Numerical analysis algebraic equation systems, solution

Some simple reaction kinetics are amenable to analytical solutions and graphical linearized analysis to calculate the kinetic parameters from rate data. More complex systems require numerical solution of nonlinear systems of differential and algebraic equations coupled with nonlinear parameter estimation or regression methods. 

To analyze the airflow pattern, simulation of airflow was carried out using a fluid flow analysis package. Fluent 6.1 [1,6-12]. To solve the three-dimensional airflow field inside the nozzles, a CFD model was developed using the above software. Fluid flow and related phenomena can be described by partial differentiation equations, which caimot be solved analytically except in over-simplified cases. To obtain an approximate solution numerically, a discretization method to approximate the differential equations by a system of algebraic equations, which can be then numerically solved on a computer. The approximations were applied to small domains in space and/or time so the numerical solution provides results at discrete locations in space and time. Much of the accuracy depends on the quality of the methodology used, for which CFD is a powerful tool to predict the flow behavior of fluid inside any object. It provides various parameters such as air velocity profiles (axial, tangential, resultant etc.) and path lines trajectory, which are important for subsequent analysis. It was for those reasons that a CFD package. Fluent 6.1, which uses a Finite Volume (FV) method, was employed for airflow simulation. 

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