The General Energy Balance Equation

In this book, both material balances and energy balances are treated on a macroscopic basis, The general macroscopic energy balance for any system is as follows  

Energy Transferred into the System through System Boundary 

Energy Generation Energy Consumption within System within System 

There are several types of energy associated with the general balance. Those energies associated with the transfer of mass either in the system or across the system boundaries include internal energy (U), kinetic energy (KE) and potential energy (PE). Energy can also be transferred across system boundaries by heat (Q) and work (W). 

---

In considering the flow in a pipe, the differential form of the general energy balance equation 2.54 are used, and the friction term 8F will be written in terms of the energy dissipated per unit mass of fluid for flow through a length d/ of pipe. In the first instance, isothermal flow of an ideal gas is considered and the flowrate is expressed as a function of upstream and downstream pressures. Non-isothermal and adiabatic flow are discussed later. 

All the examples of energy balances considered previously have been for steady-state processes where the rate of energy generation or consumption did not vary with time and the accumulation term in the general energy balance equation was taken as zero. 

Show that the general energy balance, Equation (9.3.9), can simplify to an appropriate form for either adiabatic or isothermal reactor operation. 

Suppose sys(f) is the total energy (internal + kinetic + potential) of a system, and ihm and /hout are the mass flow rates of the system input and output streams. (If the system is closed, these quantities each equal zero.) Proceeding as in the development of the transient mass balance equation, we apply the general energy balance equation (11.3-1) to the system in a small time interval from t to t + 1st, during which time the properties of the input and output streams remain approximately constant. The terms of the equation are as follows (see Section 7,4) ... 

Finally, we may substitute the expressions of Equations 11.3-3 through 11.3-11 into the general energy balance (Equation 11.3-2) to obtain for an open system... 

In this section we apply the general energy balance [Equation (8-22)] to the CSTR and to the tubular reactor operated at steady state. We then present example problems showing how the mole and energy balances are combined to size reactors operating adiabatically. 

In most problems you do not have to use all the terms of the general energy balance equation because certain terms may be zero or may be so small that they can be neglected in comparison with the other terms. Several special cases can be deduced from the general energy balance of considerable industrial importance by introducing certain simplifying assumptions ... 

Substituting Eq. 5.2.10 into Eq. 5.2.8, the general energy balance equation of closed systems becomes... 

When the gas velocity approaches the sound velocity, the kinetic energy and viscous work terms in the energy balance equation are not negligible (as assumed in Chapter 5). For these cases, we write the general energy balance equation for a differential plug-flow reactor with length dL (see Eq. 5.2.44),... 

To derive an expression for the temperature variation in a tubular plug-flow reactor, we rearrange the general energy balance equation Eq. 7.5.7 ... 

Equation (2) shows the general energy balance equation, where u [J/kg] is internal energy and J (J/(ms)] is heat flux. The structure of the equation is similar to that of equation (1). 

The general energy balance equation for the energy accumulation in a fuel cell can be written as follows ... 

Equation 6.100 is a shortened version of the general energy balance equation (Eq. 5.5) valid for simple unidirectional conduction. This is a standard handbook problem the solution is (see [1] of Chapter 5) ... 

Section 13.1 shows how to arrange the general energy balance (Equation 11-9) in a more simplified form fcH unsteady stale operation. 

---