In the highly competitive world of today, it is essential to design an efficient, versatile and cost effective system. To design such systems proper analytical, experimental and numerical tools are needed. Optimum design concepts and methods provide some of the needed tools. When these are properly implemented in to software, these give powerful numerical tools for designing best systems. Formulation of an optimum design problem involves transcribing a verbal description of problem in to a well-defined mathematical statement whose constituent elements are parameters, constraints and objective or merit function. Here, a stack design problem has been developed as a mathematical model. Design variables for the present problem are mean diameters dⁱ, shell thickness tⁱ, and height h' of i^thlift. Design expressions and constraints have been formulated. The intent of the objective function is to minimize total mass and thus, cost of steel chimney to select design vectors [h], [d] and [t] while satisfying the nine constraints. For the present problem Random Search Methods have been used to design flowchart for the optimum solution because these are quite simple to program and are very reliable in finding a nearly optimal solution.

Key words: Drag coefficient, Terrain friction drag coefficient, Dynamic lift coefficient, Strouhal number, Frequency of vortex shedding, Natural frequency, Random Search Method.