Second-grade Fluid Research Articles

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.

Second-grade nanofluid flow above a vertical slandering Riga surface with double diffusion model

The research of non-Newtonian fluids has gained the attention of scientists because of its assorted uses in biological sciences, drug reduction, damping device production and industry. Second-grade nanofluid is one of the non-Newtonian fluids. This study includes the study of second-grade nanofluid flow passing through a stretchable vertical Riga surface of variable thickness. Thermal conductivity and viscosity are taken as variables, as the function of temperature. For heat transfer, this study includes the influences of thermophoresis and Brownian motion. The Cattaneo–Christov double diffusive (CCDD) model is considered and buoyancy forces’ effects are examined. The governing equations are converted to the nonlinear ordinary differential equations (ODEs) to solve these equations easily. The solution is obtained using the MATLAB package with its bvp4c technique. Consequences of different parameters like second-grade fluid parameter modified Hartmann number, thermal time relaxation parameter, concentration time parameter, variable thermal conductivity parameter, buoyancy forces, Brownian motion parameter, Schmidt number and thermophoresis parameter are interpreted through graphs and tables. This research exposes that Buoyancy forces’ parameters have antagonistic behavior on velocity curves. Depreciation in temperature and concentration is also noted with the rise in thermal time relaxation and concentration time relaxation.

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.

Bioconvection of MHD Second-Grade Fluid Conveying Nanoparticles over an Exponentially Stretching Sheet: A Biofuel Applications

Bioconvection of MHD Second-Grade Fluid Conveying Nanoparticles over an Exponentially Stretching Sheet: A Biofuel Applications

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).

Hall, Soret, and rotational effects on unsteady MHD rotating flow of a second-grade fluid through a porous medium in the presence of chemical reaction and aligned magnetic field

The effects of Hall current, rotation and Soret effects on an unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid past an inclined plate embedded in a porous medium in the presence of chemical reaction and an aligned magnetic field are investigated. An exact analytical solution of the governing equations for fluid velocity, fluid temperature, and species concentration subject to appropriate initial and boundary conditions is obtained using the perturbation technique. Expressions for shear stress, rate of heat transfer and rate of mass transfer at the plate are derived for both ramped temperature and isothermal plates. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically, whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and Soret parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Concentration buoyancy force, hall current, and Prandtl number have tendency to reduce in skin friction whereas permeability of the porous medium, Rotation, chemical reaction, Soret number, thermal buoyancy force and mass diffusion have reverse effect on it.

Insight into the dynamics of second-grade fluid subject to inclined magnetic force, newtonian heating, slip flow, and prabhakar-like fractional kind of newtonian heating

Sequel to the significance of the dynamics of second-grade fluid in the industry, nothing is known on the increasing inclined magnetic force, Newtonian heating, slip flow and Prabhakar-like fractional kind of Newtonian heating. In this study, the novel modified and efficient fractional approach, namely, the Prabhakar fractional technique is applied on an unsteady flow of second-grade liquid flowing on an inclined oscillating plate. The flowing fluid is moving under the effects of an applied inclined magnetic field, furthermore, the Newtonian heating effect and slip on the boundaries of the wall are also considered in the boundary conditions. After nondimensionalizing the governing equations, the solution of coupled equations is attained with the help of integral transform i.e., Laplace transformation method, and some numerical approaches are also applied for the Laplace inverse. The results convey that the momentum field decrease with increase in fractional constraints. The thermal change exhibits a declining tendency for increased values of fractional parameters. Furthermore, in comparison of velocity field attained by our applied fractional system with the existing literature, the curves of both Stehfest and Tzou’s methods overlay with each other which signifies the validity of our attained outcomes of momentum profile.

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.

