The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourthorder differential equation by using similarity solutions. Homotopy analysis method HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefu...

We consider the application of a new analytic method based on homotopy analysis to the solution of the steady flow of a viscous incompressible fluid past a fixed circular cylinder. The solutions obtained using this method produce some interesting results. For instance, an analytic verification of the critical Reynolds number Rd for which a standing vortex first appears behind the cylinder is gi...

In the present paper, we have focused our attention to highlight the study of a non-Newtonian nanofluid between coaxial cylinders with variable viscosity. The governing equations of the nonNewtonian fluid with variable viscosity along with energy and nanoparticles are given. The coupled nonlinear differential equations are solved analytically with the help of the homotopy analysis method (HAM)....

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter , is provided. This paper aims to propose an eff...

This paper focuses on the usage of homotopy analysis method (HAM) to solve fractional heat conduction equation. In presented mathematical model, Caputo-type derivatives over time or space are considered. HAM, it is not necessary discretize considered domain, which its great advantage. As a result method, continuous function obtained, can be used for further analysis. For first time, equations, ...

The magnetohydrodynamic (MHD) flow of third grade nanofluid between coaxial porous cylinders was investigated in this work. Two types of series solutions were presented for constant and variable viscosity. The resulting nonlinear coupled equations were solved by employing homotopy analysis method (HAM). The convergence of the series solutions has been discussed explicitly. The recurrence formul...

Received 19 May 2010; received in revised 30 October 2011; accepted 18 January 2012 ABSTRACT This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modificat...

The spontaneous scalarization of Schwarzscild-AdS is investigated in the Einstein-scalar-Gauss–Bonnet (ESGB) theory. Firstly, we construct scalarized AdS black holes numerically. Secondly, making use homotopy analysis method (HAM), obtain analytical approximate solutions for ESGB It found that constructed numerically are consistent with whole space.

In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both se...

This work is focused on the steady boundary layer flow near the forward stagnation point of plane and axisymmetric bodies towards a stretching sheet. The no slip condition on the solid boundary is replaced by the partial slip condition. The analytical solutions for the velocity distributions are obtained for the various values of the ratio of free stream velocity and stretching velocity, slip p...