Flow Of Second Grade Fluid Research Articles

Processing to pass unsteady MHD flow of a second-grade fluid through a porous medium in the presence of radiation absorption exhibits Diffusion thermo, hall and ion slip effects

ABSTRACT ‘This research aims to look at the consequences of diffusion thermo, Hall, ion slip, and radiation absorption on the unsteady MHD turbulent rotational flow of second-grade fluid through porous materials while also regarding the outcomes of the chemical retort and heat absorption. When the ratio between the number of collisions between fluid electrons in a cyclotron and the number of collisions between electrons and atoms is large, Hall effects (the Hall parameter) become important. The regular perturbation approach investigates the outlines of velocity segments, temperature dispersion, and concentration. The statistics for shear stress, the Nusselt numeral, and the Sherwood factor are written down on the panel. Graphs show how changes in different physical parameters cause changes in a fluid’s speed, temperature, and concentration patterns. In the end, it can be said that the primary and secondary velocities speed up significantly as the Hall and ion-slip parameters get bigger. This effect was also seen in the shearing stress’s axial and transverse components. The increasing importance of the thermal diffusion parameter increases both the initial and secondary velocities’.

EMHD flow of second-grade fluid through a heated permeable disk with space dependent heat source

In this article, von Kárman MHD viscoelastic fluid flow with second-grade model through a heated permeable disk on electric field is examined thoroughly. The effects of viscous dissipation and elasticity on fluid motion around the disk, temperature and space-dependent heat source/sink are also examined. Governing partial differential equations are transmitted into ordinary differential equations with similarity functions. Later, nonlinear system of ordinary differential equations was solved with the help of Galerkin finite element method. Accuracy and validity of the method were noticed by comparing our results with the previous literature. Simulations are performed in order to capture the dynamics of the physical situations against the variation of the pertinent parameters. Nature of heat flux and stresses of the physical parameters are discussed. Physical influence of heat flux, heat transfer is exhibited graphically at the surface of disk and increases when the values of Prandtl number are increased, whereas there is a decreasing trend in the rate of heat transfer when the value of Eckert number is increased.

Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been developed by using the Lie symmetry method. PDE's (Partial Differential Equations) are transformed into ODE's (Ordinary Differential Equations) by implementing the suitable transformation. A numerical method called bvp4c is used to explain the dimensionless system (ODE's). Graphs and tables are used to interpret the impact of the significant physical parameters. The curves of temperature function declined due to enchanting the values of the thermophoresis Parameter. The temperature is produced at a low level due to enchanting the values of thermophoresis because this force transports burn at a low 10 μm diameter so the temperature becomes lessor. Increments of thermophoresis parameter which enhanced the values of concentration Function. As the concentration boundary layer increased which declined the mass transfer due increment in thermophoresis. The curves of temperature function are increasing due to enhancing the values of the Brownian parameter because addition in the Brownian motion, improved the movement of particles ultimately increasing the kinematic energy of fluid which improved the heat transfer phenomena. Increments of Brownian parameter which declined the values of concentration function. Physically, the kinematic energy improved which declined the mass transfer rate near the surface.

Effect of natural heat convection on fractional MHD second-grade fluid in an infinite vertically oscillating cylinder with Hankel transform

In this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy force. Here, the MHD flow is modeled using the Caputo-Fabrizio non-integer derivative approach. The exact solution of the governing continuity, momentum and energy equations is obtained by means of Laplace and finite Hankel transforms. The commercial simulation software, Mathematica is used for calculating the roots of the Bessel function. The effects of dimensionless parameters such as Grashof and Prandtl numbers, magnetic field and fractional parameters on the second-grade fluid flow are analyzed. Heat transfer is high at a small Prandtl number. Velocity correlates positively with Grashof number and magnetic field, and negatively with Prandtl number. The heat and mass transfer results obtained from both conventional and fractional models are compared as well.

Inspecting heat transport phenomenon in the flow of non-Newtonian fluid in the presence of Newtonian heating and inclined slip: fractional derivative framework

A fractional model is considered to the present thermodynamic aspect of heat and fluid flow of second-grade fluid with a porous medium. The mixed convection features and inclined directional magnetic force are also enrolled. The convective thermal constraints are utilized for assessing the heat transfer properties. The erect vertical with the porous medium induced the flow. Two fractional approaches, Caputo-Fabrizio (CF) and Caputo-time algorithms, are utilized for the computation of analytical tasks. The integration is facilitated with the Laplace technique. Stehfest and Tzou’s techniques are used for evaluating the Laplace inverse transformation. The physical parameters’ contribution to altering the velocity and temperature profile is justified. It is noted that velocity and temperature profiles decrease for the non-singular parameters. More decrement in velocity and temperature profiles is associated with the Caputo-time model.