Significance of Darcy-Brinkman porous drag forces and Cattaneo-Christov thermal transportation on the features of second-grade fluid flows conveying copper nanomaterials past an unsteady stretching permeable sheet heated convectively

The main thermo-hydro-rheological behaviors featuring the unsteady convective laminar motion of copper-methanol second-grade nanofluid over a linearly stretching permeable sheet is explored numerically in the framework of Cattaneo-Christov theory to provide a better understanding of the heat transfer mechanism within a Darcy-Brinkman porous medium. By adopting the single-phase nanofluid model along with the boundary layer approximations, the leading partial differential equations (PDEs) are derived properly and then converted mathematically into a differential structure of ordinary differential equations (ODEs) via appropriate similarity alterations. Accordingly, the resulting dimensionless boundary layer equations are tacked numerically for convective and suction boundary conditions by utilizing the generalized differential quadrature method (GDQM). To reveal the effect of such a pertinent flow parameter, extensive GDQM numerical data are outputted graphically for the velocity and temperature fields as well as tabularly for skin friction coefficient and the Nusselt number. As the main findings, it is noted that both the velocity profile and the wall temperature lessen with the suction parameter and the nanoparticle’s loading. However, an enhancement is depicted for the wall heat transfer rate with the reinforcement in those influences. In addition, it is witnessed that the effect of the surface drag forces is strengthened with the nanoparticle’s loading and weakened with a higher estimation of the suction effect.

A Prabhakar fractional approach with generalized fourier law for thermal activity of non-newtonian second-grade type fluid flow: a fractional approach

In this work, we studied the unsteady and incompressible flow of second-grade MHD fluid moving on a vertical oscillating plate, which is passing under the possessions of an applied inclined magnetic field. The non-dimensional governed equations are turned into a fractional model using the most advanced and effective fractional definition, Prabhakar fractional derivative, which is frequently based on generalized Fourier's and Fick's laws. The resultant system is handled using integral transform, i.e. the Laplace transformation (LT) scheme, and some numerical methods are also applied for the Laplace inverse. The graphical and numerical representation of all parameters is also deliberated to analyze the physical behavior of the effects of significant parameters. As a result, it concluded that the impact of the second-grade fluid constraint slowed down the momentum profile of the moving fluid. Furthermore, in comparing the velocity field attained by our applied fractional scheme with existing literature, the overlapping of both curves with each other indicates the validity of our attained results of momentum profile. Additionally, the overlapping of both numerical scheme curves for the Laplace inverse also verifies the study's findings.

Peristaltic pump with heat and mass transfer of a fractional second grade fluid through porous medium inside a tube

In magnetic resonance imaging (MRI), this MRI is used for the diagnosis of the brain. The dynamic of these particles occurs under the action of the peristaltic waves generated on the flexible walls of the brain. Studying such fluid flow of a Fractional Second-Grade under this action is therefore useful in treating tissues of cancer. This paper deals with a theoretical investigation of the interaction of heat and mass transfer in the peristaltic flow of a magnetic field fractional second-grade fluid through a tube, under the assumption of low Reynolds number and long-wavelength. The analytical solution to a problem is obtained by using Caputo's definition. The effect of different physical parameters, the material constant, magnetic field, and fractional parameter on the temperature, concentration, axial velocity, pressure gradient, pressure rise, friction forces, and coefficient of heat and mass transfer are discussed with particular emphasis. The computed results are presented in graphical form. It is because the nature of heat and mass transfer coefficient is oscillatory which is following the physical expectation due to the oscillatory nature of the tube wall. It is perceived that with an increase in Hartmann number, the velocity decreases. A suitable comparison has been made with the prior results in the literature as a limiting case of the considered problem.

