Flow Of Maxwell Fluid Research Articles

Heat and Mass Transfer in Unsteady Radiating MHD Flow of a Maxwell Fluid with a Porous Vertically Stretching Sheet in the Presence of Activation Energy and Thermal Diffusion Effects

The aim of this study is to analyze the effects of activation energy and thermal diffusion an unsteady MHD reactive Maxwell fluid flow past a porous stretching sheet in the presence of Brownian motion, Thermophoresis and nonlinear thermal. The non-linear partial differential equations that govern the fluid flow have been transformed into a two-point boundary value problem using similarity variables and then solved numerically by fourth order Runge–Kutta method with shooting technique. Graphical results are discussed for non-dimensional velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system. The present study is compared with the previous literature and found to be in good agreement.

Evaluation of homogeneous-heterogeneous chemical response on Maxwell-fluid flow through spiraling disks with nonlinear thermal radiation using numerical and regularized machine learning methods

ABSTRACT The present study addresses the effects of nonlinear thermal radiation and heat fall/rise on the thermal radiated viscoelastic fluid flow through spiraling disks with a homogeneous and heterogeneous chemical response. The properties of the Cattaneo-Christov heat flux model, a revised model of conventional Fourier’s law that predicts thermal relaxation properties, are examined in detail. The rotation of both the disks in the same and opposite directions is evaluated. The effect of heterogeneous-homogeneous chemical reactions is also considered in the present communication, making the study reasonably adaptable. The coupled partial differential equations, such as energy, momentum, and concentration, are transformed into ordinary differential equations by von Kármán variables. The outcomes of the present work confirm that flow behavior is reversed due to stretching action. Velocity and pressure profiles are reduced with the impact of Deborah’s number. In addition, it is noticed that increasing heterogeneous-homogeneous reaction parameters decreases the fluid concentration. Numerically computed values are compared with the predicted results using L.R. regularized L.R. and regularized S.V.R. It is observed that the regularized L.R. method outperformed the other two machine learning methods. Graphical illustrations of axial, radial, and tangential flows and concentration and temperature profiles are illustrated in graphs.

Chemical reaction effect across the moving flat plate with heat generation and MHD flow of Maxwell fluid with viscous dissipation

In this paper, the investigation centered on examining a Maxwell fluid’s convective double diffusive flow carefully considers factors such as chemical reactions, radiation, and the presence of a permeable moving flat plate. Additionally, the study encompassed the effects of heat generation and magnetohydrodynamics (MHD). The governing equations, initially expressed as partial differential equations, were converted into ordinary differential equations using a similarity transformation technique to facilitate the analysis. The computational power of MATLAB’s BVP4C software was harnessed to solve this resultant system of ODEs efficiently. The outcomes of this investigation were presented in the form of graphical representations that vividly depicted the behavior of the flow field, energy conservation, and concentration profiles under various parameter combinations. The research findings were thoughtfully summarized in a table, offering a comprehensive overview of temperature, velocity, and mass profiles across various parameters. These parameters included the Deborah number, chemical reaction rate, Eckert number, Lewis number, Prandtl number, porosity parameter, and MHD parameter. A notable discovery emerging from this study was the inverse relationship observed between nondimensional concentration contours and the magnitude of the chemical reaction rate. Simultaneously, it was observed that higher values of the Maxwell fluid led to a rise in the thickness of the temperature boundary layer. These findings offer valuable insights into the intricate interplay of physical and chemical phenomena in convective flows involving complex fluid properties and boundary conditions. The temperature outline diminishes as the heat generation rate increases, while the concentration profile declines with an elevation in the chemical reaction rate.

