Oldroyd 8-constant Fluid Research Articles

Investigation of heat and mass transfer of oldroyd – 8 constant fluid in wire coating process employing response surface methodology

Wire coating is widely used for electrical insulation, shock protection, preventing leakage, and facilitating smooth current flow. This study aims to evaluate the applicability of Oldroyd-8 constant fluid for wire applications in a magnetic field using a pressure-type die. Based on the Buongiorno model with a constant pressure gradient and temperature-dependent thermophysical properties, governing equations are developed. These equations are transformed into dimensionless form and solved numerically. The study thoroughly investigates key features, including momentum, thermal distribution, nanoparticle volume fraction, and shear stress rate. Also, this study employs Response Surface Methodology to optimize heat transfer and shear stress rates in coated wire. Quadratic models, developed through a central-composite design, determine optimal levels for the Oldroyd-8 constant fluid parameter and nanofluid parameters, ensuring optimal heat transfer and shear stress rates for the melt. Nanofluid parameters contribute to an improvement in the thermal distribution profile. Optimal heat transfer and shear stress rate occur when the nanofluid parameters are minimized, and non – Newtonian fluid parameter is maximized.

Unveiling the role of MHD forces in Oldroyd 8-constant fluid during Forward roll-coating: Comparing numerical and analytical computations

In this article, the rheological effects of an Oldroyd 8-constant fluid model in the presence and absence of magnetic force (MHD) are investigated while traveling between the two rolls rotates in the same direction. The governing equations of the fluid flow have been simplified using the lubrication approximation theory (LAT). Analytical solutions in the presence and absence of MHD are presented using (i) Adomian’s decomposition method (ADM), (ii) Homotopy analysis method (HAM), and numerical simulations are performed by (iii) the finite difference method. We present the results of our findings through various graphs and validate the numerical and analytical methods through detailed tables of error comparisons. It has been found that non-Newtonian and magnetic parameters have a significant impact on the velocity profiles, pressure gradient, pressure distribution, separation points, and coating thickness. The material parameters α1 (dilatant parameter) and α2 (pseudoplastic parameter) notably affect the velocity profile of the fluid flow between two rolls. Increasing α1 causes shear thickening and decreases the velocity profile, while increasing α2 results in shear thinning and increases the velocity profile due to diminished internal resistance. A relationship exists between the MHD parameter m and the flow velocity. The greater the MHD force, the higher the resistance in fluid flow, resulting in lower velocity. A reasonable agreement has been found between Newtonian fluid and Oldroyd 8-constant fluid, assuming all the non-Newtonian parameters to be zero. The results provided a comprehensive methodology for regulating the coating thickness by adjusting the modified Capillary’s number in the industry.

Dynamics of comparative analysis of Reynold’s and Vogel’s models (variable viscosity) in a wire coating process filled with magnetized porous

In this paper, we investigate the analysis of Oldroyd 8-constant fluid flow with nanoparticle suspension via a porous media during the coating of wire is carried out. A constant magnetic field and electrically conducting fluid are considered. The governing equations thus obtained for the present model are converted to nonlinear differential equations using variables in dimensionless form. These equations are analytically solved. The influence of some parameters, like magnetic field parameter, porosity parameter, dilatant constant, pseudo-plastic constant and Brinkman number on velocity and temperature distributions are discussed graphically. For fluctuating viscosity, two models, Reynold’s and Vogel’s are considered. It is observed that the magnetic parameter and the Brinkman number increase, both temperature and velocity profiles show a retarding effect in both Reynold’s and Vogel’s models.

