The aim of this paper is the study of the influence of magnetic field on unsteady
flow of the second-grade fluid with constant viscosity. The equations which
controlled this type of fluid flow are complicated, so finding an analytical solution is
not easy, because it is a system of partial differential equations.We obtained an
expression for the velocity by using homotopy analysis method HAM.
It is found that the equations motion are controlled by many dimensionless
parameter, namely magnetic field parameter M and material constant α,
dimensionless film thickness β and unsteadiness parameter S.We have been studied
the influence of all the physical parameters, that mentioned above on the velocity
field, also a

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.

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

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.

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 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

"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.

A numerical investigation was performed for the radiative magnetohydrodynamic (MHD) viscous nanofluid due to convective stretching sheet. Heat and mass transfer were investigated in terms of viscous dissipations, thermal radiation and chemical reaction. The governing Partial Differential Equations (PDEs) were transformed into an arrangement of non-linear Ordinary Differential Equations (ODEs) by using the similarity transformation. The resulting system of ODEs is solved numerically by using shooting method along with Adams-Moulton Method of order four with the help of the computational software FORTAN. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. The
numerical

During this article, we have a tendency to show the peristaltic activity of magnetohydrodynamics flow of carreau fluid with heat transfer influence in an inclined tapered asymmetric channel through porous medium by exploitation the influence of non-slip boundary conditions. The tapered asymmetric channel is often created because of the intrauterine fluid flow induced by myometrial contraction and it had been simulated by asymmetric peristaltic fluid flow in an exceedingly two dimensional infinite non uniform channel, this fluid is known as hereby carreau fluid, conjointly we are able to say that one amongst carreau's applications is that the blood flow within the body of human. Industrial field, silicon oil is an example of carreau