Grade Fluid Research Articles

Numerical and analytical investigation to fractional third grade viscoelastic fluids in rotating frame with slip boundary conditions

In order to obtain the mixture or separation of the biological or chemical fluids with viscoelastic characteristics, the rotating electro-osmotic flow of fractional third grade fluids in a microchannel is investigated. The momentum equation is solved by Laplace and Fourier Transforms after linearization by small parameter perturbation method. Furthermore, the numerical solutions also are obtained by finite difference method. The velocity distribution influenced by different physical parameters is discussed. Two interesting phenomena can be observed. One of them is that reverse flow appears at the center of the channel for some physical parameters. Another one is that the velocity in the microchannel will arrive at a steady state from oscillation at last. However, with the increase of fractional derivative parameters, the amplitude of the oscillation becomes bigger at the center and the time arriving at the steady state is delayed.

Perturbation Analysis of Magneto hydrodynamic Flow of Third Grade Fluid in an Inclined Cylindrical Pipe

In this paper, analysis of magnetohydrodynamic third grade fluid in an inclined cylindrical pipe was considered. The flow was assumed to be induced by the axial pressure gradient. The resulting governing equations of flow were solved using the regular perturbation method. Results show that the Brinkmann and the Eckert numbers have the tendency to slow the movement of the fluid in the centre line of the cylinder, as a result, the velocity increases near the wall associated with the constant flow rate at each section of the cylinder. Results further show that increase in the Grashhof parameter slightly reduced the temperature of the system, with the profiles converging to zero, satisfying the boundary condition and the walls of the cylinder isothermally stable.

MHD Flow of Second Grade Fluid with Heat Absorption and Chemical Reaction

The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional model has been developed using the generalized Fick’s and Fourier’s laws. The Caputo-Fabrizio (CF) fractional derivative has been used to solved the model. Initially, the flow modeled system of partial differential equations are transformed into dimensional form through suitable dimensionless variable and then Laplace transform technique has been used to solved the set of dimensionless governing equations for velocity profile, temperature profile, and concentration profile. The influence of different parameters like diffusion-thermo, fractional parameter, magnetic field, chemical reaction, heat obsorption, Schmidt number, time, Prandtl number and second grade parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number, Prandtl number, magnetic parameter, and chemical reaction, whereas velocity field decreases with decreasing values of diffusion-thermo and mass grashof number. In order to check the athenticity of present work, we compare the present work with already published model graphically.

Magnetohydrodynamic pulsatile flow of third grade hybrid nanofluid in a porous channel with Ohmic heating and thermal radiation effects

In this work, magnetohydrodynamic pulsatile flow of third grade hybrid nanofluid in a porous channel under the impacts of viscous dissipation, thermal radiation, and Ohmic heating has been analyzed. Blood (the base fluid) is considered as a third grade fluid, while gold and alumina are as nanoparticles. This investigation is significant in the field of food processing system, pressure surges (pulsatile flow application), biomedical engineering, cancer therapeutic, and nano-drug suspension in pharmaceuticals. The literature shows that the investigations are related to the pulsating flow of nanofluid only. The study related to the pulsating flow of third grade hybrid nanofluid with Joule heating and thermal radiation did not report so far. The novelty of the present work is the investigation of the pulsatile hybrid nanofluid flow with thermal radiation and Joule heating effects in a permeable channel. The governing partial differential equations are transformed into system of ordinary differential equations by employing the perturbation method, then solved by adopting 4th order Runge–Kutta method along with the help of the shooting method. The impressions of pertinent parameters and emerging variables are portrayed via graphical illustrations. The results depict that the velocity decreases with a rise in Hartmann number and non-Newtonian parameter. The temperature of nanofluid is enhanced with increasing viscous dissipation. A high heat transfer rate is observed with the enhancement of viscous dissipation while a lower heat transfer rate is observed with increasing magnetic field and thermal radiation.

