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The purpose of this study is to examine the non-Newtonian physical model of Eyring–Powell fluid for the rheology inside a long circular pipe.

Although many research studies are available now on this topic, none gives full solutions explicitly accessible.

It is proven here that the hydrodynamically fully developed fluid flow acknowledges the exact solution, influenced by a non-Newtonian parameter as well as the adverse pressure gradient parameter prevailing the flow domain. These parameters are unified under a new parameter known as the generalized Eyring–Powell parameter. Without the presented analytical data, it is impossible to detect the validity range of such physical non-Newtonian solutions, which is shown to be restricted.

Full solution of the energy equation for the thermally fully developed laminar regime is also presented under the assumption of uniform wall temperature at the pipe wall. The physical impacts of pertinent parameters on the rheology of the non-Newtonian fluid with regard to the Reynolds number, Darcy friction factor and pressure drop are easy to interpret from the derived formulae. Particularly, a decrease in the centerline velocity and an increase in the rate of heat transfer are clarified for the considered flow configuration.

The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm alumina-water nanofluid within the thin boundary layer in the presence of quartic autocatalytic kind of chemical reaction effects, and to unravel the effects of a magnetic field parameter, random motion of the tiny nanoparticles and volume fraction on the flow.

The chemical reaction between homogeneous (Eyring-Powell 36 nm alumina-water) bulk fluid and heterogeneous (three molecules of the catalyst at the surface) in the flow of magnetohydrodynamic three-dimensional flow is modeled as a quartic autocatalytic kind of chemical reaction. The electromagnetic radiation which occurs within the boundary layer is treated as the nonlinear form due to the fact that Taylor series expansion may not give full details of such effects within the boundary layer. With the aid of appropriate similarity variables, the nonlinear coupled system of partial differential equation which models the flow was reduced to ordinary differential equation boundary value problem.

A favorable agreement of the present results is obtained by comparing it for a limiting case with the published results; hence, reliable results are presented. The concentration of homogeneous bulk fluid (Eyring-Powell nanofluid) increases and decreases with ϕ and P_r, respectively. The increase in the value of magnetic field parameter causes vertical and horizontal velocities of the flow within the boundary layer to decrease significantly. The decrease in the vertical and horizontal velocities of Eyring-Powell nanofluid flow within the boundary layer is guaranteed due to an increase in the value of M. Concentration of homogeneous fluid increases, while the concentration of the heterogeneous catalyst at the wall decreases with M.

Considering the industrial applications of thermal stratification in solar engineering and polymer processing where the behavior of the flow possesses attributes of Eyring-Powell 36 nm alumina-water, this paper presents the solution of the flow problem considering 36 nm alumina nanoparticles, thermophoresis, stratification of thermal energy, Brownian motion and nonlinear thermal radiation. In addition, the aim and objectives of this paper fill such vacuum in the industry.

This study aims to deal with entropy generation and thermal analysis of magnetic hybrid nanofluid containing silver and gold as nanoparticles (Au-Ag/NPs) in the Eyring–Powell fluid.

The blood is used as a base fluid to study the rheological effects in a wavy asymmetric channel. The effect of viscous dissipation is also taken into account. The mathematical model is developed using the lubrication technique. The perturbation method is used to solve the nondimensional nonlinear differential equations, whereas the pumping properties have been analyzed using numerical integration.

The impact of entropy generation, Brinkman number, Hartmann number, nanoparticles volume fraction, thermal Grashof number, Brinkman number and Eyring–Powell fluid parameter is examined on the velocity profile, temperature profile and pumping characteristics. It is observed that the introduction of gold and silver nanoparticles boosts the velocity field in a smaller segment of the channel. The temperature profile rises for the increasing values of Hartmann number, Brinkman number and nanoparticle volume fractions while the temperature profile is restrained by the Eyring–Powell fluid parameter. The pumping rate rises in all sections as the thermal Grashof number and Hartmann number increase; however, the Eyring–Powell fluid parameter has the reverse effect. The volume of the trapping boluses is significantly affected by the Eyring–Powell fluid parameter, thermal Grashof number and fluid parameter.

