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The main objective of this research is to analytically study an innovative, viscous, time-independent, and incompressible (HFN) hybrid nanofluid flow on a slanderous stretched surface. This study examines thermal conductivity, heat absorption/omission, thermal radiation, and the magnetic effect of in the existence of HFN. Incorporating an external heat source into the heat transfer process increases the effect of the dissipative heat and thermal radiation. The flow characteristics are governed by the mathematical form which is further transferred to ordinary differential equations (ODEs) via appropriate assumptions regarding similarity variables and stream functions. The strong nonlinearity was successfully solved using the analytical technique homotopy analysis method (HAM) for these nonlinear equations. The results and discussion section provides a thorough explanation of the main outcomes of the study. This research focuses on the enhancement of heat transfer and the effects. [ABSTRACT FROM AUTHOR]

This research article, examines the film flow of two-dimensional fluid along with the transfer of heat in a magnetic field on an unsteady extending sheet. To gain the appropriate outputs for the flow efficiency and rate of transfer of heat, the Power law fluids are mixed with the viscoelastic fluids which reduce the viscosity of the fluids. The heat transfer rate is further improved with the inclusion of nanoparticles. The flow and heat transmission characteristics of a Maxwell, Power-law-model-fluid along with Joule absorption and changeable liquid sheet thickness are examined. The combined model of the two non- Newtonian fluids also incorporated the nanofluid's influence. To create the coupled comparable ordinary differential equations (ODEs) that the homotopy analytical method (HAM) along with appropriate similarity transformations are used. Impacts of variations of different significant factors like the number of fluid flow of fluid film with the transfer of heat are perceived. The influence of the unsteadiness factor on a thin film is discovered analytically for various estimations. Despite this, the implanted factors utilized for understanding the physical demonstration, like magnetic factor, inertial parameter, Eckert number, penetrability factor, Prandtl number Pr and Deborah number have been offered by graphs and deliberated in detail. [ABSTRACT FROM AUTHOR]

The fractional-order differential equations that exist in the field of science and engineering have been studied in this paper. The 2D fluid flow problems are recommended for the classical- and fractional-order analysis. It has been found that the nonlinear fractional-order problems are more realistic than the classical models to describe the proposed flow problems since the behavior of the stress of the model problem is not linear. The similarity variable in this study has been used in fractional form to transform the modeled governing equations from partial PDEs. The acquired equations are the nonlinear ordinary differential equations (ODEs) in fractional form. The electromagnetic field has also been imposed into the fluid motion to calculate the embedded constraints in the case of classical and noninteger orders. The nonlinear problems are attempted using the FDE-12 technique. The important physical phenomena including Nusselt number and skin friction are also calculated in case of the integer- and noninteger-order problems. The electric and magnetic fields are examined and discussed in the case of fractional form and classical form. [ABSTRACT FROM AUTHOR]

• Casson-Maxwell fluid flow in the gap of the disk and cone system is considered for heat and mass transfer applications. To the best of our knowledge and belief, it is the pioneer attempt to consider the combination of two fluids for this unique kind of geometry. The combination of non-Newtonian and viscoelastic nature properties plays a vital role in heat and mass transfer analysis. • Magnetic field in combination with the Casson-Maxwell fluid flow over the rotating con and disk is also a new addition. • The Artificial Neural Network (ANN) strategy is used to solve the problem. The results are validated through error estimation. • The various cone and disk rotations are considered to analyze the flow behavior. The Casson-Maxwell nanofluid is affected by the same and opposite rotations of the devices, which are also derived and discussed in detail. The Casson-Maxwell model is particularly useful for studying viscoplastic fluids or fluids with yield stress, making it applicable to various engineering applications, including extrusion processes, coating applications, and biomedical fluid dynamics. Casson-Maxwell fluid flow enhances mass transfer rates due to the combined effects of non-Newtonian viscosity and viscoelastic behavior. This is particularly useful in processes where mass transfer limitations play a significant role, such as in multiphase reactions or reactive distillation systems. In the context of the above applications the present model, is the combination of Casson- Maxwell fluids that flow through the varying gap of the spinning cone and disk system (CDS) for the heat transfer enhancement. The magnetic field is also imposed in the upright direction to the flow field. The solution of the transform equations has been obtained through artificial neural networks (ANN). The skin friction, heat transfer rate, and comparative analysis have been done. The Casson-Maxwell parameters that depend on the viscoelastic behavior and high viscosity term, causes the fluid to slow down and tends to store the temperature, for a long time as compared to traditional fluids. The radial component of velocity decreases due to the increase in magnetic field. The relative error of the reference and targeted dates is calculated to demonstrate the best precision efficiency of ANN, with a range of 10−3 to 10−4. [ABSTRACT FROM AUTHOR]

