Governing Equations in Continuous Integral Form

The Navier-Stokes equations in Cartesian integral form for an arbitrary control volume V with differential surface area may be written:

(37)

where:

(38)

and , , E, and p are the density, velocity, total energy per unit mass, and pressure of the fluid, respectively. is the viscous stress tensor, is the heat flux vector, and is the position vector.

Total energy is related to the total enthalpy H by:

(39)

where:

(40)

and . is the vector of body forces.