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The present study deals with MHD mixed convection stagnation point flow over a stretching sheet with the effects of heat source/sink and viscous dissipation including convective boundary conditions. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. These equations are then solved numerically by using finite difference scheme known as the Keller Box method. The effects of various parameters on velocity and temperature profiles are presented graphically interpreted and the results are discussed.

The study of MHD, boundary layer flow with heat transfer from a stretching sheet has several applications in many industrial fields. Magnetic fields can be used to manage thermal energy in flowing electrically conducting polymers (Garnier [

In fluid dynamics, the stagnation point flow and flow over a stretching surface are important in theoretical and applications point of view. In fluid dynamics, stagnation is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. Stagnation flow towards a stretching sheet is investigated by Wang [

This paper provides the solution to the problem of fluid flow, heat transfer of mixed convection MHD stagnation point flow over a stretching surface by considering the effects of heat source/sink and viscous dissipation including convective boundary conditions by adopting the Keller box method.

Consider two-dimensional steady, incompressible MHD stagnation point flow of a viscous fluid over a stretching sheet with convective boundary condition. It is assumed that the stretching velocity

Considering u, v as velocity components in the directions of x and y respectively in the flow field. The governing equations of continuity, momentum, energy and concentration are given by

where

magnetic induction,

co-efficient of viscosity,

where

Introducing the similarity transformations

where

The boundary conditions are reduced to

where

The governing equations with boundary equations are solved numerically by using finite difference scheme known as Keller box method which is described by Cebeci and Bradshaw [

Step 1: Reducing higher order ODEs (systems of ODES) in to systems of first order ODEs.

Step 2: Writing the systems of first order ODEs into difference equations using central difference scheme.

Step 3: Linearizing the difference equations using Newton’s method and writing it in Vector form.

Step 4: Solving the system of equations using block elimination method.

In this process the step size

In this study, the following values are used for the numerical computations

from the fact that when

Yacob and Ishak [ | Wang [ | Present | |
---|---|---|---|

0.0 0.5 2.0 | 1.23258 0.71329 −1.88730 | 1.23258 0.71329 −1.88730 | 1.2326 0.7133 −1.8873 |

Γ | Λ | Ec | S | |||
---|---|---|---|---|---|---|

1.0 1.0 1.5 2.5 1.0 1.0 1.0 1.0 1.0 1.0 | 2.0 3.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 | 0.1 0.1 0.1 0.1 1.0 3.0 0.1 0.1 0.1 0.1 | 0.1 0.1 0.1 0.1 0.1 0.1 1.5 2.0 0.1 0.1 | 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.0 1.0 | 1.8814 4.2831 1.8775 1.8730 1.7030 1.3216 1.8747 1.8723 1.8830 1.8789 | 0.2285 0.0764 0.2875 0.3550 0.2429 0.2695 0.6733 0.9924 0.3475 0.0674 |

sheet. For this case, the boundary layer thickness increases with the increase of

Increasing the values of the Ec generates heat in the fluid due to frictional heating.

The numerical solutions for mixed convection MHD stagnation point flow over a stretching surface with the effects of various parameters were analyzed. The effects of various parameters on heat flow characteristics were also discussed. From the graphical representations, we have the following observations.

・ The velocity increases with increasing values of the magnetic parameter M.

・ An increase in the mixed convection parameter λ increases the velocity profiles.

・ An increase in the value of є reduces the temperature, and increases the velocity profiles.

・ With increasing values of conjugate parameter γ the temperature profile increases.

・ An increase in the Eckert number Ec increases the temperature profile.

Kankanala Sharada,Bandari Shankar, (2016) Mixed Convection MHD Stagnation Point Flow over a Stretching Surface with the Effects of Heat Source or Sink and Viscous Dissipation. Journal of Applied Mathematics and Physics,04,578-585. doi: 10.4236/jamp.2016.43063