plate by the influence of radiation

The current research paper aims to investigate the Maxwell fluid flow over a flat plate under slip conditions and suction/injection parameters. Radiation, velocity slip conditions, and heat generation are also considered for this study. The governing equations are changed into ordinary differential equations with the appropriate similarity transformations. Then these equations are answered using the shooting technique and the Runge-Kutta 4th-order method. The impact of Deborah number (De), suction/ injection (fw), thermal radiation (Rd), viscous dissipation (Ec), velocity slip parameter (λ) and heat generation (Q) are displayed through graphs and tables. The main target of this investigation is to discuss the impact of the Nusselt number profile for the suction parameter (fw) against momentum slip (λ), thermal slip conditions (β) and radiation parameter. Skin friction profile for suction parameter also discussed against Maxwell fluid parameter (De). Numerical findings are compared to previously published research using bvp4c in MATLAB programme. The critical solutions of this study are that the Nusselt number outline increased for increasing the value of momentum slip, radiation parameter and thermal slip conditions. Still, it got decreases for viscous dissipation (Ec) against radiation. Skin friction profile decreased for increasing value of suction parameter against Deborah number.

Upper-convected flow of Maxwell fluid near stagnation point through porous surface using Cattaneo-Christov heat flux model

The aspiration of this study is to concentrate on a numerical inspection of the magnetohydrodynamic stagnation point flow of Maxwell fluid over upper-convected Joule heating effects by engaging the Cattaneo-Christov heat flux model. For motivation of the problem, the influence of heat and mass transfer are taken into account. The set of proposed model nonlinear partial differential equations is renovated into a couple of ODEs by exercising helpful similarity functions. Numerical elucidation of these model ODEs is obtained by the well-known scheme shooting approach, and the acquired numerical outcomes are compared with the Bvp4c command of MATLAB. Impression of several emerging parameters on velocity f′, temperature θ′ and concentration φ′ field are explained by graphs and tables. We observed that the velocity distribution reduced for the ascending value of the Deboreh number Γ magnetic number M. The enrichment in the values of the Prandtl number Pr decreased in the temperature profile. In-depth discussion is had regarding how various physical factors affect flow and heat transfer characteristics.