Studies of Mhd Flow on Stretching Surface Through Porous Medium With Heat Transfer

The problem of MHD 2-D laminar flow through a porous medium has very important in recent year particularly in the field of agricultural engineering to study the underground water resources, seepage of water river beds, in chemical engineering for filtration purification process; in petroleum technology to study the movement of natural gas, oil and water through the oil reservoirs. The purpose of the present paper is to study the hydro magnetic effects of electrically conducting two-dimensional flow of viscous incompressible fluid through a porous medium, which is bounded by an infinite porous plate. Ahmadi (1971), Gupta (1977) discussed Heat and mass transfer on stretching sheet with suction or blowing. Raptis (1983) discussed about the unsteady flow through a porous medium bounded by an infinite porous plate subjected to a constant suction variable temperature. Dutta (1985) discussed the Temperature field in the flow over stretching surface with uniform heat flux. Massoudi et all (1992) used a perturbation technique to solve the stagnation point flow and heat transfer of a non-Newtonian fluid of second grade. Ariel (1994) gives the Hiemenz Flow in Hydromantic. Young (2000) unsteady MHD convective heat transfer as a semi vertical porous moving plate with variable suction. Singh et al (2001) analyzed the effect of periodic variation of suction velocity. Attia (2003) discussed Hydro magnetic stagnation point flow with heat transfer over a permeable surface. Kumar (2004) discussed the hall current effect on MHD convection flow through a porous media with semi-infinite vertical plate with mass transfer. Mohammad et al (2005) analyzed the

(2006) discussed the unsteady MHD couette and heat transfer of dusty fluid variable physical properties. Haken (2007) discussed the tuncay yilm two-dimensional natural convection in a porous triangular enclosure with a square body. Ahamad (2007) effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium. Hayat et al (2008) discussed the heat transfer analysis on the MHD flow of a second grad fluid in channel with porous medium.

We consider the 2-D MHD flow in a porous medium of viscous incompressible fluid near a stagnation point at a. the flow being in a region y>0 and we consider two equal and opposing forces along the x-axis and keeping the origin fixed. The potential flow that arrives from the y-axis. The viscous flow must adhere to the wall, where as the potential slides along it. (u*,v*) are the components for the potential flow of velocity at the point (x*,y*) for the viscous flow, where as (U,V) are the components for the potential flow. The velocity distribution in the frictionless MHD flow is given by U (x*) = dx*, V (x*) = - dy* … (1) Where the constant d >0 is the distance of the velocity from the stretching surface y = 0 The continuity and momentum equation for 2-D steady-state problems is given by

)2(...0*

* * *

)3(...)(*20*2*

*2 **

***

Where is the density of fluid, 0 is the magnetic field component along y*. K is the Darcy permeability and is the electric conductivity of porous medium. The boundary condition of above flow problem is given by

**** ***

:, : 00

… (4)

Where c is positive constant. The continuity and momentum equations admit a similarity solution )5(...),(),(),(*****ycfcvfcxyxu Where υ = μ/ρ is the kinematics viscosity of fluid and prime denotes the differentiation with respect to η. Using equation (4) the continuity equation (2) is satisfied and using (4) and (5) the equation (3) reduce in the form

)6(...0)1(

MUCCffff

0

And the boundary of this situation

The energy equation of such problem is given by

)8(...)(**2*

*2 * * *

Where Cp is the heat capacity at pressure of fluid, K is thermal conductivity of fluid, T is the constant temperature far away from the stretching surface, Q is the volumetric rate of heat generation, T is the temperature profile, Tw and Tare the wall and stream temperature respectively are constant. The thermal boundary conditions are

)9(...

;

;;0

***

**

******

ww Applying the boundary (9) the energy equation (8) reduced in the form )10(...0PrPrBf

dim

Pr

Figure (1) and (2) shows the velocity profile for the varies values of C and M. these figure shows that increasing the parameter C then increasing both f and f/. For C<1, increasing M then increasing f and f/. For C>1, increasing M then decreasing both f and f/. These figures show the effect of C on both f and f/. More ever, increasing C decreasing the boundary layer thickness. Figure (3) represent the temperature for varies value of c and M and for Pr = 0.6 and B =0.1. It is clear that increasing C decreasing . This figure indicates that the thermal boundary layer thickness decreasing when increasing and increasing M decreasing for all C. In this problem the result indicate that increasing the stretching velocity increasing the velocity components but decreasing the velocity boundary layer thickness. But increasing stretching velocity decreasing the temperature as well as the thermal boundary layer thickness. The effect of the stretching parameter on the velocity and temperature is apparent for the smaller values of porosity parameters. Figure 1. Effect of the parameters C and M on the profile of f

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 12345678910111213141516171819

Figure 2. Effect of the parameters C and M on the profile of f’

0 1 2 3 4 5 6 7 8 9

-0.2

0

0.2 0.4 0.6 0.8

1

1.2 12345678910111213141516171819

Fig.-3 temperature distribution

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45.

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