Thermosolutal Marangoni Bioconvection of a Non-Newtonian Nanofluid in a Stratified Medium

Abstract Bioconvection due to the movement of the micro-organism cells is universal and affects many ecological and biological processes, including infection, reproduction, and marine life ecosystems. The impact of the bioconvection is more significant in nanofluids. In the present problem, we investigate the Marangoni triply stratified bioconvective flow of non-Newtonian (second-grade) nanofluid with the presence of motile micro-organisms over a permeable inclined plate. The problem provides an analysis of the impact of second-order effects, namely, viscous dissipation, radiation, and chemical reaction, allowing a set of similarity transformations to convert the governing PDEs into coupled nonlinear DEs. Thereafter, Runge–Kutta Fehlberg's numerical method is employed to find the solution of the DEs for some chosen values of different flow influencing parameters. The impact of crucial parameters on the velocity, temperature, nanoparticles volume fraction, the motile density of micro-organisms, and the quantities of physical interest, namely, local Nusselt number, local Sherwood number, and local motile micro-organism density number are illustrated through the plots and tables. It is revealed that the second-grade fluid parameter indicates a prominent correlation with the Marangoni convection in the bioconvective transport mechanism. Also, the Marangoni convection is significant in bioconvective flows for large Péclet numbers.

Analysis of Heat and Mass Transfer of Fractionalized MHD Second-Grade Fluid over Nonlinearly Moving Porous Plate

This study investigates the heat and mass transfer in the MHD flow of fractionalized second-grade fluid induced by impulsively moved bottom porous plate with nonlinear velocity of the magnitude KTD. To acquire the fractionalized nondimensional set of flow administering differential equations, fractional calculus and dimensionless variables are considered. The solution process utilizes Laplace transform and results in the acquired outputs in terms of generalized functions. The exact solutions for concentration, temperature, velocity, and the shear stress are then reduced by certain limits into fractional/traditional second-grade and Newtonian fluids as per the special cases within and out of the magnetic and porous effects. It is observed that these special cases occur in the previous published literature which verify the results of this study. The results are pictorially visualized to perform the analysis for impacts of diverse physical parameters and dimensionless quantities on concentration, temperature, and velocity fields. It is learned from the analysis that magnitude of viscoelastic parameter is directly proportional to velocity whereas the porous and magmatic effects are inversely proportional. Increasing fractional parameter values reduce flow fields of velocity and temperature. Effects of dimensionless parameters for heat and mass transfer are analysed in detail.

The Rayleigh–Stokes Problem for a Heated Generalized Second-Grade Fluid with Fractional Derivative: An Implicit Scheme via Riemann–Liouville Integral

The goal of this study is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) with Riemann–Liouville time fractional derivative using the fast algorithm. The modified implicit scheme, which is formulated by the Riemann–Liouville integral formula and applied to the fractional RSP-HGSGF, is proposed. Numerical experiments will be carried out to demonstrate that the scheme is simple to implement, and the results will reveal the best way to implement the suggested technique. The proposed scheme’s stability and convergence will be examined using the Fourier series. The method is stable, and the approximation solution approaches the exact solution. A numerical demonstration will be provided to demonstrate the applicability and viability of the suggested strategy.

Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics

This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes the Laplace transform of the Caputo derivative. The impact of the used fractional operator is presented; especially, the acceleration effect is noticed in the paper. The parameters’ influences are focused on the dynamics such as the Prandtl number (Pr), the Grashof numbers (Gr), and the parameter η when the fractional-order derivative is used in modeling the second-grade fluid model. Their impacts are also analyzed from a physical point of view besides mathematical calculations. The impact of the fractional parameter α is also provided. Finally, it is concluded that the graphical representations support the theoretical observations of the paper.

Heat transfers thermodynamic activity of a second-grade ternary nanofluid flow over a vertical plate with Atangana-Baleanu time-fractional integral

The impact of the Atangana-Baleanu (AB) time-fractional integral on second-grade fluid with ternary nanoparticle suspension across an infinite vertical plate was studied in this paper. By generalized Fourier's law, the generalized fractional constitutive equation for the thermal flux explains a thermal process with memory. Closed-form solutions are calculated using Laplace transform and represented using Lorenzo and Hartley G–functions and integral forms. The numerical effects of physical and fractional parameters are presented.