A mathematical model of time-dependent thin-film flow of Carreau liquid over a stretching surface is studied in this investigation in the presence of couple stress and uniform magnetic field. To explain the properties of heat and mass transport phenomena, the influence of both thermophoresis and Brownian motion variables is used. For the conversion of the model framework (momentum, heat, and concentration expression with boundary conditions) into a set of ordinary differential equations, the appropriate transformation technique is followed. By using analytical tool, HomotopyAnalysis Method (HAM), the transformed model expressions are solved. For different estimations of the affected physical factors, the numerical results involving skin-friction coefficient, Nusselt number, Sherwood number, fluid velocity profile, thermal profile, and concentration profile are displayed graphically. Besides, the findings for skin-friction coefficient, Nu x , and ϕ η are given in the table format. In raising the fluid temperature, the effect of thermophoresis and magnetic parameters is beneficial. With the Brownian motion and Schmidt number, the solute concentration is found to reduce. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics flow of a nanofluid over an exponentially curved stretching surface is deeply focused in the current study. By using the assumption on the curved stretching surface, the governing equations are established. We obtain nonlinear partial differential equations by utilizing the boundary layer estimation on the Navier–Stokes condition. These equations are converted into nondimensional system ordinary differential equations, using a suitable similarity transformation. The governing system of equations is tackled through an analytical method. The impacts of different pertinent parameters involved in the governing equations are illustrated graphically, whereas the numerical values of Res1/2Cf, Res1/2Shs, and Res1/2Nu are also tabulated. The velocity profile declines with an increase in values of magnetic parameter and porosity parameter. The temperature profile is increasing, when the value of a thermophoretic parameter and Brownian motion parameter increases. A higher activation energy displays a stronger concentration profile. The concentration profile decreases for increasing values of the Schmidt number. The concentration profile shows the inverse impact for increasing values of the thermophoretic parameter and Brownian motion parameter. The focus of this study was to examine the heat transfer rate of nanoparticles. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic hybrid second-grade nanofluid flow towards a stretching/shrinking sheet with thermal radiation is inspected in current work. Main concern of current investigation is to consider hybrid A l 2 O 3 - C u nanofluid which is perceived by hanging two dissimilar kinds of nanoparticles known as alumina and copper within the base fluid. The fluid motion is produced by non-linear stretching/shrinking sheet. The modeled equations which comprise of energy, motion and continuity equations are changed into dimensionless form using group of similar variables. To determine the solution of transformed problem, the Homotopy Analysis technique is used. The findings of this work revealed that the magnetic parameter improves the heat transfer rate. This work also ensures that there are non-unique solutions of modeled problem for shrinking case and a unique solution for stretching case. Higher values of Re x results in declining of flow field. Rise in M agrees to a decline in velocity distributions. Higher values of second order fluid parameter reduces the viscosity of fluid and accordingly velocity increases. Velocity profile is also a decreasing function of volume friction. [ABSTRACT FROM AUTHOR]

In this article, the hydrodynamic stability of the Couette flow of an electrically conducting fluid flowing in a parallel-plate channel with a normal magnetic field is investigated through a porous medium. The transport phenomena in the porous medium have been of enduring interest from the last few decades. The linear perturbation theory of hydrodynamic stability along with the presumption of low magnetic Reynolds number is applied to the governing equations to derive the governing magnetohydrodynamic stability equation. A Chebyshev collocation method is operated to numerically elucidate the magnetohydrodynamic stability equation. A linearized velocity solution for developing flow is used in the stability calculations. The numerically determined neutral stability results for the fully developed Couette flow are in excellent agreement with those of the analytical solution. The results presented here for Hartmann flow are believed to be more accurate owing to the more exact nature of the numerical solution. [ABSTRACT FROM AUTHOR]

