Third-grade Fluid Research Articles

A STUDY OF MAGNETOHYDRODYNAMIC POUISILLE FLOW OF A THIRD-GRADE FLUID IN NON-DARCIAN POROUS PLATES WITH SLIP EFFECT AND HEAT TRANSFER

In this paper, the MHD Pouisille flow of a third-grade fluid in a non-Darcian porous plate with a slip effect has been studied. The flow flux and the heat transfer analysis were carried out. The governing non-linear ordinary differential equations (ODE) were non-dimensionalize and the resulting ODE is solved by perturbation techniques. The result obtained was illustrated and presented in form of graphs. The effect of various governing flow parameters on velocity and temperature profile was taken into account. It is found that the effect of cross Renold’s number, the porosity of the medium, and the Magnetic parameter are to slow down the velocity profile of the fluid while it increases with an increase in Darcy’s number and slip parameter. Also, it is noticed that the temperature profile of the fluid increases with the increase in the value of the Prandtl number.

Heat and mass transfer of a molten polymer conveying nanoparticles in a wire coating process with temperature-dependent fluid properties: Optimization using Response surface method

Heat and mass transfer rates play a significant role in achieving a high-efficiency, low-cost wire coating process. Therefore, the flow analysis of molten polymer (polyvinyl chloride) carrying nanoparticles inside a pressure-type die is presented. The third-grade liquid model is used for the constitutive equation of the polyvinyl chloride (PVC), while the non-homogeneous biphasic model is used for nanoparticles. The properties of PVC are temperature-dependent. The melt flow is governed by the modified Navier-Stokes equation for the third-grade fluid, energy conservation, and nanoparticles' continuity equation. The finite difference method-based routine is applied to solve the nonlinear differential equations that include nine physical parameters. The Response Surface Method (RSM) is implemented to optimize the heat/mass transfer rate coated wire's eminence depends on the coating material's rheological characteristics of PVC. Full quadratic correlation models for heat/mass transfer rate of melt are proposed through central-composite-design (CCD). The optimal level of third-grade fluid factor and nanofluid factors was determined to achieve an optimum heat/mass transfer rate of the melt. The rheological characteristics of PVC have been improved due to the temperature-dependent viscosity and shear thickening/thinning property of the melt. The nanofluid factors improve the thermal field and subsequently reduce the Nusselt number. Maximum heat transfer occurs for a low level of Brownian factor, a high level of thermophoresis factor, and a third-grade fluid factor of 0.2177, also reaching the maximum mass transfer simultaneously.

Numerical investigation on transient third-grade magnetized nanofluid flow and radiative convection heat transfer from a stationary/moving cylinder: nanomaterial and nanoparticle shape effects

In this study, a mathematical model is developed for analyzing the time-dependent magneto-convective flow and heat transfer characteristics of an electrically conducting (functional) third-grade Reiner-Rivlin non-Newtonian nanofluid from a moving or stationary hot cylinder in the presence of magnetic field and thermal radiation. A well-tested convergent Crank–Nicolson type finite difference algorithm is employed to solve the transformed, nonlinear boundary value problem. The Tiwari-Das nanofluid volume fraction model is adopted for nanoscale effects and the Rosseland algebraic flux model for radiative heat flux effects. It has been shown that the shape of nanoparticles remarkably contributes to the enhancement of heat transfer. Several metallic nanoparticle types such as Al2O3, Cu, and TiO2 are examined. It is found from the investigation that the viscoelastic nanofluid with TiO2 nanoparticles results in more heat transfer than the other nanoparticles. Lower velocity and higher temperature values are computed at transient conditions with a higher third-grade fluid parameter for the flow of nanofluid (Al2O3-SA). The plots of transient friction and heat transfer coefficients are visualized at the surface of a hot cylinder. The tabulated heat transfer coefficient is comparatively more for the moving cylinder than the stationary cylinder. Detailed validation of results of the numerical scheme with previous studies is included. The simulations find applications in coating deposition (enrobing) of magnetic nanomaterial at high temperatures, functional nanomaterial synthesis, etc.

