A heat exchanger transfers energy between two or more fluids via a separating wall. Common configurations include counterflow, parallel tubes, cross-flow, and shell-and-tube designs. When applying an energy balance to a heat exchanger, kinetic and potential energy changes can be ignored, as well as heat transfer between the exchanger and surroundings. The balance simplifies to an equation relating the mass flow rates and enthalpy changes of the fluids. For a condenser example, assumptions allow the energy balance to drop certain terms and solve for the ratio of cooling water to steam mass flow rates.

1. exchanger is one in which a gas or liquid is separated from another gas or
liquid by a wall
through which energy is conducted. These heat exchangers, known as recuperators,
take many
different forms. Counterflow and parallel tube-within-a-tube
configurations are shown in
Figs. 4.12b and 4.12c, respectively. Other configurations include cross-flow, as
in automobile
radiators, and multiple-pass shell-and-tube condensers and evaporators.
Figure 4.12d illus-trates a cross-flow heat exchanger.
The only work interaction at the boundary of a control volume enclosing a heat
exchanger
is flow work at the places where matter enters and exits, so the term of the
energy rate
balance can be set to zero. Although high rates of energy transfer
may be achieved from
stream to stream, the heat transfer from the outer surface of the
heat exchanger to the sur-roundings is often small enough to be neglected.
In addition, the kinetic and potential ener-gies of the flowing streams can
often be ignored at the inlets and exits.
The next example illustrates how the mass and energy rate balances are applied
to a con-denser at steady state. Condensers are commonly found in power
plants and refrigeration
systems.Each of the two control volumes shown on the accompanying sketch is at
steady-state.
2. There is no significant heat transfer between the overall condenser and its
surroundings, and
3. Changes in the kinetic and potential energies of the flowing streams from
inlet to exit can be ignored.
4. At states 2, 3, and 4, h ! h
f
(T ) (see Eq. 3.14).
Analysis: The steam and the cooling water streams do not mix. Thus, the mass
rate balances for each of the two streams re-duce at steady state to give
(a) The ratio of the mass flow rate of the cooling water to the mass flow rate
of the condensing steam, can be found
from the steady-state form of the energy rate balance applied to the overall
condenser as follows:
The underlined terms drop out by assumptions 2 and 3. With these
simplifications, together with the above mass flow rate
relations, the energy rate balance becomes simply
Solving, we get
The specific enthalpy h
1
can be determined using the given quality and data from Table A-3. From Table A-
3 at 0.1 bar, h
f !
191.83 kJ/kg and h
g ! 2584.7 kJ/kg, so
Using assumption 4, the specific enthalpy at 2 is given by (T
2
) ! 188.45 kJ/kg. Similarly, (T
3
) and (T
4
),
giving h
4 " h
3 ! 62.7 kJ/kg. Thus
(b) For a control volume enclosing the steam side of the condenser only, the
steady-state form of energy rate balance is
The underlined terms drop out by assumptions 2 and 3. Combining this equation
with the following expression for
the rate of energy transfer between the condensing steam and the cooling water

2. results:
Dividing by the mass flow rate of the steam, and inserting values
where the minus sign signifies that energy is transferred from the condensing
steam to the cooling water.
Alternatively, (h
4 " h
3
) can be evaluated using the incompressible liquid model via Eq. 3.20b.
Depending on where the boundary of the control volume is located, two different
formulations of the energy rate balance
are obtained. In part (a), both streams are included in the control volume.
Energy transfer between them occurs internally
and not across the boundary of the control volume, so the term drops out of the
energy rate balance. With the control
volume of part (b), however, the term must be included.S