A computational study of the calendering processes using Oldroyd 8-constant fluid with slip effects

The analyses of the calendering processes using Oldroyd 8-constant fluid model with the non-linear slip condition effects are discussed in this paper. To model the flow equations for the study of calendering, we utilized the conservation of mass, momentum equations, and Oldroyd 8-constant model. The final equations are reduced into fourth order differential equations by utilizing lubrication approximation theory (LAT). MATLAB’s built-in function bvp4c is employed to calculate the stream function and the fluid velocity. Furthermore, pressure gradient, pressure, and mechanical quantities of calendering processes are obtained by fourth-order Runge-Kutta method. The effects of the slip and material parameters of Oldroyd 8-constant fluid on the physical quantities related to calendering are illustrated via graphical figures. The presence of slip is resistive to length of contract and pressure distribution. On the other hand the pressure showed the increasing trend with increase the value of material parameter ([Formula: see text]). The engineering quantity such as force function show decreasing with increase the values of the slip parameter K. As evident from the study, the material parameters play a crucial role in controlling the pressure, thereby influencing the final sheet thickness and separating force. With an increase in the material parameter [Formula: see text], both the sheet thickness and roll-separating force show a corresponding increase.

Significance of Darcy porous and hydro-magnetic dynamical flow with heat transfer of Oldroyd-8 fluid with deferment of nanoparticles in wire coating process

The wire coating method is an engineering development to cover a wire for wadding, motorized forte and ecological protection. In wire coating analysis, moreover, the polymer extruded on the wire is hauled into interior of a die occupied with melted polymer. By considering this significance, the magneto-hydrodynamic flow and heat transmission of Oldroyd-8 constant fluid with suspension of nanoparticles in the wire coating development had been investigated. The fluid with fixed viscosity is considered in porous medium. The flow is conducted with uniform magnetic field. The arising physical governing system is modelled mathematically. The mathematical model is executed by incorporation of thermal radiation and nanoparticles (Embedded in [Formula: see text] nanoparticles). The wire coating is scrutinized mathematically with four cases ([Formula: see text] with constant viscosity and also included in the Reynolds model for constant viscosity. The subsequent flow and heat transmission system were elucidated via the Runge–Kutta technique and the possessions of appropriate governing factors are presented in graphically. The outcome of the current investigation was equated with the previous available outcomes as a specific situation. The results were executed with nanofluid and without nanofluid as well as with positive and negative pressure gradients [Formula: see text]. It is seen that the temperature circulation is augmented due to the upsurge in magnetic parameter M. It is interesting to note that the positive pressure gradient with nanofluid has less momentum distribution compared to rest of the cases. It is also noted that the with negative pressure gradient, the distribution is more compared to positive pressure gradient case.

A novel approach to find analytical solutions for Oldroyd 6-constant fluid

A novel approach to find analytical solutions for Oldroyd 6-constant fluid

A note on the slip effects of an Oldroyd 6-constant fluid: Optimal homotopy asymptotic method

We study here the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving non-linear differential equations of non-Newtonian fluids. To this consequence, we consider the Oldroyd 6-constant fluid when it demonstrates slippage between the plate and fluid generating non-linear boundary value problems. The problems of plane Couette flow, generalized Couette flow, and plane Poiseuille flow are considered. Graphs of the results are plotted to show the performance of the method in terms of velocity profile. It is observed that the method is quite easy to implement, having latent potential to handle such kinds of non-linear problems and yield accurate results at minimum to low computational work.

Analysis of thin film flows of Pseudo-Plastic and Oldroyd 6-constant fluids using modified residual power series algorithm

This manuscript presents the detailed analysis of thin film flows of two non-Newtonian fluid models by proposing a new modification of residual power series method (RPSM). The numerical algorithm is extended to boundary value problems (BVPs) in the current scenario. Major advantage of RPSM is its direct usage with discretization, linearization or perturbation. Convergence analysis of the proposed algorithm is also performed for the implication of RPSM to thin film phenomena. The governing equations of Pseudo-Plastic and Oldroyd 6-constant fluids leads to highly nonlinear ordinary differential equations (ODEs) in lifting and drainage cases. Due to highly nonlinear nature of the modeled problems, exact solutions do not exist. As a result, validity of the obtained solutions is confirmed by computing residuals in each case. Furthermore, detailed graphical analysis is performed to check the effects of different fluid parameters on the velocity profile in lifting and drainage situations. It is observed that magnetic parameter and non-Newtonian parameter have similar, while stokes number has opposite effects on the velocity in lifting and drainage of thin film of Pseudo-Plastic fluid. On the other hand, in case of Oldroyd 6-Constant fluid, gravitational parameter and involved material constants are showing opposite behavior on the velocity profile in lifting and drainage. Analysis of the numerical solutions and errors reveals that proposed modification ensure reliable solutions and hence may be used for more advanced problems in science and engineering.

