A full expression requires the formalism of Tensors. Here is another comment I once wrote in a discussion (not worth much but...):
The energy flux happens to equal the momentum density (*c2), while these are 2 different concepts. Usual conventions on tensors assume c=1 so that "mass" and energy are the same. If we don't put c=1, as the stress-energy tensor is defined as twice contravariant, its 0,0 component is the mass density; its 0,i and i,0 equal components are the density of momentum and the flux of "mass" where "mass" = energy * c2. You can see this considering that for a twice contravariant tensor, the space and time components have the same magnitude when describing an object going at 1 m/s, as they are given by the tensor product of both parallel vectors (1,speed) and (mass, momentum) that are tangent to the movement of the object in space-time. The magnitudes of the flux of mass and density of momentum are ordinary, while the flux of energy would be huge at is is the energy of mass mc2 of the object that is moved. The energy, is the sum of all possible forms of energies for all kinds of particles and forces.