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The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications.

The approach to calculating a new form of the exact analytic solution of thin film fluid flows rests upon a sequence of transformations including the modification of the classic technique due to Scipione del Ferro and Niccolò Fontana Tartaglia. Next the authors establish a lemma that justifies the new expression of the exact analytic solution for thin film fluid flows of fourth-grade fluids. Second, the authors apply a modification of the systematic ADM to quickly and easily calculate the sequence of analytic approximate solutions for this strongly nonlinear model of thin film flow of fourth-grade fluids. The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific and engineering applications. Herein, the authors seek to establish the relative merits of the ADM in the context of the thin film flows of fourth-grade fluids.

The ADM is shown to closely agree with the new expression of the exact analytic solution. The authors have calculated the error remainder functions and the maximal error remainder parameters in the error analysis to corroborate the solutions. The error analysis demonstrates the rapid rate of convergence and that we can approximate the exact solution as closely as we please; furthermore the rate of convergence is shown to be approximately exponential, and thus only a low-stage approximation will be adequate for engineering simulations as previously documented in the literature.

This paper presents an accurate work for solving thin film flows of fourth-grade fluids. The authors have compared the approximate analytic solutions by the ADM with the new expression of the exact analytic solution for this strongly nonlinear model. The authors commend this technique for more complex thin film fluid flow models.

The purpose of this paper is to study the thin film flow of a fourth grade fluid subject to slip conditions in order to understand its velocity profile.

An exact expression for flow velocity is derived in terms of hyperbolic sine functions. The practical usage of the exact flow velocity is restrictive as it involves very complicated integrals. Therefore, an approximate solution is also derived using a Galerkin finite element method and numerical error analysis is performed.

The behavior of fluid velocity with respect to various flow parameters is discussed. The results are not restrictive to small values of flow parameters unlike those obtained earlier using homotopy analysis method and homotopy perturbation method.

An approximate solution based on finite element technique is derived.

The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

The main purpose of this paper is to study the effect of heat transfer on the peristaltic flow of a magnetohydrodynamic Walters B fluid through a porous medium in an inclined asymmetric channel.

The approximate analytical solutions of the governing partial differential equations are obtained using the regular perturbation method by taking wave number as a small parameter. The solutions for the pressure difference and friction forces are evaluated using numerical integration.

It is noticed that the pressure gradient and pressure difference are increasing functions of inclination angle and Grashof number. The temperature and heat transfer coefficients both increase with increase in inclination angle, Darcy number, Grashof number and Prandtl number. Increase in Hartmann number and phase difference decreases the size of trapped bolus.

The problem is original, as no work has been reported on the effect of magnetohydrodynamics on the peristaltic flow of a Walters B fluid through a porous medium in an inclined asymmetric channel with heat transfer.

The purpose of this paper is to investigate the three fundamental flows (namely, both the plates moving in opposite directions, the lower plate is moving and other is at rest, and both the plates moving in the direction of flow) of the Ree-Eyring fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the intention of the study is to examine the effect of different physical parameters on the fluid flow.

The mathematical modeling is performed on the basis of law of conservation of mass, momentum and energy equation. The modeling of the present problem is considered in Cartesian coordinate system. The governing equations are non-dimensionalized using appropriate dimensionless quantities in all the mentioned cases. The closed-form solutions are presented for the velocity and temperature profiles.

The graphical results are presented for the velocity and temperature distributions with the pertinent parameters of interest. It is observed from the present results that the velocity is a decreasing function of Hartmann number. Temperature increases with the increase of Ree-Eyring fluid parameter, radiation parameter and temperature slip parameter.

First time in the literature, the authors obtained closed-form solutions for the fundamental flows of Ree-Erying fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the results of this paper are new and original.

The purpose of this paper is to investigate the peristaltic flow of an incompressible Newtonian fluid in a channel with compliant walls. The effects of rotation and heat and mass transfer are also taken into account. The governing equations of two dimensional fluid have been simplified under long wavelength and low Reynolds number approximation. An exact solutions is presented for the stream function, temperature, concentration field, velocity and heat transfer coefficient.

The effect of the concentration distribution, heat and mass transfer and rotation on the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation and heat and mass transfer.

The results indicate that the effect of the permeability and rotation are very pronounced in the phenomena.

The objective of the present analysis is to analyze the effects of rotation, heat and mass transfer and compliant walls on the peristaltic flow of a viscous fluid.

The purpose of this paper is to study the peristaltic flow of a Jeffrey fluid in an asymmetric channel, subjected to gravity field and rotation in the presence of a magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. Involved problems are analyzed through long wavelength and low Reynolds number.

The analytical expressions for the pressure gradient, pressure rise, stream function, axial velocity and shear stress have been obtained. The effects of Hartmann number, the ratio of relaxation to retardation times, time-mean flow, rotation, the phase angle and the gravity field on the pressure gradient, pressure rise, streamline, axial velocity and shear stress are very pronounced and physically interpreted through graphical illustrations. Comparison was made with the results obtained in the asymmetric and symmetric channels.

The results indicate that the effect of the Hartmann number, the ratio of relaxation to retardation times, time-mean flow, rotation, the phase angle and the gravitational field are very pronounced in the phenomena.

In the present work, the authors investigate gravity field, and rotation through an asymmetric channel in the presence of a magnetic field has been analyzed. It also deals with the effect of the magnetic field and gravity field of peristaltic transport of a Jeffrey fluid in an asymmetric rotating channel.

The purpose of this paper is to predict the effects of magnetic field, heat and mass transfer and rotation on the peristaltic flow of an incompressible Newtonian fluid in a channel with compliant walls. The whole system is in a rotating frame of reference.

The governing equations of two-dimensional fluid have been simplified under long wavelength and low Reynolds number approximation. The solutions are carried out for the stream function, temperature, concentration field, velocity and heat transfer coefficient.

The results indicate that the effects of permeability, magnetic field and rotation are very pronounced in the phenomena. Impacts of various involved parameters appearing in the solutions are carefully analyzed.

The effect of the concentration distribution, heat and mass transfer and rotation on the wave frame is analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. A comparison was made with the results obtained in the presence and absence of rotation, magnetic field and heat and mass transfer.

This article aims to describe the effect of an endoscope and heat transfer on the peristaltic flow of a Jeffrey fluid through the gap between concentric uniform tubes.

The mathematical model of the present problem is carried out under long wavelength and low Reynolds number approximations. Analytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained.

The results indicate that the effect of the wave amplitude, radius ratio, Grashof number, the ratio of relaxation to retardation times and the radius are very pronounced in the phenomena. Also, a comparison of obtaining an analytical solution against previous literatures shows satisfactory agreement.

Analytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained. Numerical integration is performed to analyze the pressure rise and frictional forces on the inner and outer tubes.

This paper aims to investigate the consequence of the combined impacts of an induced magnetic field and thermal radiation on peristaltic transport of a Carreau nanofluid in a vertical tapered asymmetric channel. The model applied for the nanofluid comprises the effects of Brownian motion and thermophoresis.

The governing equations have been simplified under the widespread assumption of long-wavelength and low-Reynolds number approximations. The reduced coupled nonlinear equations of momentum and magnetic force function have also been solved analytically using the regular perturbation method.

The physical features of emerging parameters have been discussed by drawing the graphs of velocity, temperature, nanoparticle concentration profile, magnetic force function, current density, heat transfer coefficient and stream function. It has been realized that the magnetic force function is increased with the increase of Hartmann number, magnetic Reynolds number and mean flow rate.

It may be first paper in which the effect of induced magnetic field on peristaltic flow of non-Newtonian nanofluid in a tapered asymmetric channel has been studied.