Free Convection Flow in an Inclined Plate with Variable Thermal Conductivity by Scaling Group Transformations

The Lie group analysis of natural convection flow over an inclined semi-infinite plate with variable thermal conductivity is studied. The fluid thermal conductivity is assumed to vary as a linear function of temperature. A scaling group of transformation is applied to the governing partial differential equations and then used to reduce them to a system of ordinary differential equations. Numerical solutions of the ordinary differential equations are also obtained. From the numerical results it is found that the momentum and thermal boundary layer thicknesses increase with thermal conductivity parameter. The velocity increases and temperature decreases with increasing the Grashof number.