On rate type fluid flow induced by rectified sine pulses

<abstract><p>This investigation aims to present the unsteady motion of second grade fluid in an oscillating duct induced by rectified sine pulses. Some of the most dominant means for solving problems in engineering, mathematics and physics are transform methods. The objective is to modify the domain of the present problem to a new domain which is easier for evaluation. Such modifications can be done by different ways, one such way is by using transforms. In present work Fourier sine transform and Laplace transform techniques are used. The solution thus obtained is in form of steady state, with combination of transient solution which fulfills all required initial and boundary conditions. The influence of various parameters of interest for both developing and retarding flows on the flow characteristics will also be sketched and discussed. Also, the problem is reduced to the flow model where side walls are absent by bringing the aspect ratio parameter (ratio of length to width) to zero.</p></abstract>

An Implicit Numerical Approach for 2D Rayleigh Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

In this research work, our aim is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) involving Riemann–Liouville time fractional derivative. We suggest the modified implicit scheme formulated in the Riemann–Liouville integral sense and the scheme can be applied to the fractional RSP-HGSGF. Numerical experiments will be conducted, to show that the scheme is stress-free to implement, and the outcomes reveal the ideal execution of the suggested technique. The Fourier series will be used to examine the proposed scheme stability and convergence. The technique is stable, and the approximation solution converges to the exact result. To demonstrate the applicability and viability of the suggested strategy, a numerical demonstration will be provided.

Outlining the influence of thermal and solutal stratifications on mixed convection second grade fluid flow near an irregular cylinder with induced magnetic field

In this analysis, thermal and solutal stratifications in three-dimensional mixed convection flow of second grade fluid along an irregular cylinder through porous medium is demonstrated. Effect of induced magnetic induction is considered to deal many technological and scientific problems like crude oil purification, plasma confinement, rotating magnetic stars and power generation. The flow narrating continuity, magnetic flux, momentum, magnetic induction, concentration and heat equations are modeled in the form of PDEs. Set of dimensionless conversions are introduced to replace non-linear PDEs into a set of ODEs. To predict numerical solution of considering model, we used an efficient numerical technique Bvp4c. The consequential outcomes are sketched for unlike values of dimensionless parameters. Parameters like mixed convection, second grade parameter, magnetic parameter, porosity parameter and buoyancy ratio parameter are initiated to control the flow field. Further, temperature and solutal stratification parameters, Prandtl, magnetic Prandtl and Schmidt numbers are found to control energy, magnetic induction and concentration distributions. Skin drag coefficients, heat and mass fluxes are investigated for inflating values of some sundry parameters. For justification of the model, we compared present numerical outcomes with previous published results.

A significant study on flow analysis of viscoelastic fluid with variable thermo-physical properties

Due to large amount of engineering applications, the flow of viscoelastic fluid due to stretched surfaces has turned out to be very famous among the challenging research field of fluid mechanics. Therefore, the main idea of this paper is to classify the instantaneous significances of thermo-physical parameters on the flow of an electrically conducting second grade fluid flow caused by stretched needle. Flow is generated due to a needle which is stretched vertically. The dimensionless transformations are used to change the leading partial differential equations including energy, mass and momentum conservation into ordinary differential form. The newly formed equations along with boundary constraints are solved by employing built in Bvp4c Matlab package. Moreover, the solutions for dimensionless concentration, fluid velocity and energy distributions are analyzed graphically. The thermo-physical embedded parameters controlling the mass, flow and heat transfer characteristics are the magnetic parameter, variable thickness parameter, second grade fluid parameter, small parameter, variable diffusivity parameter and Prandtl number.