Remarks on some unidirectional flows of Maxwell fluids through a rectangular channel filled with porous medium

AbstractExact solutions for the dynamics of incompressible fluids showing rate‐type behavior have mostly been found in circumstances where the boundary velocities are given in the body of existing research. This phenomenon results from the constitutive equation of the corresponding extra‐stress tensor, which specifies the natural relationship between velocity and shear stress. In this paper, we focus on a unique observation of the magnetohydrodynamic (MHD) movements of incompressible Maxwell fluids, and the governing equations regulating velocity and shear stress. We focus our analysis on the case of an infinite plate submerged in a porous substance. Within this framework, we do an analytical analysis of a motion issue with a boundary that has a predetermined shear stress. We can easily ascertain the shear stress associated with the motion brought on by a flat plate in order to be more exact. The fluid is subjected to a shear stress by this plate that changes over time. The velocity field from a boundary motion with a predetermined velocity is used to achieve this. We give two graphical representations of individual solutions for the sake of clarity and result verification. Last but not least, we use graphical depiction to highlight how a magnetic field and a porous media affect the fluid's flow resistance. The results show that the flow resistance of the fluid increases in the presence of a porous media and decreases when a magnetic field is present.

MHD Darcy–Forchheimer flow and double-diffusive modeling of Maxwell fluid over rotating stretchable surface: A computational study

In this work, the Cattaneo–Christov double diffusion model is used to analyze the three-dimensional boundary layer flow of an upper-convected Maxwell fluid flowing over a bi-directional stretching surface. The model assumes that the fluid’s diffusivity is concentration-dependent, whereas dynamic viscosity and thermal conductivity are temperature-dependent; and the model takes into account the influence of the magnetic field of uniform strength. The problem is formulated using the conservation rules of mass, momentum, and energy as well as the boundary layer approximation. The resulting nonlinear system is then numerically solved using the bvp4c procedure in MATLAB. The obtained results are set forth graphically to illustrate the variations of different parameters. It is contemplated that the increase in thermal relaxation parameter results in a drop in fluid temperature while there is an enhancement in the concentration profile. Also, the temperature field has a direct relationship with the temperature-dependent viscosity. This research has proven its utility in industries where there is a need to analyze fluid flow over surfaces that can stretch in two directions.

Synergistic impacts of radiative flow of Maxwell fluid past a rotating disk with reactive conditions: An Arrhenius model analysis

This study presents an analysis of the hydromagnetic radiative flow of a Maxwell fluid past a rotating disk around its own axis with an angular velocity Ω0 which has enormous applications in metal casting (help to optimize the solidification and cooling of molten metals), plastic molding and aerospace engineering (cooling system of aircraft engines). The flow is constrained by boundaries that induce convection and chemical reactions described by the Arrhenius model. By applying similarity transformations, the non-linear partial differential equations, which describe the flow phenomenon, are metamorphosed into the non-dimensional system of ordinary differential equations (ODEs). The obtained ODEs are then solved numerically using ‘Keller box method’, an efficient computational technique, by implementing the finite-difference approach. The influence of different parameters, namely magnetic field strength, radiation parameter, reaction rate constant, and convective heat transfer coefficient, on the flow and heat/mass transfer characteristics are investigated. The findings suggest that the higher activation energy leads to a slower rate of reaction. As the reaction rate decreases, the consumption of reactant molecules and the reduction in their concentration also slow down. The influence of the convective heat transfer coefficient is also examined in terms of its effect on the thermal and concentration boundary layers. As the stretching parameter increases, the Maxwell fluid undergoes greater deformation, leading to greater strain and a consequent slowing of the fluid's radial velocity. Heat transfer is enhanced by thermal radiation and convective condition at the surface of rotating disk. The findings of this study provide valuable insights into the industries dealing with Maxwell fluids, enabling them to enhance process efficiency, optimize resource utilization, and develop sustainable and environmentally friendly solutions.

