In this paper, the series solution for unsteady flow for an incompressible viscous electrically conducting fluid of second grad over a stretching sheet subject to a transverse magnetic field is presented by using homotopy analysis method (HAM). Also we examines the effects of viscoelastic parameter, magnetic parameter and time which they control the equation of motion.

The aim of this paper is to analyzed unsteady heat transfer for magnetohydrodynamic (MHD) flow of a second grade fluid in a channel with porous medium. The equations which was used to describe the flow are the momentum and energy, these equations were written to get thier non dimentional form. Homotopy analysis method (HAM) is employed to obtain a semi-analytical solutions for velocity and heat transfer fields. The effect of each dimensionless parameter upon the velocity and temperature distributions is analyzed and shown graphically by using MATHEMATICA package.

A numerical evaluation of the crucial physical properties of a 3D unsteady MHD flow along a stretching sheet for a Casson fluid in the presence of radiation and viscous dissipation has been carried out. Meanwhile, by applying similarity transformations, the nonlinear partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs). Furthermore, in the numerical solution of nonlinear ODEs, the shooting method along with Adams Moulton method of order four has been used. The obtained numerical results are computed with the help of FORTRAN. The tables and graphs describe the numerical results for different physical parameters which affect the velocity and temperature profiles.

In this paper we study the effect of magnetichydrodynamic upon the boundary
layer flow and heat transfer on a permeable unsteady stretching sheet with non –
uniform heat source / sink. It found that the momentum and energy equations are
controlled by many different dimensionless parameters such as prandtle number
pr , unsteadiness parameter A , constant pressure So , coefficient of the space
dependent  A , the temperature dependent  B , and the MHD parameter M . The
analytic solutions are obtained by using suitable similarity transformations and
homotopy analysis method (HAM).
Furthermore, we analysis the effects of all dimensionless number, there are
mentioned above, upon the velocity distribution and

"This paper presents a study of inclined magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two inclined infinite circular cylinders through a porous medium. The analytic solutions for velocity field and shear stress are derived by using the Laplace transform and finite Hankel transform in terms of the generalized G functions. The effect of the physical parameters of the problem on the velocity field is discussed and illustrated graphically.

In this article the unsteady magnetohydrodynamics oscillating flow of third order fluid with free stream velocity is proposed. It is found that the motion equation is controlled by five dimensionless parameters namely the coecostic parameter 4, viscoelostic parameter ?,acceleration/deceleration c,suction/blowing d and material constants ? . The effect of each of these parameters upon the velocity distribution is analysised

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

      In this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For  the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.

In this paper, the effect of thermal radiation and magnetic field on the boundary layer flow and heat transfer of a viscous fluid due to an exponentially stretching sheet is proposed. The governing boundary layer equations are reduced to a system of ordinary differential equations. The homotopy analysis method (HAM) is employed to solve the velocity and temperature equations.