Enhancement of heat and mass transfer of a physical model using Generalized Caputo fractional derivative of variable order and modified Laplace transform method

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

Entropy Optimized Second Grade Fluid with MHD and Marangoni Convection Impacts: An Intelligent Neuro-Computing Paradigm

Artificial intelligence applications based on soft computing and machine learning algorithms have recently become the focus of researchers’ attention due to their robustness, precise modeling, simulation, and efficient assessment. The presented work aims to provide an innovative application of Levenberg Marquardt Technique with Artificial Back Propagated Neural Networks (LMT-ABPNN) to examine the entropy generation in Marangoni convection Magnetohydrodynamic Second Grade Fluidic flow model (MHD-SGFM) with Joule heating and dissipation impact. The PDEs describing MHD-SGFM are reduced into ODEs by appropriate transformation. The dataset is determined through Homotopy Analysis Method by the variation of physical parameters for all scenarios of proposed LMT-ABPNN. The reference data samples for training/validation/testing processes are utilized as targets to determine the approximated solution of proposed LMT-ABPNN. The performance of LMT-ABPNN is validated by MSE based fitness, error histogram scrutiny, and regression analysis. Furthermore, the influence of pertinent parameters on temperature, concentration, velocity, entropy generation, and Bejan number is also deliberated. The study reveals that the larger β and Ma, the higher f′(η) while M has the reverse influence on f′(η). For higher values of β, M, Ma, and Ec, θ(η) boosts. The concentration ϕ(η) drops as Ma and Sc grow. An augmentation is noticed for NG for higher estimations of β,M, and Br. Larger β,M and Br decays the Bejan number.

Mechanical and thermal energies transport flow of a second grade fluid with novel fractional derivative

In this study, an unsteady natural convection flow of second-grade fluid over a vertical plate with Newtonian heating by constant proportional Caputo non-integer order derivative is presented. After developing a dimensionless flow model, the set of governing equations are solved with the help of integral transform, namely the Laplace transform and closed solutions are obtained. Also, some graphs of temperature and velocity field are drawn to see the subjectively of fractional parameter [Formula: see text] and other involved parameters of interest. It also shows dual nature for small and large time behavior due to the power-law kernel. Further, a comparative analysis between the temperature as well as the velocity fields with existing literature has been presented. Further, as a result, it is concluded that constant proportional Caputo derivative shows more decaying nature of the fluid flow properties than classical Caputo and Caputo-Fabrizio fractional derivatives.

Numerical Study of Unsteady MHD Second Grade Fluid Flow and Heat Transfer Within Porous Channel

Numerical Study of Unsteady MHD Second Grade Fluid Flow and Heat Transfer Within Porous Channel

Similarity solution of second grade fluid flow over a moving cylinder

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter [Formula: see text] increase, which means the momentum boundary layer increases for enhancing the material parameter [Formula: see text]. The temperature gradient reduced due enhancing the values of material parameter [Formula: see text] because thermal boundary layer reduced for higher values of material parameter [Formula: see text].

On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝ N

Abstract We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝ N , which is derived from a non-Newtonain fluid for a generalized second grade fluid with Riemann-Liouville fractional derivative. We show that a solution operator involving the Laplacian operator is very effective to discuss the proposed problem. In this paper, we are concerned with the global/local well-posedness of the problem, the approaches rely on the Gagliardo-Nirenberg inequalities, operator theory, standard fixed point technique and harmonic analysis methods. We also present several results on the continuation, a blow-up alternative with a blow-up rate and the integrability in Lebesgue spaces.

Convective Flow of Second Grade Fluid Over a Curved Stretching Sheet with Dufour and Soret Effects

Convective Flow of Second Grade Fluid Over a Curved Stretching Sheet with Dufour and Soret Effects

Significance of induced magnetic field and variable thermal conductivity on stagnation point flow of second grade fluid

Significance of induced magnetic field and variable thermal conductivity on stagnation point flow of second grade fluid

Electroosmotic flow of generalized fractional second grade fluid with fractional Cattaneo model through a vertical annulus