Lubricated surface oblique stagnation point flow of second-grade fluid with heat and mass transfer phenomenon: applications to hydraulic systems

The lubrication phenomenon with heat and mass transfer phenomenon justified applications in ploy engineering, polymer processes, compressor oils, piston oils, hydraulic systems, and paint industries. This contribution attributes the significance of heat and mass transfer due to the lubricated surface. The enhancement in the lubricated phenomenon is further suggested by incorporating the nonlinear radiative impact and chemical reaction. The viscoelastic fluid flow is confined in the zone of stagnation point of the lubricated surface. The axial and tangential velocities are presented for no-slip and full-slip cases. Moreover, a comparative analysis is carried out for temperature distribution over lubricated and non-lubricated surfaces for linear and nonlinear radiations. The problem is modeled in view of fundamental conservation laws, and the similarity variables are used to transfer them to the system of coupled nonlinear boundary value problem which is approximated by the Keller box method. The obtained results are validated with the existing literature as a particular case of the present study. It is noted that the local Nusselt number and Sherwood number are reduced by decreasing the efficiency of the lubricant also the nonlinear thermal radiation assists the heat transfer rate. The increase in chemical reaction declined the concentration phenomenon.

Time-dependent fractional second-grade fluid flow through a channel influenced by unsteady motion of a bottom plate

<abstract> <p>This investigation theoretically describes the exact solution of an unsteady fractional a second-grade fluid upon a bottom plate constrained by two walls at the sides which are parallel to each other and are normal to the bottom plate. The flow in the fluid is induced by the time dependent motion of the bottom plate. Initially the flow equation along with boundary and initial conditions are considered which are then transformed to dimensionless notations using suitable set of variables. The Laplace as well as Fourier transformations have been employed to recover the exact solution of flow equation. The time fractional differential operator of Caputo-Fabrizio has been employed to have constitutive equations of fractional order for second-grade fluid. After obtaining the general exact solutions for flow characteristics, three different cases at the surface of bottom plate are discussed; namely (i) Stokes first problem (ii) Accelerating flow (iii) Stokes second problem. It has noticed in this study that, for higher values of Reynolds number the flow characteristics have augmented in all the three cases. Moreover, higher values of time variable have supported the flow of fractional fluid for impulsive and constantly accelerated motion and have opposeed the flow for sine and cosine oscillations.</p> </abstract>

Analysis of second grade hybrid nanofluid flow over a stretching flat plate in the presence of activation energy

The research of fluid containing nanoparticles for the heat transport characteristics is very famous because of its variety of real-life applications in various thermal systems. Although the thermal efficiency of the nanofluid was effective but still the nano scientists were trying to introduce some new advance class of fluid. Therefore, an advance class of fluid is developed by the dispersion of two different nano sized particles in the conventional base fluid known as “Hybrid nanofluid” which is more effective compared to simple nanofluids in many engineering and industrial applications. Therefore, motivated from the hybrid type of nanofluids in the current research we have taken two-dimensional laminar and steady flow of second grade fluid passing through porous plate. The engine oil base fluid is widely used fluid in the engineering and industrial problems. Keeping these applications in mind the engine oil is considered and two different nanoparticles Copper and aluminum oxide are added in ordered to get the required thermal characteristics. In addition to this the thermal radiation, chemical reaction, activation energy, Brownian motion and thermophoresis are also addressed during the current research. The present proposed higher-order PDE’s is transformed to the non-linear system of ODE’s. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the present analysis and experimental study, it has been proved that the performance of hybrid nanofluid is efficient in many situations compared to nanofluid and regular fluid. For physical interpretation all the flow parameters are discussed through graphs. The impact of volume fraction is also addressed through graphs. Moreover, the comparative analysis between hybrid and nanofluid is carried out and found that hybrid nanofluid performed well as compared to nanofluid and regular fluid. The engineering quantities obtained from the present research have been presented in tables.

Chemical reaction and Soret effects on MHD convective flow of second grade fluid through an absorbent medium with ramped wall temperature as well as ramped surface concentration

In the present paper, the heat generating and/or absorption as well as thermo-diffusion on the unsteady free convection MHD gyrating flow of radiation and chemical reactive second grade fluid past an unbounded perpendicular plate during absorbent medium have been discussed. Here, it is assumed that, the confining plate has the ramped wall temperature with ramped surface concentration and isothermal temperature with ramped surface concentration. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration profiles are analyzed with quite few figures. It is determined that, velocity, temperature and concentration distribution sketches in case of ramped temperature as well as ramped surface concentration are not as much of as those of isothermal temperature as well as ramped surface concentration. In addition to the idioms of skin friction, Nusselt number as well as Sherwood number are achieved and characterized numerically with tabular format.