The main objective of this article is to study the inventive conception of the electrical Magneto hydrodynamics (MHD) rotational flow of Single and Multi-Walled Carbon nanotubes (SWCNTs/MWCNTs) base on the fluids (water, engine oil, ethylene glycol and kerosene oil). The thermal radiation impact is taken to be varying the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. Kerosene oil is taken as based nanofluids because of its unique attention due to their advanced thermal conductivities, exclusive features and applications. The fluid flow is assumed in steady state. The basic Navier Stocks equations have been transformed through similarity variables in the form of nonlinear differential equations. The solution of the problem has been obtained through Homotopy Analysis Method (HAM). Results obtained for single and multi-wall carbon nanotubes are compared. Plots have been presented in order to examine how the velocities and temperature profile get affected by various flow parameters. The numerical outputs of the physical properties are shown trough tables. The impact of Skin fraction coefficient and Nusselt number are shown in tables. [ABSTRACT FROM AUTHOR]

In this article the modeling and computations are exposed to introduce the new idea of MHD three-dimensional rotating flow of nanofluid through a stretching sheet. Single wall carbon nanotubes (SWCNTs) are utilized as a nano-sized materials while water is used as a base liquid. Single-wall carbon nanotubes (SWNTs) parade sole assets due to their rare structure. Such structure has significant optical and electronics features, wonderful strength and elasticity, and high thermal and chemical permanence. The heat exchange phenomena are deliberated subject to thermal radiation and moreover the impact of nanoparticles Brownian motion and thermophoresis are involved in the present investigation. For the nanofluid transport mechanism, we implemented the Xue model (Xue, Phys B Condens Matter 368:302-307, 2005). The governing nonlinear formulation based upon the law of conservation of mass, quantity of motion, thermal field and nanoparticles concentrations is first modeled and then solved by homotopy analysis method (HAM). Moreover, the graphical result has been exposed to investigate that in what manner the velocities, heat and nanomaterial concentration distributions effected through influential parameters. The mathematical facts of skin friction, Nusselt number and Sherwood number are presented through numerical data for SWCNTs. [ABSTRACT FROM AUTHOR]

The thin film flow of fluid over a stretching sheet with variable fluid properties under the effect of thermophoresis has been investigated. A transverse magnetic field is also applied to the fluid flow in the presence of thermal radiation. The governing equations have been transformed through suitable similarity variables into nonlinear coupled differential equations with physical conditions. The solution of the coupled problem has been obtained by using the second alternative of OHAM (OHAM-2). The solution of the coupled problem through this new method and its fast convergence is mainly focused in this work. The effect of physical parameters appears in the problem are shown graphically and discussed. Finally, the obtained results are compared with a numerical (ND-Solve) method to authenticate the code of the OHAM-2. The physical and numerical agreement of these two methods has been shown. © 2017 American Institute of Chemical Engineers AIChE J, 2017 [ABSTRACT FROM AUTHOR]

In the present work we examine the motion of an incompressible unidirectional magnetohydrodynamics thin film flow of a third grade fluid over an oscillating inclined belt embedded in a porous medium. Moreover, heat transfer analysis has been also discussed in the present work. This physical problem is modeled in terms of non-linear partial differential equations. These equations together with physical boundary conditions are solved using two analytical techniques namely optimal homotopy asymptotic method and homotopy perturbation method. The comparisons of these two methods for different time level are analyzed numerically and graphically. The results exposed that both methods are in closed agreement and they have identical solutions. The effects of various non-dimensional parameters have also been studied graphically. [ABSTRACT FROM AUTHOR]

This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically. [ABSTRACT FROM AUTHOR]

This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed. [ABSTRACT FROM AUTHOR]

In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest. [ABSTRACT FROM AUTHOR]

The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM). Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, volume flux, skin friction, average velocity, and the temperature distribution across the film. Theeffects of model parameters on velocity, skin friction and temperature variation have been studied. Optimal homotopy asymptotic method (OHAM) is also used for comparison. The numerical results and absolute errors are derived in tables. [ABSTRACT FROM AUTHOR]