Abstract: The reactive fluid dynamics of transonic flows in nozzles is an important area of experimental and theoretical research. This paper consists of two parts. In the first part an algorithm for the solution of the Euler Equations in conservative form is discussed which simplifies a generalization of Murman Scheme 1 that is presented in Reference 2. Chattot's work is discussed and calculations for flows with shocks are presented. In the second part, transonic flows with friction, heat addition and dissipation is considered. Specific attention is given to detonations with one-step Arrhenius chemistry. A part of this study is to understand the interaction between friction and transonic flow with combustion. The details of the numerical algorithms will be presented along with validation examples from the literature.