MHD MIXED CONVECTIVE SLIP FLOW OF CASSON FLUID OVER A POROUS INCLINED PLATE WITH JOULE HEATING, VISCOUS DISSIPATION AND THERMAL RADIATION

The present study examines numerically heat and mass transfer on mixed convective Casson fluid flow over an inclined plate in presence of non-uniform magnetic field. The impact of Joule heating, viscous dissipation and thermal radiation are taken into consideration. The resulting ordinary differential equations obtained from the governing partial differential equations of the flow are solved by using MATLAB bvp4c method. The effects of relevant parameters on velocity, temperature and concentration are discussed graphically, while skin-friction coefficient, rate of heat transfer and mass transfer are presented in tabular structure.


INTRODUCTION
The problem of mixed convective magneto-hydrodynamic flows over a vertical plate encountered in various engineering and technological applications such as electronic devices cooled by fans, heat exchangers in a low velocity environment, drying technologies, fluid flows in ocean and in atmosphere [1,2]. Bejan [3] and Pop and Ingham [4] described the subject in their monographs. Some relevant literatures are found in [5][6][7][8][9][10][11][12][13][14]. This constitutive equation can be used to explore rheological character of materials such as honey, jelly, tomato sauce concentrated fruit juice, soup, mercury amalgams etc. Hayat et al. [16] examined mixed convective flow of Casson fluid in a stretching sheet with convective boundary conditions employing homotopy analysis. Raju et al. [17] examined Casson fluid for the influence of magnetic field over a stretching sheet and obtained that the induced magnetic parameter raises the heat transfer rate. Imran et al. [18] examined slip effects on convective flow of Casson fluid past an oscillating vertical surface. They found that the velocity field decrease due to the influence of the slip parameter. Shaw et al. [19] studied the Casson fluid flow under convective boundary conditions over a horizontal plate using similarity transformations. They found that the influence of Casson parameter reduced the momemtum boundary layer thickness.
Reddy et al. [20] presented a description on collective effects of frictional and irregular heat over Maxwell and Casson fluids. They found that the velocity profiles for Casson fluid are maximum than that of Maxwell fluid.
Das et al. [10] analyzed the effects of Joule heating and viscous dissipation on MHD mixed convective flow for Newtonian fluid over a porous plate with non-uniform magnetic field and slip boundary conditions. They found that fluid velocity increases as the magnetic parameter increases and the impact of slip parameter causes deceleration in fluid velocity.
In this paper, the work of Das et al. [10] is extended to Casson fluid to study heat and mass transfer with heat radiation and nth-order chemical reaction on the MHD mixed convective flow.
Solutions are obtained numerically by using MATLAB bvp4c method and it is observed that the results in absence of Casson parameter, chemical reaction and heat radiation are agreed with that of Das et al. [10]. is applied along the y -axis. The induced magnetic field is neglected Cowling [21] by assuming Reynolds number is very small. Let ) , , ( w v u and ) , , (

MATHEMATICAL FORMULATION
In view of the above assumptions, the conservation of mass, momentum, energy and mass transfer of the problem can be written following (Chen [6], Das et al. [10]) as is the Casson parameter, pressure, density, acceleration due to gravity, dynamic viscosity, kinematic viscosity, coefficient of heat transfer, coefficient of mass transfer, fluid temperature, species concentration, specific heat at constant pressure, inclination of the plate with vertical, mass diffusivity, coefficient of chemical reaction and order of chemical reaction respectively. The last three terms in the equation (4) Using the above assumptions, the equations (2) and (4) .
Using Rosseland approximation [22], we get Using (9) , where U is the velocity slip parameter, is the concentration slip parameter.
The governing higher order non-linear differential equations (13)

RESULTS AND DISCUSSION
To get insight into the flow problem, we assign the following numerical values to the physical parameter for computation as follows: In the absence of chemical reaction and thermal radiation and when  →  , the values of skin friction and Nusselt number are compared with that of the values of Das et al. [10] and it was found that they are in good agreement which is shown in Table1.