Novel Adaptive Bayesian Regularization Networks for Peristaltic Motion of a Third-Grade Fluid in a Planar Channel

In this presented communication, a novel design of intelligent Bayesian regularization backpropagation networks (IBRBNs) based on stochastic numerical computing is presented. The dynamics of peristaltic motion of a third-grade fluid in a planar channel is examined by IBRBNs using multilayer structure modeling competency of neural networks trained with efficient optimization ability of Bayesian regularization method. The reference dataset used as inputs and targets parameters of IBRBN has been obtained via the state-of-the-art Adams numerical method. The data of solution dynamics is created for multiple scenarios of the peristaltic transport model by varying the volume flow rate, material parametric of a third-grade fluid model, wave amplitude, and inclination angles. The designed integrated IBRBNs are constructed by exploiting training, testing, and validation operations at each epoch via optimization of a figure of merit on mean square error sense. Exhaustive simulation of IBRBNs with comparison on mean square error, histograms, and regression index substantiated the precision, stability, and reliability to solve the peristaltic transport model.

Study of Third-Grade Fluid under the Fuzzy Environment with Couette and Poiseuille Flows

In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane Couette–Poiseuille flow of a third-grade non-Newtonian fluid between two horizontal parallel plates separated by a finite distance in a fuzzy environment are considered. The governing nonlinear differential equations (DEs) are converted into fuzzy differential equations (FDEs) and explain our approach with the help of the membership function (MF) of triangular fuzzy numbers (TFNs). Adomian decomposition method (ADM) is used to solve fundamental flow problems based on FDEs. In a crisp environment, the current findings are in good accord with their previous numerical and analytical results. Finally, the effect of the α -cut α ∈ 0,1 and other engineering constants on fuzzy velocity profile are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF.

Application of Arrhenius chemical process on unsteady mixed bio-convective flows of third-grade fluids having temperature-dependent in thermo-rheological properties

This article presents the unsteady mixed convective flow of third-grade fluid flow comprising nanoparticles and gyrotactic microorganisms past a stretching sheet. The fluid flow is assumed to be laminar and incompressible. The fluid flow is considered to be highly magnetized by applying a strong magnetic field. Newtonian viscous dissipation, chemical reactions, and Arrhenius activation energy are taken into consideration. The transformed system of equations is solved by HAM. Convergence analysis of the HAM is displayed with the help of figures. The relations of physical factors with fluid flow profiles are displayed with the help of figures and tables. It is reported that the greater material and mixed convection factors have escalated the fluid’s velocity. The higher Eckert number and thermal conductivity constant have augmented the thermal function, while the higher Prandtl number has reduced the temperature profile. The greater activation energy factor has augmented the concentration profile, while the augmenting chemical reaction and Schmidt number have reduced the concentration profile. In the streamlines of the steady and unsteady flows, there is also a significant difference in behavior.

Impacts of Joule heating and viscous dissipation on MHD pulsatile flow of third grade nanofluid in a channel

The current exploration deals with the third grade hydromagnetic pulsating flow of blood-gold nanofluid in a channel with the presence of Ohmic heating, viscous dissipation and radiative heat. In the present analysis, blood (base fluid) is considered as third-grade fluid and gold (Au) as nanoparticle. This investigation is useful in the fields of food processing system, pressure surges (pulsatile flow application), biomedical engineering, nano drug delivery, radiotherapy, and cancer therapeutic (nanofluid application). Perturbation method is employed to transform the set of governing partial differential equations (PDEs) into the ordinary differential equations (ODEs) and then solved by employing the fourth order Runge-Kutta method with the aid of the shooting technique. The impacts of emerging dimensionless parameters of velocity, temperature, and heat transfer rate of blood-Au nanofluid are analysed via pictorial outcomes in detail. The obtained results depict that the improvement in viscous dissipation and heat source enhanced the temperature of third grade nanofluid. The velocity and temperature of the nanofluid are declining functions with the enhancement of frequency parameter, material parameter, and non-Newtonian parameter respectively. Intensifying the volume fraction of nanoparticle dwindles the velocity and temperature of nanofluid. Enhancing volume fraction and viscous dissipation accelerates the heat transfer rate of nanofluid. The velocity, temperature, and heat transfer rates are decreased by an escalation of the Hartmann number. Further, enhancing the radiation parameter reduces the heat transfer rate and temperature of nanofluid.