Heat and mass transfer features of transient second-grade fluid flow through an exponentially stretching surface

Heat and mass transfer features of transient second-grade fluid flow through an exponentially stretching surface

Impact of nanoparticles and radiation phenomenon on viscoelastic fluid

In recent years, nanotechnologies have been widely used in several fields regarding their rapid developments which create a lot of prospects for researchers and engineers. More specifically, replacement of conventional liquids with nanoliquids is considered as an innovative solution to heat transfer problems. This research work reports mixed convective phenomenon of viscoelastic fluids with variable stretched surface. This study prospects the applications in biotechnology and irrigation systems. Characteristics of thermophoresis, nonlinear thermal radiation and Brownian moment are examined. Significant influence of no mass flux relation and variable thicked surface on second grade is studied in this work. Moreover, heat-mass transportation phenomenon is explored through thermophoresis, nonlinear thermal radiation and Brownian diffusion. Transformation procedure is adopted in order to achieve required ODEs. HAM procedure is adopted to obtain the series solution. Outcomes of physical parameters for velocity, temperature and concentration fields are discussed. Here velocity profile of second-grade fluid is detected to be a declining function K (local second-grade parameter). Higher [Formula: see text] (Brownian moment parameter) intensifies the temperature profile while concentration of viscoelastic liquid dwindles against [Formula: see text].

Heat transport in entropy-optimized flow of viscoelastic fluid due to Riga plate: analysis of artificial neural network

In this paper, we focus to design intelligence numerical computing through artificial neural networks (ANNs) which are backpropagated with Levenberg–Marquard technique (NN-BLMT) for the theoretical approach of physical aspects of heat generation in second-grade fluid (PA-HG-SGF) due to Riga plate. The Riga plate (RP) is known as the physical interaction stimulus, which consists of electrodes and enduring electromagnets that are located on plane surface. The purpose of NN-BLMT is to learn the weight of neural networks on the basis of optimization of the fitness value based on mean-square error between the proposed result and reference numerical solution. The innovation and reliability of NN-BLMT used will be greatly better as compared to traditional numerical techniques that are used to solve commercial and industrial problems. NN-BLMT is fast and easy to apply on nonlinear problems and get best results. The original model PA-HG-SGF in term of PDEs is first converted into system of nonlinear ODEs through suitable transformation and then numerically solved. Through Adam numerical technique (AMT) in Mathematica software, a dataset for PA-HG-SGF is attained for different scenarios of PA-HG-SGF by variation of second-grade parameter, heat-generation parameter, Hartman number, thermal lamination parameter, thermal composure parameter and Prandtl number. Expected solutions are described for PA-HG-SGF through the NN-BLMT testing, training, and validation process. In addition, NN-BLMT relative studies and performance analysis are validated by histogram studies, regression analysis and MSE and then analyzed PA-HG-SGF.

Exact solutions for 2D boundary layer flow of two types of viscoelastic fluids and heat transfer on a permeable shrinking sheet with thermal radiation and variable surface temperature: existence of multiple solutions

A study with existence of multiple exact solutions has its own importance, and if the study is performed for a viscoelastic fluid, then the attraction becomes very high. So, here an attempt is performed, where the flow of two types of viscoelastic fluids and heat transfer due to shrinking of a permeable sheet is described. In the energy flow, the impacts of thermal radiation and variable temperature of the wall are simultaneously undertaken. By using similarity approach, in addition to single solution, the dual and triple closed-form solutions of the flow field and temperature are obtained in some specific flow situations of two fluids, namely, second-grade and Walters liquid B. Dual solutions for the flow of second-grade fluid are detected only for stronger mass suction with smaller viscoelastic parameter of second-grade fluid and for both weaker and stronger mass suctions (for two ranges) with larger viscoelastic parameter and unique solution in case of mass injection. However, for the flow of Walters liquid B, boundary layer solution is attained for mass suction only, and most importantly, triple solutions for some mass suction range are found. Now for heat flow, an exceptional result is witnessed: if the wall temperature distribution is assumed suitably, then the heat transfer rate is not dependent on the fluid rheology. Also, influences of involved physical parameters on velocity, temperature and other important quantities are described through some graphs.