Not sure what is bothering you: In general fluid equations in differential or integral form specify how a quantity changes. Perhaps the integral form is simpler to visualize in our daily experence : The rate of change of any quantity, i.e. total mass, momentum, ang.momentum or energy in a volume is the net influx into that volume plus whatever is generated

inside, if any sources are present: This is as simple as taking a tank of water with an inlet and outlet: rate of change of mass for instance=(whet enters-what leaves)/unit time. If there are sources inside, add them to the balance.

Dear Kikani,

Please consulte the document in the folloxing link:

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=2ahUKEwjfsLD2mc_gAhUHVhoKHXOlAfsQFjABegQICBAB&url=https%3A%2F%2Fcanvas.harvard.edu%2Ffiles%2F1834693%2Fdownload%3Fdownload_frd%3D1%26verifier%3DVWL4y10vfyg9XmTFhHjDCk10G0tvsMFNZyQqU1na&usg=AOvVaw05BC1yXINme0BDGMT1x4m3

Following article may be useful

https://warwick.ac.uk/fac/sci/physics/research/cfsa/people/valery/teaching/hse/l4-8.pdf

Dr. Purvi Kikani, if the energy equation for the MHD is taken into consideration, then the kinetics of the fluid can be resolved.

I explain further, quantities such as the thermal conduction coefficient - kij and the heat-loss function L defined as the energy output minus the energy input per unit mass and time can be accounted for.

I attach a screenshot of the energy equation in MHD written in tensor notation.