I think i had an insight after your answer, georgeverghese.
The variation of the energy is the same as internal energy. dE/dt=dU/dt.
Using the control volume we have: dU/dt= −2Aqn.
In other hand, we have the definition of Internal energy of multi-component systems:
dU=(∂U/∂T)dT+(∂U/∂V)dV +...
It's an exercise solved by the author.
The book is Conduction Heat Transfer - Arpaci.
Actually, the author developed three formulations: lumped, integral and differential.
I agree that this problem is not real, however, the intention of the author is to explore the approximation with...
Here is the question:
Consider a pool reactor (Fig. 2-33) whose core is constructed from a number of vertical fuel plates of thickness 2L. Initially the system has the uniform temperature T; then assume that the constant nuclear internal energy u"' is uniformly generated in these plates. The...