The results are original and contribute to discover the role of hybrid nanoparticles under the influence of entropy generation viscous dissipation and magnetic fields. Pharmaceutical technology may use this research for things like better mucoadhesive drug delivery systems and more productive peristaltic micropumps.

The purpose of this study is, mixed convection on magnetohydrodynamic (MHD) flow of Eyring–Powell nanofluid over a stretching cylindrical surface in the presence of thermal radiation, chemical reaction, heat generation and Joule heating effect is investigated and analyzed. The Brownian motion and thermophoresis phenomenon are used to model nanoparticles (Buongiorno’s model).

The numerical method is applied to solve the governing equations. Obtained results from the effects of different parameters changes on velocity, temperature and concentration profiles are reported as diagrams.

As a result, velocity profile has been reduced by increasing the Hartman number (magnetic field parameter) because of the existence of Lorentz force and increasing Eyring–Powell fluid parameter. In addition, the nanoparticle concentration profile has been reduced because of increase in chemical reaction parameter. At the end, the effects of different parameters on skin friction coefficient and local Nusselt number are investigated.

Eyring–Powell nanofluid and MHD have significant influence on flow profile.

This paper aims to investigate the effect of Powell–Eyring fluid induced by a stretched sheet. Heat and mass transfer under the influence of magnetic dipole over a stretching sheet are taken into account.

Nonlinear coupled governing equations are solved using the optimal homotopy asymptotic technique, and a computer software package BVPh 2.0 is used for numerical computations.

Impact of significant quantities is graphically examined. It is seen that the heat transfer deceases for higher values of viscous dissipation parameter, radiation parameter, Dufour number, whereas it increases for bigger values of Prandtl number. The numerical results have been validated through comparison with existing literature as a special case of proposed model and perceived that the Soret number has reining role to increase the rate of heat transfer.

To the best of the authors’ knowledge, this study is reported for the first time.

This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.

The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.

The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.

The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.

The purpose of this study is to examine the effects of heat and mass transfer on the peristaltic flow of Eyring‐Powell fluid in a diverging tube.

The governing equations for Eyring‐Powell are modelled in cylindrical coordinates using long wavelength and low Reynolds number approximation. The resulting nonlinear differential equations are solved for velocity, temperature and concentration profile and pressure gradient using regular perturbation technique. Also, the numerical solutions for velocity profile have been computed employing finite difference technique. A comparative study is also presented for both the solutions.

Numerical integration has been performed to get the expression of pressure rise and frictional forces. Graphical results have been presented for pressure rise, frictional forces, temperature and concentration profile for various physical parameters of interest for five considered wave forms.

Trapping phenomena have been discussed at the end of the article.

The purpose of this paper is to investigate the dynamical behavior of heat and mass transfer of non-Newtonian nanofluid flow through parallel horizontal sheet with heat-dependent thermal conductivity and magnetic field. The effects of thermophoresis and Brownian motion on the Eyring‒Powell nanofluid heat and concentration are also considered. The flow fluid is propelled by squeezing force and constant pressure gradient. The hydromagnetic fluid is induced by periodic time variations.

The dimensionless momentum, energy and species balance equations are solved by the spectral local linearization method that is employed to numerically integrate the coupled non-linear differential equations.

The response of the fluid flow, temperature and concentration to variational increase in the values of the parameters is graphically presented and discussed accordingly.

The validity of the method used was checked by comparing it with previous related article.

When the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE). To solve the reduced models, ansatz-based methods are considered. Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. This study aims to discuss the aforementioned solution.

One of the non-Newtonian fluids is Eyring-Powell (EP) fluid which is derived from the kinetic theory of fluids. Two variations of EP model are considered to obtain the exact solutions that are missing in the literature. In order to obtain exact solutions, one of the ansatz-based methods is considered. The effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. The results will guide to develop the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available.

Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number are shown in the figures. The results will guide to develop of the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available. For the modified EP models, only special cases are considered. The generalized form, i.e. the modified EP models, which include deformation parameters, will be considered in the authors’ future work.

When the literature is reviewed carefully, the analytical solutions of these types of models are missing so by this work, the gap in the literature is filled. The explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures.

The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip.

A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system.

Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters.

This model is investigated for the first time, as the authors know.