Melting heat transmission of Maxwell nanofluid flow caused due to a stretchable cylindrical pipe through Finite Element Technique

AbstractThe objective of current investigation is to examine Maxwell fluid flow generated by cylindrical stretching pipe. Thermophoresis and Brownian moment phenomena will also incorporate on the said fluid. Melting heat shifting phenomenon incorporated at the surface of the elongating cylinder. Mathematical formulation is supported by boundary layer assumption. Suitable similarity transformations diminishes model of nonlinear partial differential equations into a model of nonlinear ordinary differential equations that ultimately solved via numerical technique named Finite Element Technique. The properties of numerous effective variables are graphically displayed and examined. Further the physical quantities like velocity gradient, heat and mass fluxes are tabulated numerically and analyzed. The dimensionless temperature distribution rises for rising values of curvature parameter and Brownian motion parameter however an opposite behavior is observed for melting parameter and Prandtl number. Moreover, a reduction occurs in heat and mass fluxes for sufficiently high values of curvature parameter.

Analytical solutions for hyaluronic acid flow and heat transfer between joints with periodic oscillations under the magnetic field

Osteoarthritis (OA) is a globally prevalent disease that poses significant challenges to the daily work and life of patients. Viscosupplementation is one of the most commonly used drug treatments for OA, which involves injecting hyaluronic acid (HA) into the joint cavity to alleviate synovial inflammation. The current research aims to explore the rheological and thermal behavior of HA between joints by studying the axisymmetric squeezing flow and heat transfer of incompressible Maxwell fluid under the action of static magnetic field between two rigid spheres with partial wall slip. The analytical solutions for velocity and temperature are obtained by using the Laplace integral variational theory. Detailed explanations are provided on the effects of different fluid parameters on velocity and temperature, presented in the form of charts. It can be shown that as the magnetic field intensity increases, the viscosity of HA increases with the increasing of relaxation time, thereby fluid motion is weakened and a strong damping effect is produced. As the frequency of joints motion increases, the velocity distribution becomes more uniform in the central region, and the overall distribution deviates from a parabolic distribution. In addition, as Reynolds number, Prandtl number and squeezing depth increase, the heat transfer capacity of the fluid decreases, resulting in a lower temperature at the top wall and a higher temperature at the bottom wall. This study provides theoretical support for exploring the rheological and thermal behavior characteristics of HA in the treatment of OA.

The analysis of electromagnetic maxwell nanofluid flow over an axisymmetric cylindrical surface using artificial neural networks for active and passive control

ABSTRACT This work presents a novel approach to active and passive control of fluid flow on a stretching cylinder, considering the collective effects of electromagnetism, and chemical reactivity. The Maxwell fluid flow over the stretched surface of a cylinder is responsible for the improvement in heat transfer. The proposed methodology leverages the power of Artificial Neural Networks (ANN) to effectively manipulate and optimize fluid flow behavior in this complex system. By integrating ANN into the control strategy, we achieve enhanced propulsion system design and optimization capabilities, enabling improved performance around cylinders. Additionally, insights into the interconnection of electromagnetic effects and heat sources provide valuable implications for thermal management systems, where understanding and controlling fluid flow behavior are essential for efficient heat transfer. The design approach for addressing different aspects of the fluid problem consists of a sequence of operations, which encompass training, testing, and validation using a reference dataset. Furthermore, visual representations are employed to portray the flow model parameters concerning momentum, energy, and concentration profiles, effectively illustrating the results of the investigation, all of which are closely aligned with each other on average 10−8.

Exploring the Steady Flow of a Viscoelastic Fluid Passing over a Porous Perpendicular Plate Subjected to Heat Generation and Chemical Reactions

This study aims to bridge the gap by conducting a numerical analysis of Maxwell fluid behaviour on a perpendicular plate within a porous medium, considering both chemical reaction and heat generation. The investigation also encompasses the study of energy and mass transfer within magnetohydrodynamic (MHD) Maxwell fluids. We utilise a transformation technique employing similarity variables to address the challenge posed by the nonlinear partial differential equations (PDEs). These transformed equations are subsequently solved via the bvp4c solver in MATLAB. The obtained results exhibit a high degree of agreement with the previously published work. The study systematically explores the influence of chemical reaction, energy generation, and Deborah number parameters on temperature and velocity, as well as concentration, presenting the outcomes graphically. In addition, we calculate local Sherwood numbers, Nusselt numbers, and skin friction coefficients to assess the impact of chemical reactions. Our findings notably indicate that Sherwood numbers and skin friction coefficients increase with higher levels of chemical reaction, while local Nusselt numbers decrease as chemical reactions become more pronounced. By studying Maxwell fluid flow over a perpendicular plate with chemical reactions, this research contributes to optimizing processes, enhancing product quality, and providing deeper insights into the behaviour of complex fluids in real-world scenarios.