Because of the rapid advancement of microdevices technologies, electroosmotic flow (EOF) has gotten a lot of coverage in recent years. EOF has a range of benefits over other micropumps, including the ability to create continuous pulse-free flows and elimination of moving parts. Our aim is to investigate the unsteady electroosmotic flow (EOF) of an electrolyte solution of generalized fractional second grade hybrid nanofluid (Cu-TiO2/Water) confined between vertical two coaxial tubes. The energy equation will be altered by the fractional Cattaneo model. The finite Hankel technique and Laplace transformation will be employed to acquire the solution of the mathematical model. Since obtaining the inversion of Laplace of the transformed functions in the closed-form is a challenging task, the numerical inversion algorithm will be used. The results showed that the hybrid nanofluid became more viscous with increasing the volume concentration which reduces the electroosmotic (EO) velocity and the flow rate. Moreover, the electroosmotic flow is boosted by the free convection force.

Effect of Magnetic Field with Parabolic Motion on Fractional Second Grade Fluid

This paper is an analysis of the flow of magnetohydrodynamics (MHD) second grade fluid (SGF) under the influence of chemical reaction, heat generation/absorption, ramped temperature and concentration and thermodiffusion. The fluid was made to flow through a porous medium. It has been proven in many already-published articles that heat and mass transfer do not always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such a dynamical process very accurately; thus, a different concept of differentiation is needed to capture such a process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The equations for heat, mass and momentum are established in the terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional derivatives. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of existing parameters. It is concluded that the fluid velocity shows increasing behavior for κ, Gr and Gm, while velocity decreases for Pr and M. For Kr, both velocity and concentration curves show decreasing behavior. Fluid flow accelerates under the influence of Sr and R. Temperature and concentration profiles increase for Sr and R. Moreover, the ABC fractional operator presents a larger memory effect than C and CF fractional operators.

New modeling and analytical solution of fourth grade (non-Newtonian) fluid by a stretchable magnetized Riga device

The aim of this paper is to examine the influence of heat source/sink on boundary layer flow of a fourth-grade liquid over a stretchable Riga plate on taking account of induced magnetic field and mixed convection. Analysis of mass and heat transport is studied through modified Fourier heat flux model. The governing flow issue is demonstrated with the help of momentum, energy, temperature and concentration equation. The modeled equations are reduced into nondimensional ODEs by opting suitable similarity transformations. The analytic solutions are discussed by means of the optimal technique of homotopy analysis. The influence of several nondimensional parameters on velocity, thermal and concentration gradients are deliberated by using suitable graphs. Also, the skin friction is discussed with the help of graphs. The result outcomes reveal that, velocity of fluid diminishes for advanced values of viscoelastic parameter and fourth-grade liquid parameter but contrary movement is seen for third grade fluid parameters. Fluid temperature boosts up for thermal relaxation parameter and concentration is abridged for rising values of solutal concentration parameter and Schmidt number.

Supervised Learning Algorithm to Study the Magnetohydrodynamic Flow of a Third Grade Fluid for the Analysis of Wire Coating.

In the present study, modeling of intelligent numerical computing through Levenberg–Marquardt back propagation-based supervised neural network (LMB-SNN) is incorporated to analyze the magnetohydrodynamic flow of a third grade fluid for wire coating analysis (MHD-TGFWCA). The original mathematical formulations in terms of partial differential equations for MHD-TGFWCA are converted into a system of ordinary differential equations through dimensionless parameters and a suitable transformation mechanism. A reference dataset for the LMB-SNNs scheme is created with Adam’s numerical technique for various scenarios by variation of different physical quantities such as third grade fluid parameter, magnetic parameter, and the velocity ratio parameter. To compute the approximate solution for MHD-TGFWCA in terms of various scenarios, the training, testing, and validation operations are carried out in parallel to adjust neural networks by developing the mean square error function (MSEF) through Levenberg–Marquardt back-propagation. The comparative analyses and performance studies through outputs of MSEF, regression illustrations, and error histograms validate the effectiveness of the suggested solver LMB-SNNs. The method’s precision is verified by the closest numerical outputs of both built and dataset values with similar levels 10^{-5} to 10^{-9}.