HEAT AND MASS TRANSFER OF AN UNSTEADY MHD PERISTALTIC FLOW IN A POROUS MEDIUM WITH CROSS DIFFUSION EFFECT

In this work the significance of Cross Diffusion effect on unsteady MHD peristaltic flow in a porous medium with heat and mass transfer is investigated. The governing partial differential equations are transformed into dimensionless equations by using dimensionless quantities. Stream function, velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are obtained. The results are discussed for various emerging parameters encountered in the problem under investigation. The importance of main parameters on the present study is explained graphically.


INTRODUCTION
The heat and mass transfer of an unsteady MHD flow attracted by the researchers, because it is most useful to many fields such as production process, chemical-engineering application of a physical and the peristaltic flow used in pump and other mechanical systems.The most important mechanism of fluid transport is peristalsis and it is formed by the propagation of a peristaltic wave on the channel walls.
Influence of wall flexibility and cross diffusion on the peristaltic transport of a MHD dissipative fluid in the presence of Joule heating are presented by Sucharitha, G. et al [1]. The effects of MHD couple stress fluid in peristaltic flow with the porous medium under the impact of slip, heat transfer and wall properties attempted by Sankad, G. C. and Nagathan, P.S. [2]. The heat and mass transfer effects on MHD flow of a steady viscous incompressible and electrically conducting fluid through a non-isothermal parallel flat wall the presence of Soret effect is investigated by Panneerselvi, R. and Subhasree, D. [3]. Raju, C.S.K.et al [4] analyzed the steady two dimen-sional flow over a vertical stretching surface in presence of aligned magnetic field, cross diffussion and radiation effect.
The influence of heat transfer on the peristaltic flow of a conducting PHAN-THIEN-TANNER fluid in an asymmetric channel with porous medium is studied by Vajravelu, K. et al [5]. Jayachandra Babu, M. and Sandeep, N. [6] studied the presence of cross-diffusion effects on MHD non-newtonian fluid flow over a slandering sheet by viewing velocity slip. The effect of heat transfer and elasticity of flexible walls in swallowing food bolus through the oesophasus supposed to be jeffrey fluid is analyzed by Arun Kumar, M. et al [7]. Dheia, G. and Salih Al-Khafajy [8] constructed a mathematical model is constructed to study the effect of heat transfer and elasticity of flexible walls with the porous medium. The effect of heat transfer and inclined magnetic field on the peristaltic flow of williamson fluid in an asymmetric channel through porous medium is investigated by Ramesh, K. and Devakar, M. [9]. The effects of both wall slip conditions and heat transfer on the MHD peristaltic flow of a Maxwell fluid in a porous planar channel with elastic wall properties have been studied by Kalidas Das, [10].
Keeping in mind the importance of heat and mass transfer of an MHD Peristaltic fluid with cross diffusion effects in porous medium under the influence of inclined magnetic field, we have gone for a detailed study. The stream function is used to solve governing coupled nonliner partial differential equations.

MODELLING OF THE PROBLEM
In this, the peristaltic transport of a viscous fluid in a two dimensional porous channel between two elastic walls is considered. The flow is generated by a peristaltic wave propagated along the elastic walls of the channel with a *Correspondence: Panneerselvi, R., Department of Mathematics, PSGR Krishnammal College for Women, Coimbatore, Tamil Nadu,India.
Page 131-142 constant speed c. Here, Joule heating diffusion and dissipation effects are considered. The dimensional of the uniform channel flow in a porous medium is given as the width of the uniform channel 2d, wave amplitude a. the angle of inclined magnetic field is taken as α, x is the axial coordinate and y is normal to it. .

Fig. 1.Configuration of the Problem
The geometry of the surface wall is given as, Consider the motion of the elastic wall as, Here L denotes the flexible wall motion with viscosity damping force is given by,   (5) Page 132-142 Here, the fluid velocities are u and v along x and y axis. As the plane is symmetrical, the normal velocity is zero. Here ρ,µ denotesthefluiddensityandthecoefficient of viscosity of the fluid. Also p, T, C, σ represents the pressure, the temperature of the fluid, the concentration of the fluid and the electrical conductivity of the fluid.
Appropriate boundary conditions are given as follows, From Mittra and Prasad [5], the dynamic boundary conditions are given as, The dimensionless parameters used are, Non-dimensional variables are introduced in the equations (4) - (8), after dropping the primes, we get, Pr cos Pr Pr Pr Re

METHOD OF SOLVING THE PROBLEM
Considering the wavelength of the peristaltic wave to be large and the Reynolds number to be small, equation (14)      Thetemperatureprofilefordifferentvalues ofSoretnumber(Sr)andBrinkmannumber(Br)areshownthroughfigures8and 9. It is explained clearly from the figure that temperature profile is enhanced with the increase in these two parameters.

CONCLUSION
In this study, exact solution for the stream function, the velocity profile, thetemperatureprofileandtheconcentratio nprofileintheexistenceofCrossdiffusioneffe ct,andPermeabilityparameteronanunstead yMHDflowareconstructed. TheeffectofheatandmasstransferonCrossdi ffusionofanunsteadyMHDflowis analyzed in detail. Graphical results reveal the consequence of the variousdimensionless parameters which exists in the problem underanalysis.
The succeeding results are made based on the results and discussion: As amplitude ratio (s) increases, the mean velocity profile also increases andsameresultsariseforwalltensio n(E1)andmasscharacterization(E2) .