Lie Group Analysis of Mixed Convection Flow with Mass Transfer over a Stretching Surface with Suction or Injection

The mixed convection flow with mass transfer over a stretching surface with suction or injection is examined. By using Lie group analysis, the symmetries of the equations are calculated. A four-finite parameter and one infinite parameter Lie group transformations are obtained. Two different cases are discussed, one for the scaling symmetry and the other for spiral symmetry. The governing partial differential equations are transformed into ordinary differential equations using these symmetries. It has been noted that the similarity variables and functions available in the literature become special cases of the similarity variables and functions discussed in this paper

An Exact Solution of MHD Boundary Layer Flow of Dusty Fluid over a Stretching Surface

This paper deals with the boundary layer flow of electrically conducting dusty fluid over a stretching surface in the presence of applied magnetic field. The governing partial differential equations of the problem are transformed to nonlinear nondimensional coupled ordinary differential equations using suitable similarity transformations. The problem is now fully specified in terms of characterizing parameters known as fluid particle interaction parameter, magnetic field parameter, and mass concentration of dust particles. An exact analytical solution of the resulting boundary value problem is presented that works for all values of the characterizing parameters. The effects of these parameters on the velocity field and the skin friction coefficient are presented graphically and in the tabular form, respectively. We emphasize that an approximate numerical solution of this problem was available in the literature but no analytical solution was presented before this study

Mixed convection flow of a nanofluid past a non-linearly stretching wall

This paper deals with the boundary-layer mixed convective flow of a viscous nanofluid past a vertical wall stretching with non-linear velocity. The governing equations are transformed into self similar ordinary differential equations using appropriate transformation. Using group theoretic method it is shown that the similarity solutions are possible only for the non-linear stretching velocity having specific form. Numerical solution of the coupled governing equations is obtained using Keller Box method. Correlation expression of reduced Nusselt and Sherwood numbers are obtained by performing linear regression on the data obtained from numerical results. The authenticity of these results is established by calculating the percentage error between the numerical results and correlation expression which is observed to be less than 5%. Effects of Brownian and thermophoretic diffusions and nanoparticles concentration flux on the Nusselt and Sherwood numbers are discussed

Similarity solution for flow over an unsteady nonlinearly stretching rotating disk

The unsteady laminar flow of an incompressible viscous fluid over a nonlinearly stretching rotating disk is investigated. The axisymmetric three-dimensional boundary layer equations are reduced into self-similar form with the help of new similarity transformation. The resulting coupled nonlinear equations are solved numerically using shooting method coupled with Range-Kutta 6 (RK-6). An exact analytical solution for the large stretching parameter is also presented. Some interesting observations are made while interpreting the results physically. Dual solutions are obtained due to the presence of unsteadiness parameter for the nonlinear stretching of the rotating disk. The analytical results reveal that for large stretching parameter the azimuthal velocity becomes negligible and the flow behaviors turn into steady state, which is the most surprising observation of the paper. These results are also verified numerically by solving original self similar equations using shooting method