Radiation effects on MHD flow of second grade fluid through porous medium past an exponentially stretching sheet with chemical reaction

This article looked at the effects of electromagnetic force, chemical radiation, and thermal radiation on second-grade fluid passing through an exponentially stretched sheet with a heat sink and a porous medium. Using similarity transformations, the governing system of nonlinear partial differential equations has been converted into a system of ordinary differential equations. The Successive Linearization Method is then used to solve the system numerically. Graphs are used to display the numerical findings for the profiles of velocity, temperature, and concentration. The effects of various parameters are looked at and evaluated. The numerical values of the local Sherwood number, local Nusselt number, porosity, retardation number, and skin friction coefficient are presented and examined. The findings show that a wide range of variables significantly affect the fluid flow patterns. The reaction rate parameter had a significant impact on the concentration profiles, and as the reaction rate parameter grew, the boundary layer's concentration thickness reduced. The analysis's findings and the findings of previous studies were compared, and it was discovered that they were in excellent agreement.

Thermo diffusion impacts on the flow of second grade fluid with application of (ABC), (CF) and (CPC) subject to exponential heating

The aim of this article is to investigate the exact solution by using a new approach for the thermal transport phenomena of second grade fluid flow under the impact of MHD along with exponential heating as well as Darcy’s law. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.

Hall Current and Soret Effects on Unsteady MHD Rotating Flow of Second-Grade Fluid through Porous Media under the Influences of Thermal Radiation and Chemical Reactions

The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

Recent Development of Heat and Mass Transport in the Presence of Hall, Ion Slip and Thermo Diffusion in Radiative Second Grade Material: Application of Micromachines.

This article describes the incompressible two-dimensional heat and mass transfer of an electrically conducting second-grade fluid flow in a porous medium with Hall and ion slip effects, diffusion thermal effects, and radiation absorption effects. It is assumed that the fluid is a gray, absorbing–emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. It is assumed that the liquid is opaque and absorbs and emits radiation in a manner that does not result in scattering. It is considered an unsteady laminar MHD convective rotating flow of heat-producing or absorbing second-grade fluid across a semi-infinite vertical moving permeable surface. The profiles of velocity components, temperature distribution, and concentration are studied to apply the regular perturbation technique. These profiles are shown as graphs for various fluid and geometric parameters such as Hall and ion slip parameters, radiation absorption, diffusion thermo, Prandtl number, Schmidt number, and chemical reaction rate. On the other hand, the skin friction coefficient and the Nusselt number are determined by numerical evaluation and provided in tables. These tables are then analysed and debated for various values of the flow parameters that regulate it. It may be deduced that an increase in the parameters of radiation absorption, Hall, and ion slip over the fluid region increases the velocity produced. The resulting momentum continually grows to a very high level, with contributions from the thermal and solutal buoyancy forces. The temperature distribution may be more concentrated by raising both the heat source parameter and the quantity of radiation. When one of the parameters for the chemical reaction is increased, the whole fluid area will experience a fall in concentration. Skin friction may be decreased by manipulating the rotation parameter, but the Hall effect and ion slip effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.

Insight into hybrid nanofluid induced by a Riga plate: investigation on second grade fluid model

Riga plate is an innovative magnetic mechanism that originated from the cluster of arranged changeless magnets and alternative electrodes over a plane surface. This innovative magnetic mechanism initiates a wall-parallel Lorentz force by postponing the boundary layer separation and decreasing the turbulence impact. In this study, the flow behavior of hybrid nanofluid on second-grade models over a Riga plate is investigated. By employing the similarity transformation, the governing model is converted to a system of ordinary differential equations, which could then be solved using the Runge Kutta–Fehlberg method coupled with a shooting technique. Analysis of the obtained results has proved that the flow of second-grade fluid is influenced significantly by the controlling parameters. Both EMHD parameter and hybrid nanoparticles have a role in the thermal development of this non-Newtonian working fluid. The velocity and temperature profiles are intensified due to the instigation of Lorentz force through the EMHD parameter. Augmentation of the temperature is observed on account of rising Al2O3/H2O and Cu/H2O concentrations. As compared to Cu/H2O nanofluid, the distributions of skin friction and heat transfer are pronounced for Al2O3-Cu/H2O hybrid nanofluid which signifies the capacity of hybrid nanofluid as a novel procreation fluid having high thermal performance.

