ABSTRACT
The general transient equations are difficult to solve because of the coupling between the momentum and energy equations and the nonlinear nature of these general equations. However, it is possible to simplify these equations as described in the text in two ways: (1) by approximating the velocity distribution in the channel to decouple the momentum and energy equations. This approach encompasses the momentum integral method and (2) by transforming the partial differential equations into ordinary differential equations that can be solved separately in the time and space domains. This approach is the foundation of the method of characteristics. The transient problem solution can also be facilitated by using the following approximations to decouple the momentum and energy equations which are demonstrated.
By approximating the velocity distribution in the channel to decouple the momentum and energy equations. This approach encompasses the momentum integral method and other related methods described in Section 3.2.
By transforming the partial differential equations into ordinary differential equations that can be solved separately in the time domain and the space domain. This approach is the foundation of the method of characteristics, which is described in Section 3.3.
