In this paper, we present a generic computer tool based on the Nakamura finite difference scheme in order to solve laminar fluid flow problems.  The present study is restricted to the category of one-dimensional, two-dimensional and three-dimensional fluid flows expressed in one spatial coordinate. All problems are assumed to be time dependant. The equations describing the flow and other relevant parameters are defined in a generic file which is used as input to the system. A generic interpreter is used to generate postfix codes that it will interpret in the process of calculations. For the purpose of application, we consider a two-dimensional unsteady flow of an incompressible electrically conducting viscous fluid along an infinite flat plate. The effects of the various parameters entering into the problem are discussed extensively and shown graphically.