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The purpose of this paper is to study a two‐dimensional steady convective flow of a micropolar fluid over a stretching sheet in the presence of radiation with constant temperature.

The corresponding momentum, microrotation and energy equations are analytically solved using homotopy analysis method (HAM).

To validate the method, investigate the accuracy and convergence of the results, a comparison with existing numerical and experimental results is done for several cases. Finally, by using the obtained analytical solution, for the skin‐friction coefficient and the local Nusselt number as well as the temperature, velocity and angular velocity, profiles are obtained for different values of the constant parameters, such as Prandtl number, material, boundary and radiation parameter.

In this paper, a series solution is presented for the first time.

The present critical analysis has been performed to explore the steady stagnation point flow of Jeffery fluid toward a stretching surface, in the presence of convective boundary conditions. It is assumed that the fluid strikes the wall obliquely. The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. Optimal homotopy analysis method (OHAM) is operated to deal the resulting ordinary differential equations. OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed. The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case. The paper aims to discuss these issues.

The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. OHAM is operated to deal the resulting ordinary differential equations.

OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed.

The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case.

The purpose of this paper is to present, for the first time, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication. In this way, the smart fluid, as a lubricant with controlled variable viscosity, is proposed and applied to minimize the power loss in the interaction between liner and skirt.

Based on signal processing, the relationships between viscosity of lubricant and the friction loss, the hydrodynamic and contact friction force consequently are found, as part of an effective approach to acquire the function of variable viscosity.

It is shown that hydrodynamics and contact friction forces can be controlled and minimized by using the variable viscosity signal with the optimized viscosity signal technique.

In this paper, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication is presented for the first time.

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

Three terms from HPM solution are used.

The results show that this method is very effective and simple and can be applied to other nonlinear problems.

Comparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.

It is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.

In this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

The purpose of this paper is to investigate the heat transfer of laminar and turbulent pulsating Al203/water nanofluid flow in a two-dimensional channel. In the laminar flow range, with increasing Reynolds number (Re), the velocity gradient is increased. Also, the Nusselt number (Nu) is increased, which causes increase in the overall heat transfer rate. Additionally, in the change of flow regime from laminar to turbulent, average thermal flux and pulsation range are increased. Also, the effect of different percentage of Al₂O₃/water nanofluid is investigated. The results show that the addition of nanofluids improve thermal performance in channel, but the using of nanofluid causes a pressure drop in the channel.

The pulsatile flow and heat transfer in a two-dimensional channel were investigated.

The numerical results show that the Al₂O₃/Water nanofluid has a significant effect on the thermal properties of the different flows (laminar and turbulent) and the average thermal flux and pulsation ranges are increased in the change of flow regime from laminar to turbulent. Also, the addition of nanofluid improves thermal performance in channels.

The originality of this work lies in proposing a numerical analysis of heat transfer of pulsating Al₂O₃/Water nanofluid flow -with different percentages- in the two-dimensional channel while the flow regime change from laminar to turbulent.

The purpose of this paper is to present the problem of three‐dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate.

The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained HPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results.

Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered.

Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Padé approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan‐Thien techniques.

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series.

The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique are often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs).

A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter.

To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem.

The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

The purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM).

In this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time.

A highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method.

This is the first study to apply ADM to JTP.

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.

The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.

The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.

This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.

This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.