Design of inverse multiquadric radial basis neural networks for the dynamical analysis of wire coating problem with Oldroyd 8-constant fluid

Wire coating is a commercial method to insulate wires for mechanical intensity and environmental protection. In this experimental study, the technique of computational intelligence is used for nonlinear wire coating analysis by soaking the wires in Oldroyd 8-constant fluid under a constant pressure gradient with the help of feed forward artificial neural networks (ANNs). The system of partial differential equations generated for the process of wire coating is transformed into a nonlinear dimensionless ordinary differential equation. One of the salient features of ANNs is the mathematical modeling of transformed equations by exploring the unsupervised error. A new scheme based on inverse multiquadric neural networks (IMQNNs) is used with a hybridization process of well-known genetic algorithms (GAs) and sequential quadratic programming (SQP) to obtain expeditious convergence, i.e., IMQNNs-GA-SQP. The applicability of the problem is investigated by altering the values of the dilatant constant, pressure gradient, shear stress, and pseudo-plastic constant, the outcome of which is in the form of varying polymer coating thickness. Comparison of highly accurate results in the shape of error analysis based on absolute errors of obtained results with those of the reference solution, calculated using the Adams numerical technique using MATHEMATICA software, statistical analysis such as root-mean-square error, Theil’s coefficient for inequality, E-R2 (error function based on the coefficient of determination), E-VAF (variance accounted for), E-NSE (Nash–Sutcliffe efficiency), mean absolute error, box plot analyses, and the cumulative distributive function through histogram analyses, is also carried out in this research, which guarantees the effectiveness of the used scheme.

On the hydromagnetic reaction of Oldroyd 8-constant Arrhenius exothermic fluid and explosion slice-chain in a plane Couette

A theoretical study of hydromagnetic reaction of Oldroyd 8-constant exothermic liquid and explosion bifurcation slice is examined. The temperature distribution of the reactive molecular diffusion of the non-Newtonian liquid takes place in a plane bounded Couette. Without displacement of currents and material consumption, the viscoelastic fluid is completely exothermic with low thermal equilibrium. The dynamical flow momentum is not stimulated by the species reaction, but by the chain branched order, Arrhenius generalized kinetics, initiation rate and the flow medium upper plate motion. The nonlinear exothermic reaction differential model is completely solved by adopting a consistent and convergent collocation weighted residual analytical procedure. The qualitative results in graphs and tables are presented for the flow dynamic, heat propagation and ignition bifurcation slice. The results revealed that the viscoelastic property of the material is augmented by an increasing magnetic term. Also, exothermic heat diffusion is enhanced by initiation rate and reaction exponential factor. Hence, heat generation terms must be controlled to prevent thermal science and engineering devices from blowup.

Homotopic fractional analysis of thin film flow of Oldroyd 6-Constant fluid

The analysis of Oldroyd fluids; a class of Maxwell fluids which also bears Newtonian properties under some conditions, has important implications for different scientific and engineering/industrial applications. Examples of these fluids are typically dilute polymer solutions which demonstrate both viscous and elastic behaviors when subjected to strain. For unidirectional steady flows, the Oldroyd-B (3-Constant) model is the simplest when it comes to describing these behaviors. This model is not sufficient in certain cases, for instance, convergent flow channels, pulling effects, and other extensional flows. In all such scenarios, its application may lead to having out of bound tensile stresses. Hence, in all practicality, higher constants of the Oldroyd model are required to include different tensorial invariants. In this article, we perform this analysis in fractional space on Oldroyd fluids in thin-film flow context using the Oldroyd 6-Constant model for both lifting and drainage scenarios. Solutions to the highly non-linear fractional differential equations are obtained by means of the Homotopy Perturbation Method (HPM) along with fractional calculus. Validation and convergence of the solutions are confirmed by finding residual errors. To the best of our knowledge, the given problem has not been attempted before in fractional space. Various physical aspects, such as the velocity profile, volumetric flux and average velocities are determined and analyzed both graphically and in tabulation form as part of this analysis.

