NUMERICAL TECHNIQUES FOR A VISCOUS REACTlNG FLOW IN A TUBE

Abstract

A viscous fluid flowing through a cylinder is studied. The flow is reacting and heat is generated through reaction and viscosity. To ensure that the problem represents a physical problem we discuss the existence and uniqueness of the problem. It is shown that.the solution is unique when the parameters a and d are greater than zero and h-mesh size is such that h <: 2 .0/ (11/ a-3a (~a)% I) and h < 2.0/ (11/ d, - 3d, (~dl);'-01 ) for Equations (2.27) and (2.33). The problem has no analytical solution, hence, we investigate the problem using numerical techniques based on Shooting method and Finlte difference Scheme. The methods are compared and the best recommended based on a test solution. Finally, the effects of the parameters a,b, d., d2, d3 and viscosity on the temperature was discovered. The results show that the temperature of khe reacting system increases as the parameters a, d2 and d3 increase. On the other hand the parameters band di have opposite effects on the temperature, that is, the temperature decreases as the two parameters increase. Moreover, our numerical scheme confirmed what is physically expected the temperature increases as we increase the viscosity of the reactants. Graphs depicting the relationships between, the temperature and the parameter, and that of the temperature and the space variable feature prominently in the thesis.