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The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter
*β*. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.

In recent decades the scientists and engineers are interested to study the flow caused by steady or unsteady stretching sheets because of its rigorous applications in various engineering fields for eg: Polymer sheet extruded continuously from a dye, cooling of metallic plate in a cooling bath and heat-treated materials that travel between feed and wind-up rolls or on a conveyor belt, etc. The exact solution for the flow due to stretching of flat surface was first obtained by Crane [

All the above studies are considered only for a linear stretching sheet, but it is true that not in all cases the stretching sheet is linear. It was first identified by Gupta and Gupta [

Casson fluid is one kind of Non-Newtonian fluid. This behaves like a solid elastic and the yield shear stress exists in the consecutive equation for this fluid. Fredrickson [

Since most of the Fluid flow problems are nonlinear so the methods of solving the nonlinear equations are very important. Till today there are different types of Exact methods. In tradition, the perturbation technique is used to find out the approximations to the nonlinear equation similarly Adomin Methods [

The steady two-dimenional incompressible flow of a Casson fluid bounded by a stretching sheet at y = 0 has considered. The flow is confined to y > 0. Here x-, y-axes are the directions of the plate and normal to the plate respectively. The rheological equation of state for an isotropic and incompressible ﬂow of the Casson ﬂuid is given by

where

where u, v are the velocity components in x, y directions respectively, v is the kinematic viscosity,

The suitable boundary conditions are given by

Using the Rosseland approximation

Here,

With the help of following similarity transformations

The Equations (1), (2) and (3) are transformed in to coupled non linear ordinary differential equations as follows.

and the boundary conditions are transformed into

where

Hence the dimensionless form of Skin friction

where

The effect of Radiation parameter

The results obtained with this method agreed with Vajravelu results for Skin friction coefficient

Vajravelu | Present Study | |||||
---|---|---|---|---|---|---|

n | f"(0) | θ'(0) | f"(0) | θ'(0) | ||

Pr | 0.72 | 7.0 | Pr | 0.72 | 7.0 | |

1 | −1.0000 | −0.4590 | −1.8953 | −1.0000 | −0.4590 | −1.8954 |

5 | −0.1945 | −0.4394 | −1.8610 | −1.1944 | −0.4396 | −1.8616 |

10 | −1.2348 | −0.4357 | −1.8541 | −1.2348 | −0.4356 | −1.8547 |

of nonlinear stretching parameters n. It is noticed that the skin friction coefficient is increased with the increase of

The nature of velocity profile with variation in non linearly stretching parameter n has been discussed in

profile is negligible for large values of n since the coefficient

the other hand the temperature increases with increase of n this result is exhibited in

The effect of Casson parameter

The effect of the Prandtl number on the velocity profile has been depicted in

the Prandtl number means an increase of fluid viscosity, which causes a decrease in the temperature distribution.

more heat to the stretching sheet which increases its temperature. This increases the thermal boundary layer thickness. In the ﬂow of ﬂuid which reduce the velocity of the ﬂow. In addition to this it is also the velocity approaches to zero as the distance from the sheet increases.

The basic governing equations are transformed into coupled nonlinear ordinary differential equations. Keller Box method is used to perform the numerical computations. The effects of nonlinear stretching parameter, Cassson fluid parameter, Prandtl number, radiation parameter and heat source/sink parameters on the heat transfer characteristics are examined with the help of graphs. Finally got an excellent agreement with the previous paper [

1) Both the skin friction coefficient and local Nusselt number increased with the increase in Casson parameter

2) The velocity of the fluid is found to be decrease with the increase in n where as the temperature is increased in this case.

3) The decreasing of momentum boundary layer thickness with the increase in

4) The increasing effect of the Prandtl decreases the temperature.

5) An increment in the radiation parameter increases the temperature distribution.

6) The increase in the heat source increases the temperature of the fluid.

ChennaSumalatha,ShankarBandari, (2015) Effects of Radiations and Heat Source/Sink on a Casson Fluid Flow over Nonlinear Stretching Sheet. World Journal of Mechanics,05,257-265. doi: 10.4236/wjm.2015.512024