Energy Balance Around the Jacket

Next, we write an energy balance around the jacket. Again, neglecting the kinetic and potential energy and the shaft work:

accumulation = in by flow + in by heat transfer - out by flow

and using the assumptions of constant density, volume and heat capacity, we find

or

but

is a constant, so

and

we also have the relationship for heat transfer from the jacket to the tank

substituting the expression for Q into the tank and jacket energy balances yields the two modeling equations for this system