RETRACTED: Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel

• MHD electro-osmotic flow of non-Newtonian fluid. • Perturbation and Pseudo-Spectral collocation methods. • Velocity of the fluid retards subject to strong magnetic fields. • Velocity and temperature diminishing via electro-kinetic parameter Γ 2 . The electro-osmatic flow of non-newtonian fluid in a micro-channel is investigated in this article. The governing equations are derived with the help of a stress tensor then later transformed into dimensionless form with non-dimensional quantities. The perturbation method is used to obtain the approximate analytical solution of the given problem. The viscosity of the fluid is taken as a variable in terms of temperature. The validity of the perturbation solution is provided. The Pseudo-spectral collocation method is used to calculate the error in the perturbation solution of velocity and temperature. The magnitude of error in velocity and temperature is 10 −4 and 10 −2 , respectively. The impact of emerging parameters on velocity and heat profiles is also presented. The computational results reveal that the velocity profile diminishing via non-Newtonian parameter Γ 1 , electro-kinetic parameter Γ 2 , magnetic field parameter M and viscosity parameter D while an opposite behavior is noted in the velocity versus pressure gradient parameter Γ 3 , viscosity parameter E and wall's temperature θ w , respectively. Further, the temperature profile increases against the enhancement of Brinkman number, Joule heating parameter, pressure gradient parameter, wall's temperature, viscosity parameter D while reverse behavior is observed via electro-kinetic and magnetic field parameters. This study will help to understand the basic idea of MHD electro osmotic flow of non-Newtonian fluid bounded within a microchannel under the influence of variable viscosity. Further, this research can be useful to design the different types of biomedical lab-on-a-chip and thermal microfluidic devices. The developed devices can be helpful in DNA analysis and biomedical diagnosis etc.

Double-layer coating using MHD flow of third-grade fluid with Hall current and heat source/sink

Abstract Multiple coating assessments of fiber optics utilizing micropolar convection non-Newtonian third-order liquid in the existence of Hall effect are examined and executed throughout this academic article. The wet-on-wet (WOW) coating process is used in the research. The fourth Runge–Kutta–Fehlberg algorithm is used to computationally solve the governing equations which dictate the movement of fluid inside the container. In this research, the RK4-Fehlberg algorithm is applied to get numerical results for a list of nonlinear ordinary differential equations (ODEs) describing liquid motion. Pictorially, the contribution of regulating variables on velocity and temperature profiles is examined. It is observed that the velocity profile enhances as the viscoelastic parameter increases and the velocity profile increases for both the non-Newtonian and Hall current increasing parameters in the presence and absence of magnetic parameter M. It is observed that the velocity of the fluid decreases with the increasing values of the Hartmann number m, Brinkman number Br, and magnetic parameter M. Furthermore, the temperature profile increase for B r Br , K, M, and opposite effect is observed for β \beta increases. The suggested approach is compared to homotopy analysis method (HAM) for verification purpose, and excellent agreement is obtained. In addition, as a restricted scenario, a connection is made with the existing literature.

Numerical Solution for Unsteady Acceleration MHD Third-Grade Fluid Flow in a Rotating Frame Through Porous Medium Over Semi-Infinite Boundary Condition with a Presence of Heat Transfer

The aim of this work is to present a suitable numerical solution for unsteady non-Newtonian third-grade fluid which rotates at z -axis and pass through a porous medium. The fluid flows in magnetic field with constant acceleration and the semi-infinite boundary condition are highlighted. The fluid problem is also deal with heat transfer. The nonlinear partial differential equation is discretised using the finite difference method (FDM). The linear system obtained for three different domains (lengths). Consequently, the asymptotic interpolation method is merged to solve problems of large sizes. This hybrid method yielded results that satisfied the boundary condition that reaches zero as length grows to infinite length. For velocity profile and temperature distribution, a comparison of FDM and hybrid method is shown. It is discovered that the hybrid method produces better results than FDM for this infinitely large problem. Several analyses have been carried out to investigate the effect of various fluid parameter values. The findings reveal that as the porosity parameter increases, the velocity decreases. The Grashof and Prandtl numbers demonstrate the relationship to the temperature distributions. The effects of the magnetic field and the non-Newtonian parameters were also illustrated, as these parameters influence the velocity distribution of the fluid flow.

Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

Third Grade Fluid Flow in a Microchannel Crammed with Permeable Media Liable to Non-linear Thermal Radiation

This work unveils the impact of third-grade fluid flowing in microchannel placed vertically and packed by porous media. Walls facilitate injection/suction of concerned fluid. Slip and convective situations are employed. Active action of non-linear radiation and heat source are contemplated. Pressure gradient is the aspect that's responsible for the flow. The equations modeled consider the contribution of buoyancy forces on geometry with viscous dissipation. The outcomes of the customized equations for the above-narrated flow are assessed by the tactic of reducing the dimensions of equations to one. Owing to the flow and heat transport, entropy and Bejan number are effectually learned with the aid of the Runge Kutta Fehlberg method using graphical manifestation. The consequence of this scrutiny upholds that the rise of third-grade fluid parameter depletes the flow profile. Radiation parameter plummets temperature and entropy produced. The heat source parameter effect is reflected on thermal profile by boosting temperature.

Numerical Investigation of Thin Film Flow of a Third-Grade Fluid on a Moving Belt Using Evolutionary Algorithm-Based Heuristic Technique

This paper presents a stochastic heuristic approach to solve numerically nonlinear differential equation (NLDE) governing the thin film flow of a third-grade fluid (TFF-TGF) on a moving belt. Moreover, the impact on velocity profile due to fluid attribute is also investigated. The estimate solution of the given NLDE is achieved by using the linear combination of Bernstein polynomials with unknown constants. A fitness function is deduced to convert the given NLDE along with its boundary conditions into an optimization problem. Genetic algorithm (GA) is employed to optimize the values of unknown constants. The proposed approach provided results in good agreement with numerical values taken by Runge–Kutta and more accurate than two popular classical methods including Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The error is minimized 10[Formula: see text] times to 10[Formula: see text] times.

Implementation of Stochastic Optimization Method-Assisted Radial Basis Neural Network for Transport Phenomenon in Non-Newtonian Third-Grade Fluids: Assessment of Five Optimization Tools

Implementation of radial basis neural network is demonstrated by considering a test case of non-Newtonian third-grade fluid flow and heat transfer through two parallel plates. Five commonly used stochastic optimization methods: genetic algorithm, global search algorithm, multiple starting point algorithm, simulated annealing algorithm, and pattern search algorithm, are employed to optimize the RBNN. Flow of a non-Newtonian third-grade fluid through two parallel plates, subjected to uniform heat flux, is considered. At first, governing equations, describing the flow and heat transfer problem, are solved by the least-square method, a semi-analytical tool. The velocity and the temperature profiles are obtained for different values of third-grade fluid parameter ‘A’, which are then used for training different stochastic optimization method-assisted RBNNs (SOMARBNNs). For proper functioning of RBNN, a suitable value for an important attribute called ‘spread’ is required. Deciding the value for ‘spread’ requires experience and knowledge of neural networks. The present approach makes the selection of proper value of ‘spread’ very easy, and beginners can use the RBNN for problem-solving. With the help of different stochastic optimization methods, the value of spread for the RBNN is determined. Once all SOMARBNNs are trained, the temperature profile and the corresponding third-grade fluid parameter ‘A’ are obtained as output, corresponding to any new velocity profile fed as input. Further, the data for training are perturbed by different levels of noise, and different SOMARBNNs are successfully employed to get the output. The performance evaluation of different SOMARBNNs is carried out in terms of CPU time and error in result. The results indicate that PSAARBNN is better than other SOMARBNNs, as it is able to generate results with high accuracy for both low noise data and high noise data. Moreover, the CPU time requirement by PSAARBNN is lowest.

Heat and Mass Transfer of Rotational Flow of Unsteady Third-Grade Fluid over a Rotating Cone with Buoyancy Effects

Objective of this paper is a study of the impact of heat and mass transfer on time-dependent flow of a third-grade convective fluid due to an infinitely rotating upright cone. An interesting fact is observed that the similarity solutions only exist, if we take the angular velocities of the cone and far away from the fluid as an inverse function of time. The analytical solutions of the reduced ordinary differential equations of third-grade fluids are offered by the optimal homotopy analysis method (OHAM). The results for important parameters are illustrated graphically as well as in tabular form. The precision of the present results is also checked by comparison with the numerical outcomes published earlier. The impact of non-Newtonian fluid parameters is found to decrease the primary skin-friction coefficient. There is an aggregate in Nusselt and Sherwood numbers for increasing the ratio of the buoyancy forces.

