## Journal of Generalized Lie Theory and Applications

### Lie Group Method for Studying the Heat Generation Effect on Freeconvection Laminar Boundary-layer Flow Over a Vertical Flat Plate

#### Abstract

The nonlinear equations of heat and mass transfer in two-dimensional free-convection, laminar, boundary layer flow of a viscous incompressible fluid over a vertical plate with thermophoresis and heat generation effect have been considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Liegroup method starts out with a general infinitesimal group of transformations under which the given partial differential equations are invariant. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the system. The effect of the heat generation parameter He, the Prandtl number Pr, the Schimted number Sc, the thermophoretic parameter $\tau$, the solutal Grashof number Gc and the thermal Grashof number Gr on velocity, concentration and temperature have been studied and the results are plotted.

#### Article information

Source
J. Gen. Lie Theory Appl., Volume 9, Number 2 (2015), 9 pages.

Dates
First available in Project Euclid: 2 February 2016

https://projecteuclid.org/euclid.jglta/1454422006

Digital Object Identifier
doi:10.4172/1736-4337.1000232

Mathematical Reviews number (MathSciNet)
MR3642243

Zentralblatt MATH identifier
06538943

#### Citation

Abd-el-Malek, MB; Badran, NA; Hassan, HS; Abbas, HH. Lie Group Method for Studying the Heat Generation Effect on Freeconvection Laminar Boundary-layer Flow Over a Vertical Flat Plate. J. Gen. Lie Theory Appl. 9 (2015), no. 2, 9 pages. doi:10.4172/1736-4337.1000232. https://projecteuclid.org/euclid.jglta/1454422006