A new soft computing approach for studying the wire coating dynamics with Oldroyd 8-constant fluid

In this paper, a mathematical model for wire coating in the presence of pressure type die along with the bath of Oldroyd 8-constant fluid is presented. The model is governed by a partial differential equation, transformed into a nonlinear ordinary differential equation in dimensionless form through similarity transformations. We have designed a novel soft computing paradigm to analyze the governing mathematical model of wire coating by defining weighted Legendre polynomials based on Legendre neural networks (LeNN). Training of design neurons in the network is carried out globally by using the whale optimization algorithm (WOA) hybrid with the Nelder–Mead (NM) algorithm for rapid local convergence. Designed scheme (LeNN-WOA-NM algorithm) is applied to study the effect of variations in dilating constant (α), pressure gradient (Ω), and pseudoplastic constant β on velocity profile w(r) of fluid. To validate the proposed technique's efficiency, solutions and absolute errors are compared with the particle swarm optimization algorithm. Graphical and statistical performance of fitness value, absolute errors, and performance measures in terms of minimum, mean, median, and standard deviations further establishes the worth of the designed scheme for variants of the wire coating process.

Double exothermic reaction of viscous dissipative Oldroyd 8-constant fluid and thermal ignition in a channel

The theoretical study of double exothermic combustible reaction and thermal ignition of viscous dissipative Oldroyd 8-constant liquid is examined in a channel. Without consumption of material, the fully developed two-step combustible reaction for the non-Newtonian fluid occurred in a bounded medium. The flow is propelled by reaction activation energy, upper wall motion and pre-exponential chemical kinetics that stimulates internal temperature. The overall solutions for the dimensionless viscoelastic exothermic reaction model is obtained by integrating collocation weighted residual techniques. In graphical and tabular form, the solution results are presented for the fluid flow rate, energy field and the branch-chain bifurcation.

Branch-chain criticality and thermal explosion of Oldroyd 6-constant fluid for a generalized Couette reactive flow

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.

Nonlinear Convective Flow of Magnetohydrodynamic Oldroyd 8-Constant Fluid in a Channel With Chemical Reaction and Convective Boundary Condition

Abstract The present work concentrates on the two-dimensional steady incompressible flow of an Oldroyd-8 constant fluid between vertical plates influenced by a magnetic field. The cross diffusive and second-order chemical reactions are incorporated into the study. The homotopy analysis method (HAM) is used to obtain the series solutions of the transformed system of nonlinear equations. The effects of these parameters on the dimensionless velocity, temperature, concentration, skin friction, and Nusselt and Sherwood numbers are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity, temperature, and concentration establishing thinner related boundary layer. Another important outcome is that an increase in the Dufour parameter upsurges the rate of heat transfer at the wall y = 0 while peters out at y = 1. Finally, the second-order chemical reaction parameter reduces the concentration distribution. The novel outcomes of this investigation will be helpful in the field of the aerosol technology.

Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity

Abstract The most important plastic resins used in wire coating are high/low density polyethylene (LDPE/HDPE), plasticized polyvinyl chloride (PVC), nylon and polysulfone. To provide insulation and mechanical strength, coating is necessary for wires. Simulation of polymer flow during wire coating dragged froma bath of Oldroyd 8-constant fluid incompresible and laminar fluid inside pressure type die is carried out numerically. In wire coating the flow depends on the velocity of the wire, geometry of the die and viscosity of the fluid.The non-dimensional resulting flow and heat transfer differential equations are solved numerically by Ruge-Kutta 4th-order method with shooting technique. Reynolds model and Vogel’s models are encountered for temperature dependent viscosity. The numerical solutions are obtained for velocity field and temperature distribution. The solutions are computed for different physical parameters.It is observed that the non-Newtonian propertis of fluid were favourable, enhancing the velocity in combination with temperature dependent variable. The Brinkman number contributes to increase the temperature for both Reynolds and Vogel’smodels. With the increasing of pressure gradient parameter of both Reynolds and Vogel’s models, the velocity and temperature profile increases significantly in the presence of non-Newtonian parameter. Furthermore, the present result is also compared with published results as a particular case.