Second law analysis of MHD third-grade fluid flow through the microchannel

The present study analyses the phenomena of entropy generation of magneto third-grade fluid flow through the microchannel. The significance of Joule heating, viscous heating and internal heat source is also scrutinised. The non-dimensional forms of the corresponding governing equations of the physical phenomenon with the associated boundary conditions for third-grade fluid flow and heat transfer has been solved using finite element method. The impact of various parameters on the flow and heat transfer behaviour, entropy generation and Bejan number is explained using graphs. The obtained results are examined through the plots. The results showed that an increase in the fluid parameter reduces the activity of the fluid flow and, as a result, the temperature is diminished. An enhancement in fluid motion and temperature is obtained by increasing the viscosity index. We noted that the effect of Hartmann number on the rate of local entropy generation and Bejan number is sinusoidal in nature.

Mathematical modeling of multiphase flows of third-grade fluid with lubrication effects through an inclined channel: analytical treatment

This article aims to address lubrication effects on multiphase flows. Bi-phase flows are composed of third-grade fluid as the main carrier, while Hafnium and crystal particles of tiny size are used to obtain different suspensions. Fluid dynamics of two-phase flows are analyzed through a steep channel. An external magnetic field is applied on bi-phase flows due to the magnetic susceptibility of the metal. In order to attenuate walls roughness, lubrication effects are also taken into account. The nonlinear ordinary differential equation subject to nonlinear slip boundary conditions is solved analytically with the help of “Perturbation method.” Contribution of the most significant variables and parameter is examined through graphs and different tables. It is inferred that slippery walls and magnetic fields have an opposite impact on the flow. Multiphase flow suspended with Hafnium particles is better than the one crystal particles.

Modeling and simulation of capillary ridges on the free surface dynamics of third-grade fluid

Abstract Most of the viscoelastic fluids have deformation while flowing over a heated plate. A typical feature of a thin viscous or viscoelastic fluid is the formation of the capillary ridges over locally heated plates. The creation of such ridges in the thin-film surface can affect the smoothness of the coating. This work particularly concerned the flow of non-Newtonian third-grade fluid over an inclined heated plate and the formation of ridges. The conservation laws associated with free surface and wall boundary conditions model the two-dimensional fluid flow. The long wave approximation of the model results in an equation of evolution to explain the structure of free surfaces. The resulting equation is discretized implicitly using the finite volume method. The obtained results are discussed for different flow parameters that affect capillary ridge emergence on the free surface. Variation in the height of capillary ridges of third-grade fluid is compared with the second-grade fluid and Newtonian fluid flow. We observe, the ridge size gets smaller for the third-grade fluid compared to the Newtonian and the second-grade fluid. Our analysis investigates how the third-grade viscoelastic parameters affect the dynamics of the free surface and the size of the capillary ridge concerning temperature changes and other phenomena of interest.

Thermo-bioconvection in stagnation point flow of third-grade nanofluid towards a stretching cylinder involving motile microorganisms

The intention of the current flow model is to investigate the significance of bioconvection in stagnation point flow of third grade nanofluid containing motile microorganisms past a radiative stretching cylinder. The impacts of activation energy and stagnation point flow are also considered. In addition the behavior of thermophoresis diffusion and Brownian motion are observed. Nanofluid can be developed by dispersing the nanosized particles into the regular fluid. Nano-sized solid materials for example carbides, grephene, metal and alloyed CNT have been utilized for the preparation of nanofluid. Physically, regular fluids have low thermal proficiency. Therefore, nano-size particles can be utilized to enhance the thermal conductivity of the host fluid. Nanofluids have many features in hybrid power engine, heat transfer, and can be used in cancer therapy and medicine. The formulated system of flow problems are transformed into dimensionless coupled ordinary differential expressions system via appropriate transformation. The systems of converted governing expressions are computed numerically by employing well known bvp4c solver in MATLAB software. The outcomes of emerging physical flow parameters on the velocity profile, volumetric concentration of then nanoparticles, rescaled density of the motile microorganisms and nanofluid temperature are elaborated graphically and numerically. Furthermore, velocity of third-grade fluid intensifies for higher values of third-grade fluid parameter and mixed convection parameter while opposite behavior is detected for buoyancy ratio parameter and mixed convection parameter. Temperature distribution grows for higher estimation of temperature ratio parameter and Biot number. Higher amount of Prandtl number and Lewis number decreases the concentration of nanoparticles. Concentration of microorganisms reduces by growing the values of velocity ratio parameter and bioconvection Lewis number.