Nagwa A. Badran

Solution of the Rayleigh problem for a power law non-Newtonian conducting fluid via group method

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u (y, t) has been studied and the results are plotted.

Group method analysis of steady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder

The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder. The application of two-parameter group reduces the number of independent variables by two, and consequently the system of the governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. The ordinary differential equations are solved numerically using a fourth-order Runge-Kutta scheme and the gradient method. Numerical results are obtained for the study of the boundary-layer characteristics. The general analysis developed in this study corresponds to the case of surface temperature that varies exponentially with time and uniform with respect to the axial coordinate, i.e., in the formT w =ae bt , wherea andb are constants. The effect of Prandtl number,Pr, andb on the boundary layer characteristics and the maximum value of the vertical component of the velocity are studied.

New solutions for solving Boussinesq equation via potential symmetries method

This work deals with the Boussinesq equation that describes the propagation of the solitary waves with small amplitude on the surface of shallow water. Firstly, the equation is written in a conserved form, a potential function is then assumed reducing it to a system of partial differential equations. The Lie-group method has been applied for determining symmetry reductions of the system of partial differential equations. The solution of the problem by means of Lie-group method reduces the number of independent variables in the given partial differential equation by one leading to nonlinear ordinary differential equations. The resulting non-linear ordinary differential equations are then solved numerically using MATLAP package.

New solutions for solving problem of particle trajectories in linear deep-water waves via Lie-group method

The nonlinear equations of the two-dimensional inviscid incompressible fluid in a constant gravitational field describing the wave propagation on the water surface are considered. The Lie-group method has been applied for determining symmetry reductions of the system of partial differential equations. Lie-group 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. Effects of the wavelength @l and time t on the particle path have been studied and the results are plotted.

Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u (y, t) has been studied and the results are plotted.