Three-dimensional MHD Mixed Convention Upper Convective Flow of Maxwell Fluid Throughout the Past in Thermophoresis and Brownian Motion with the Effects of Diffusion Thermo and Thermal Diffusion Utilizing Nonlinear Radiative Heat Flux

This article aims to investigate the impact of nanoparticles and magnetohydrodynamics (MHD) on the transfer of heat and mass using a three-dimensional upper-convected Maxwell (UCM) nanofluid flow across a stretched surface. A nonlinear radiative heat flow was included in formulating the equation that describes energy. The nonlinear partial differential equations of the issue are transformed into ordinary differential equations utilizing the similarity transformation. These equations are then solved using the well-known shooting approach in conjunction with the Runge-Kutta integration process of order four. To increase the dependability of our findings make use of the MATLAB. On the velocities, temperatures, and concentrations of the particles, the graphical and numerical representations of the effects of the main parameters, such as the Dufour parameter, the Brownian motion parameter, the Prandtl number, the thermophoresis parameter, and the magnetic parameter, are presented. It has been shown that the flow velocity decreases as a function of both the linear and nonlinear thermal radiation parameters. In addition, increasing values of the Brownian motion parameter have the effect of reducing the nanoparticle concentration profile, the same behavior has observed in the case of thermal diffusion and Diffusion thermo parameters.

Magnetized Flow of Maxwell Fluid over a Slippery Stretching Reactive Surface with Thermophoretic Deposition

This manuscript investigated mathematically magnetized Maxwell fluid over slippery stretching reactive surface with thermophoretic deposition. Similarity transformation was used to recast partial differential equations modeling flow problem to nonlinear coupled ordinary differential equations which were solved using fourth order Range-Kutta method and Newton-Raphson shooting technique. Numerical results were compared with literature-based results and found to be in good accord. Skin friction coefficient, Nusselt number, Sherwood number, velocity profiles, temperature profiles and concentration profiles which are of importance to engineers, were found to be influenced by thermo-physical parameters governing the dynamics of flow. Their effects were illustrated in tabular form and graphically. The study found that increasing Thermophoretic deposition parameter, Momentum slip parameter and Biot number amplified rate of heat transfer but decreased rate of mass transfer and Skin friction coefficients. Thermal Grashof, Solutal Grashof, and Damkohler numbers reduced skin friction coefficients but increased heat and mass transfer rates.

Analysis of MHD and Heat Transfer Characteristics of Thermally Radiative Upper-Convected Maxwell Fluid Flow between Moving Plates: Semi-Analytical and Numerical Solution

The current paper studies the MHD and heat transfer characteristics of radiative upper-convected Maxwell fluid flow between two plates approaching or receding from each other with injection at the fixed lower porous plate. The governing momentum and energy equations are reduced into non-linear ordinary differential equations employing similarity transformations. With the help of the Homotopy Perturbation Method (HPM), an approximate analytic solution is obtained. This work aims to determine the effects of Reynolds number (R), Deborah number (De), Radiation parameter (Rd), Magnetic parameter (M), and Prandtl number (Pr) on the velocity and temperature profiles. It is observed that the Deborah number has a direct impact on the velocity profile when there is a squeezed flow. It is also observed that the magnetic parameter shows an indirect impact on the temporal distribution for both the upper plate moving away and towards the lower. The variations in the significant physical parameters on the coefficient of skin friction and heat transfer rates are also calculated. The results are then compared with the classical finite difference method and are in excellent agreement. It is found that larger the magnetic parameter, the dominance of viscous forces retards the velocity in the core region, and the increase in radiation parameter suppresses the heat transfer rates. This study is helpful in industrial applications, specifically in polymer processing.

