NUMERICAL SOLUTION FOR SOME CLASS OF PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this thesis we deal with the partial differential equations. The Navier-Stockes equations are partial differential equations which describe the motion of the fluid at different situations. Some scientists interest in their works with the flow and heat transfer processes through a porous medium which has many physical and engineering applications. A similarity transformations are used to convert the coupled system of non-linear partial differential equation, which describe the problem, into a system of non-linear ordinary differential equations. The system of non-linear ordinary differential equation are solved numerically using the shooting method. The effect of various variables on the velocity distribution, temperature distribution, the skin-friction coefficient and the Nusselt number are disscused. This thesis contains four chapters. In the first one, we interest with the date and some models of partial differential equations. For example, we pre.sent in this chapter various formulae of the Navier-Stockes equations in Darcian or non­ Darcian porous medium. Also a survey of the previous works for the boundary layer problems with different situations are presented.