Runge-Kutta 4th-order method analysis for viscoelastic Oldroyd 8-constant fluid used as coating material for wire with temperature dependent viscosity

Polymer flow during wire coating dragged from a bath of viscoelastic incompreesible and laminar fluid inside pressure type die is carried out numerically. In wire coating the flow depends on the velcocity of the wire, geometry of the die and viscosity of the fluid. The governing equations expressing the heat transfer and flow solved numerically by Runge-Kutta fourth order method with shooting technique. Reynolds model and Vogel’s models are encountered for temperature dependent viscosity. The umerical solutions are obtained for velocity field and temperature distribution. It is seen that the non-Newtonian parameter of the fluid accelerates the velcoty profile in the absence of porous and magnetic parameters. For large value of magnetic parameter the reverse effect is observed. It is observed that the temperature profiles decreases with increasing psedoplastic parameter in the presence and absence of porous matrix as well as magnetic parameter. The Brinkman number contributes to increase the temperature for both Reynolds and Vogel’smmodels. With the increasing of pressure gradient parameter of both Reynolds and Vogel’s models, the velocity and temperature profile increases significantly in the presence of non-Newtonian parameter. The solutions are computed for different physical parameters. Furthermore, the present result is also compared with published results as a particular case.

Analytical and numerical solutions of Oldroyd 8-constant fluid in double-layer optical fiber coating

Polymer flow during wire coating in a pressure-type casting die has been simulated under non-isothermal conditions. The flow is dependent on the wire velocity, geometry of the die, and the viscosity of the polymer. In the present study, the constitutive equation of an Oldroyd 8-constant fluid is used to characterize the rheology of the polymer melt. The equation describing the flow of polymer melt inside the die is solved (1) analytically by applying optimal homotopy asymptotic method (OHAM) and (2) numerically by the shooting method with Runge–Kutta–Fehlberg algorithm. The convergence of the series solution is established. The effect of physical characteristics of the problem has been discussed in detail through graphs by assigning numerical values for several parameters of interest. At the end, the present study is also compared with published work as a particular case and good agreement is found.

Numerical simulation of double-layer optical fiber coating using Oldroyd 8-constant fluid as a coating material

Polymer flow during wire coating in a pressure type coating die has been simulated under nonisothermal conditions. The flow is dependent on the wire velocity, geometry of the die, and the viscosity of the polymer. The constitutive equation of an Oldroyd 8-constant fluid is used to characterize the rheology of the polymer melt. The equation describing the flow of polymer melt inside the die is solved (i) analytically by applying optimal homotopy asymptotic method and (ii) numerically by shooting method with Runge–Kutta–Fehlberg algorithm. The convergence of the series solution is established. The effect of physical characteristics of the problem has been discussed in detail through graphs by assigning numerical values for several parameters of interest. At the end, this study is also compared with the published work as a particular case and good agreement is found.

Intelligent computing approach to analyze the dynamics of wire coating with Oldroyd 8-constant fluid

In the study, intelligent computing technique is developed for solving the nonlinear system for wire coating analysis with the bath of Oldroyd 8-constant fluid having pressure gradient using feedforward artificial neural networks (ANNs), evolutionary computing, active-set algorithm (ASA) and their hybrid. Original partial differential equations of wire coating process are converted to nonlinear ordinary differential equation (NL-ODEs) in dimensionless form using similarity transformation. Strength of ANNs is exploited to develop mathematical model of the transformed equations by defining an unsupervised error. Training of design variables of the network is carried out globally using evolutionary computing techniques based on genetic algorithms (GAs) hybrid with ASA for rapid local convergence. Design scheme is applied to analyze the dynamics of the problem for number of variants based on dilatant constant, the pseudoplastic constant, the pressure gradient, shear stress under the effect of viscosity parameter and varying the coating thickness of the polymer. Results of the proposed method are compared with standard numerical solver for NL-ODEs based of Adams method to establish its correctness. Reliability of the method is further validated through the results of statistics based on different performance measures for accuracy and computational complexity.