Group-theory method on similarity solution of unsteady free-convection flow from a moving vertical surface with suction and injection

Abstract

Two-parameter transformation group-theory method is applied to presenlthc analysis and analytic solution of the problem of unsteady free-convection flow from a mavlng vertical porous surface considering suction and injection. The application of two-parallleter grOLips reduces (he llL1mher of independent variables by one, and cOl\sequently the system of governing partial differential equations with boundary conditions reduces to a system 01' ordinary differential equations with appropriate boundary conditions. The possible fonns of difference between wall temperature and (he ambient fhud temperature variations arc dem'ed, The reduced ordinary differential equations obtained from tbe mathematical model of the present problem are tben solved numerically using the shooting melhod Knll"n HS Runge-KutlH-BlIleher initial vallIe problem solver together with the Nachtsheim-S".igerl iteralion scheme described by Nachtsheim and S,~igerl. Programming codes have been written in FORTRAN 90 to implement shooting method for the presenl problem. The post processing soft,vare TECPLOT has been used to display the numel'tcal result8 graphl<;ally. The effects of different values of Prandtl number Pr, suction and injectlon parameter F", viscosity variation parameters IT and T on velocity and temperature profiles ha~e been dlSCUS8edwith the help of graphs and tables. Comparisons of suction, injection and llelltrJI position (no suction or injcetion) have been anolyzed graphlcally and in tabular forill.