In "Computational Fluid Dynamics" by John Anderson, the continuity equation is derived using the principle of conservation of mass as applied to four different models (Sections 2.5.1-2.5.4). However, the derivation of the momentum and energy equations are limited to a single model - that of an infinitesimal fluid element moving with the flow. I would like to find derivations of the momentum and energy equations for the case of an infinitesimal element fixed in space (conservation form).

Thanks

Burmeister, "Convective Heat Transfer"