Casson Fluid Flow with Variable Viscosity and Thermal Conductivity along Exponentially Stretching Sheet Embedded in a Thermally Stratified Medium with Exponentially Heat Generation

The motion of temperature dependent viscosity and thermal conductivity of steady incompressible laminar free convective (MHD) non-Newtonian Casson fluid flow over an exponentially stretching surface embedded in a thermally stratified medium are investigated. It is assumed that natural convection is induced by buoyancy and exponentially decaying internal heat generation across the space. The dimensionless temperature is constructed such that the effect of stratification can be revealed. Similarity transformations were employed to convert the governing partial differential equations to a system of nonlinear ordinary differential equations. The numerical solutions were obtained using shooting method along with the Runge-Kutta Gill method. The behaviour of dimensionless velocity, temperature and temperature gradient within the boundary layer has been studied using different values of all the controlling parameters. The numerical result show that increase in the magnitude of temperature dependent fluid viscosity parameter leads to an increase in velocity, decrease in temperature, decrease in temperature gradient near the wall and increase in temperature gradient far from the wall. The velocity profile increases, temperature distribution increases and temperature gradient increases near the wall only by increasing the magnitude of temperature dependent thermal conductivity parameter.