Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.