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The mathematical model is presented for the flow of peristaltic pumping of a conducting non-Newtonian fluid obeying Sisko model through a porous medium under the effect of magnetic field with heat and mass transfer. The solutions of the system of equations which represent this motion are obtained analytically using perturbation technique after considering the approximation of long wave length. The formula of the velocity with temperature and concentration of the fluid is obtained as a function of the physical parameters of the problem. The effects of these parameters on these solutions are discussed numerically and illustrated graphically through some graphs.

Peristalsis is a form of fluid transport induced by a progressive wave of area contraction or expansion along the walls of distensible duct containing a liquid or mixture. A peristaltic pump is a device for pumping fluids, generally from a region of lower to higher pressure, by means of a contraction wave traveling along a tube like structure. Shapiro et al. [

Peristalsis also have industrial and biological applications like sanitary fluid transport blood pumps in heart lungs machines and peristaltic transport of toxic liquid is used in nuclear industries. Some recent investigations made to discuss the mechanism of peristalsis include the works. Radhakrishnamacharya and Srinivasulu [

The effect of porous medium on the motion of the fluid has been studied by many authors. Elshehawey et al. [

The study of the influence of mass and heat transfer on Newtonian and non-Newtonian fluids has become important in the last few years. This importance is due to a number of industrial processes. Examples are food-processing, biochemical operations and transport in polymers. Eldabe et al. [

The basic equations governing the flow of an incompressible fluid are expressed as follows:

The continuity equation

The momentum equation

where

where

The temperature equation

The concentration equation

The dissipation function

Maxwell s equations

Ohm’s equation

where

bility,

is the electric field and

Consider the two-dimensional motion of an incompressible Sisko fluid in an infinite channel of width

where b is the wave amplitude,

Now, Equations (2)-(6) can be written in two-dimensional

where

Subjected to the following appropriate boundary conditions:

Choose the wave frame

In which

Then, the Equations (10)-(19) can be written as:

where

The boundary conditions are:

In order to simplify the governing equations of the motion, we may introduce the following dimensionless transformations:

where,

Substituting (30) into Equations (21)-(29) we obtain the following non-dimensional equations after dropping the star mark:

The boundary conditions are:

where, the dimensionless parameters are defined by:

By using the following definition of stream function

The system of Equations (3.30)-(3.38) can be written as:

The boundary conditions for the dimensionless stream function in the moving frame are given by:

The dimensionless form of the surface of the peristaltic wall can be written as:

where

According to long wavelength approximation

In order to solve the Equations (49)-(51) subjected to the boundary conditions, we suppose the following perturbation for small non-Newtonian parameter

Substituting (55) into (49)-(54) and comparing the coefficient of zero and first order of

With the respective boundary conditions

We shall consider the case of Dielatent fluids when n > 1, and we choose (n = 3), then we have the following system of first order of

with the respective boundary conditions

The problem of the peristaltic flow of a Sisko fluid through a porous medium with heat and mass transfer has been discussed. The effects of non-Newtonian dissipation and chemical reaction on the fluid flow have been considered. We obtained the solutions of the momentum, heat and mass equations analytically by using the perturbation technique for small non-Newtonian parameter

In

In

In

In this work, we study the peristaltic motion of magneto-hydrodynamics flow with heat and mass transfer for incompressible non-Newtonian fluid through a porous medium. The governing partial differential equations of this problem, subjected to the boundary conditions are solved analytically by using perturbation technique. The

analytical forms for the stream distribution

The study of this phenomenon is very important, because the study of flow through porous medium has many applications. It has an important role in agricultural, extracting pure petrol from crude oil and chemical engineering. There are examples of natural porous media such as wood, filter paper, cotton, leather and plastics. As a good biological example on the porous medium, the human lung galls bladder and the walls of vessels. The peristaltic motion has been found to involve in many biological organs such as esophagus, small and large intestine, stomach, the human ureter, lymphatic vessels and small blood vessels. Also, peristaltic transport occurs in many practical applications involving biomechanical systems such as finger pumps.

Nabit Tawfiq MohamedEl-Dabe,Ahmed YounisGhaly,Sallam NagySallam,KhaledElagamy,Yasmeen MohamedYounis, (2015) Peristaltic Pumping of a Conducting Sisko Fluid through Porous Medium with Heat and Mass Transfer. American Journal of Computational Mathematics,05,304-316. doi: 10.4236/ajcm.2015.53028