Radiation Effect on Heat Transfer Analysis of MHD Flow of Upper Convected Maxwell Fluid between a Porous and a Moving Plate

Radiation Effect on Heat Transfer Analysis of MHD Flow of Upper Convected Maxwell Fluid between a Porous and a Moving Plate

EFFECTS OF POROUS MEDIUM IN MHD FLOW OF MAXWELL FLUID WITH SORET/DUFOUR IMPACTS

In the energy transfer field, non-Newtonian fluid flow has an inclusive range of applications in the movement of biological fluids, oceanography, coating energy exchanger technology, melt-spinning, and the cooling of metallic plates and suspensions. Given these applications, this study examines the numerical simulation of hydromagnetic non-Newtonian Maxwell fluid flow on a horizontal plate through a porous medium. The numerical investigation of the current mathematical model is analyzed by taking the impact of magnetohydrodynamics (MHD), porous, radiation, energy generation, and Soret/Dufour with a thermal slip boundary condition. Partial differential equations with nonlinearities are transformed into ordinary differential equations by using similarity variables. The eminent numerical Runge-Kutta-Fehlberg fourth order via inbuilt software bvp4c in MATLAB and entropy generation analysis are used to determine the solution to the equations. Results were discussed via plots for Soret/Dufour effects for temperature, concentration, Nusselt number, and Sherwood number profiles. The fundamental goal and novelty of this study are to find the Bejan number (Be) and total entropy generation (<i>N</i><sub>s</sub>) for the parameters MHD, Reynold number (Re), radiation parameter (Rd), dimensionless temperature, and concentration ratio variables. We validated our code with existing work and obtained good matching. The difficult findings of this investigation are that the <i>N</i><sub>s</sub> profile surges for Re, Rd, porous, and MHD parameters but decreases for the dimensionless temperature ratio variable, and the Be profile increases for all the abovementioned parameters.

Melting heat effect in MHD flow of maxwell fluid with zero mass flux

This study delves into the investigation of Maxwell fluid flow across a sheet with a particular effort on the melting heat and zero mass flux at the boundary. A Maxwell fluid, characterized by both viscous and elastic responses, plays a pivotal role in various industrial and biological applications. The mathematical model describing Maxwell fluid flow is represented using non-linear momentum and energy equations, incorporating MHD. Similarity transformation is used to change from partial differential equation to ordinary differential equation. The introduction of a phase change term in the energy equation accounts for the melting heat effect at the boundary. The BVP4C solver using MATLAB is hired to numerically answer the system of equations, enabling the determination of the steady-state solution. The solution of this investigation offers valuable insights into the interplay between viscoelasticity and melting heat effects on various flow characteristics, including velocity and temperature profiles. The practical significance of this research is evident in polymer processing, food processing, and materials engineering, where the understanding of Maxwell fluids and their interaction with melting boundaries is essential for process optimization and product quality. So far in the literature survey no one have considered Melting heat effect along with Maxwell fluid. The conclusion for this study is that Melting heat effect increases velocity profile and decreases the temperature profile. This is the main conclusion of this research.

Analysis of the absorbing boundary condition for the Maxwell fluid flow over a semi-infinite plate with considering the magnetic field

In this paper, we analyze the flow mechanism of the Maxwell fluid over a semi-infinite plate. To handle the semi-infinite boundary, the artificial boundary method is employed and the absorbing boundary condition in the form of convolution is derived. Besides, the stability of the absorbing boundary condition is analyzed. Solutions are obtained numerically using the finite difference method and the accuracy is verified by introducing a source term to construct the exact solution. To demonstrate the validity and reasonableness of the absorbing boundary condition, a comparison with the direct truncation boundary is discussed. Our study examines the effects of the magnetic field, relaxation parameter, oscillation frequency and plate amplitude on the velocity distribution and flow mechanism of the Maxwell fluid.

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.