In this paper, the Magnetohydrodynamic (MHD) for Williamson fluid with varying temperature and concentration in an inclined channel with variable viscosity has been examined. The perturbation technique in terms of the Weissenberg number  to obtain explicit forms for the velocity field has been used. All the solutions of physical parameters of the Darcy parameter , Reynolds number , Peclet number  and Magnetic parameter  are discussed under the different values as shown in plots.

A mathematical model constructed to study the combined effects of the concentration and the thermodiffusion on the nanoparticles of a Jeffrey fluid with a magnetic field effect the process of containing waves in a three-dimensional rectangular porous medium canal. Using the HPM to solve the nonlinear and coupled partial differential equations. Numerical results were obtained for temperature distribution, nanoparticles concentration, velocity, pressure rise, pressure gradient, friction force and stream function. Through the graphs, it was found that the velocity of fluid rises with the increase of a mean rate of volume flow and a magnetic parameter, while the velocity goes down with the increasing a Darcy number and lateral walls. Also, t

In this paper, we have examined the influence of heat- transfer on the magnetohydrodynamics oscillatory flow of Williamson fluid during porous medium for two types of geometries "Poiseuille flow and Couette flow". We use perturbation technique in terms of the Weissenberg number to obtain explicit forms for velocity profiles. The results that obtained are illustrated by graphs.

     The goal of this study is to investigate the effects of heat transfer on a non-uniform inclined asymmetrical channel with couple stress fluids via a porous medium using incline magnetohydrodynamics. The governing equation is studied while using low Reynolds approximations and long-wavelength assumptions. Mathematical expressions for (pressure gradient), (temperature), (axial velocity), (heat temperature coefficient), and (stream function). A precise set of values for the various parameters in the present model has been used. The mathematical expressions for axial velocity, stream function, pressure gradient, and pressure rise per wavelength have been derived analytically. "MATHEMATICA" is used to present the computational result

"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 peristaltic transport of viscoelastic fluid through irregular microchannel under the effect of Hall current, varying viscosity and porous medium is investigated. The mathematical expressions for the basic flow equations of motion are formulated and transformed into a system of ordinary differential equations by utilizing appropriate non dimensional quantities. The exact solution for the temperature distribution is obtained, while perturbation series solution for the stream function in terms of tiny viscosity parameter is used. Graphical illustrations are  presented to capture the physical impact of embedded parameters in the fluid flow i.e. the fluid velocity field, temperature distribution, pressure rise, and

In this paper, we study the impacts of variable viscosity , heat and mass transfer on magneto hydrodynamic (MHD) peristaltic flow in a asymmetric tapered inclined channel with porous medium . The viscosity is considered as a function of temperature. The slip conditions at the walls were taken into consideration. Small
Reynolds number and the long wavelength approximations were used to simplify the governing equations. A comparison between the two velocities in cases of slip and no-slip was plotted. It was observed that the behavior of the velocity differed in the two applied models for some parameters. Mathematica software was used to estimate the exact solutions of temperature and concentration profiles. The resolution of the equatio

The properties of capturing of peristaltic flow to a chemically reacting couple stress fluid through an inclined asymmetric channel with variable viscosity and various boundaries are investigated. we have addressed the impacts of variable viscosity, different wave forms, porous medium, heat and mass transfer for peristaltic transport of hydro magnetic couple stress liquid in inclined asymmetric channel with different boundaries. Moreover, The Fluid viscosity assumed to vary as an exponential function of temperature. Effects of almost flow parameters are studied analytically and computed. An rising in the temperature and concentration profiles return to heat and mass transfer Biot numbers. Noteworthy, the Soret and Dufour number effect resul

    In this paper, we study the peristaltic transport of incompressible Bingham plastic fluid in a curved channel. The formulation of the problem is presented through, the regular perturbation technique for small values of  is used to find the final expression of stream function. The numerical solution of pressure rise per wave length is obtained through numerical integration because its analytical solution is impossible. Also the trapping phenomenon is analyzed. The effect of the variation of the physical parameters of the problem are discussed and illustrated graphically.

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.