Unsteady MHD Thin Film Flow of a Second-Grade Fluid past a Tilted Plate under the Impact of Thermal Radiation and Chemical Reaction

This paper explores the impact of chemical reaction and thermal radiation on time-dependent hydromagnetic thin-film flow of a second-grade fluid across an inclined flat plate embedded in a porous medium. The thermal radiation based on the Rosseland approximation is incorporated in the energy equation. Uniform applied magnetic field and first-order homogenous chemical reaction are included in the momentum and concentration equations, respectively. The novel mathematical flow model is constructed by using a set of partial differential equations (PDEs). The PDEs are then transformed into an equivalent set of ordinary differential equations (ODEs) and solved by applying the Laplace transform method. However, the time domain solutions are obtained by using the INVLAP subroutine of MATLAB. Physical parameters influencing thin-film velocity, temperature, and concentration are illustrated graphically, while those affecting skin friction, heat, and mass transfer rates are presented in a tabular form. It is found that thin-film velocity and temperature boost with increasing values of thermal radiation, but thin-film velocity decreases with increasing values of chemical reaction and magnetic field. The current investigation is to enhance heat and mass transfer in the design of mechanical systems involving the thin film flow of second-grade fluids over an inclined flat plate after applying thermal radiation and chemical reaction.

Significance of thermal radiation, Lorentz force, and non-Darcian porous medium on the dynamics of second-grade fluid subject to exponential stretching sheet

ABSTRACT This paper studies the non-Newtonian fluid flow over an exponential non-Darcian permeable stretching sheet. The heat generation and non-linear radiation effects are inspected for second-grade fluid flow by employing MHD normal to the flow. The mathematical model is developed in partial differential equations under the boundary layer approximations. These equations are reduced by employing similarity transformations in ordinary differential equations. The ordinary differential equations in dimensionless forms are solved by using the numerical procedure bvp4c method. The involved physical parameters impacts are explained via graphs and tables. The horizontal velocity function enlarges the porosity parameter because the porous media behaves as a barrier (opposes) to the flow. The vertical velocity diminishes with higher values of variable viscosity parameters because the rising viscosity is associated with increasing flow resistance, which lessens the fluid's velocity. The vertical velocity gets lower values as the values of magneto hydrodynamic parameter rise, causing a reduction in flow velocity, and as a result, graph vertical velocity falls. However, as the magnetohydrodynamic parameter increases, liquid surface penetration in the wall region rises.

Significance of Thermal Phenomena and Mechanisms of Heat Transfer through the Dynamics of Second-Grade Micropolar Nanofluids

Due to their unique microstructures, micropolar fluids have attracted enormous attention due to their potential for industrial application, including convective heat and mass transfer polymer production and the rigid and random cooling of particles for metallic sheets. In this context, a micropolar second-grade fluid flow over a vertical Riga plate is investigated for hidden microstructures. The novelty of the flow model allows us to explore the significance of Brownian motion and thermophoresis on the dynamics of non-Newtonian fluid. A mathematical model is developed under the flow assumptions for micropolar second-grade fluid over a vertical Riga plate of PDEs, reducing them into ODEs by invoking similarity techniques. The acquired system of non-linear ODEs is elucidated numerically using bvp4c methodology. Furthermore, comparative tables are generated to confirm the bvp4c technique, ensuring the accuracy of our numerical approach. This rheological study of micropolar second-grade fluid suggests that temperature distribution increases due to variations in the micropolar parameter (K), Eckert number (Ec), and the thermophoresis parameter (Nt), and the concentration distribution (Φ(η)) keeps rising against the boosting values of Brownian motion (Nb); however, the inverse trend is noted against thermophoresis (Nt).

Entropy Generation and Thermal Analysis on MHD Second-Grade Fluid with Variable Thermophysical Properties over a Stratified Permeable Surface of Paraboloid Revolution

Stratification is used in a wide range of energy storage fields, including solar thermal energy systems. This paper investigates entropy optimization and the effects of heat production, magnetic field, and various fluid parameters on the flow of second-grade fluid through unstratified and stably stratified paraboloids of revolution. In the heat transfer equation, stratification, linear thermal radiation, and Joule dissipation have all been explored. The similarity transformation is used to convert the governing PDEs into nonlinear ODEs. The HAM (homotopy analysis method) is used to solve dimensionless nonlinear ODEs. The impact of significant elements on various profiles is exposed and explored. Graphical results are used to examine the influence of the velocity profile, temperature, concentration, and entropy formation rate using tables to indicate the characteristics of skin friction, Nusselt number, and Sherwood number for numerous parameters. It is noticed that the velocity is enhanced by raising the stratification parameter, while the opposite behavior is observed for temperature distribution. The concentration profile declined as the solute stratification parameter was enhanced. For both the unstratified and stratified regions, incremental values of the Brinkman number and magnetic parameter depict augmentation in entropy production, while entropy production drops for a large value of the temperature ratio parameter.

Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative

In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid.

Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts

Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts