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Modern Engineering Thermodynamics

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184 CHAPTER 6: First Law Open System Applications<br />

6.8 HEAT EXCHANGERS<br />

Heat exchanger is the generic name of any device whose primary function is to promote a heat transport of<br />

energy from one fluid to another fluid. Most heat exchangers have two separate fluid flow paths, which do not<br />

mix the fluids but instead promote the transfer of heat from one fluid to another across a thermally conducting<br />

but otherwise impermeable barrier. These heat exchangers have four flow streams, two inlets and two outlets.<br />

Since the primary function of a heat exchanger is a heat transfer process, they are characteristically aergonic<br />

devices. Also, all of the heat transfer should take place inside the heat exchanger; therefore, most heat exchangers<br />

are normally adiabatic devices when the entire heat exchanger is insulated and taken to be the system. It is<br />

normal for an uninsulated heat exchanger to have a net heat transfer to or from its surroundings, but when<br />

environmental heat transfer values are not supplied in a problem statement and are not an unknown or otherwise<br />

determinable, you are to assume that the entire heat exchanger is an adiabatic system. Figure 6.8 illustrates<br />

a typical heat exchanger schematic and operating characteristics.<br />

A heat exchanger can be considered to be a pair of steady state, steady flow, single-inlet, single-outlet systems<br />

that have equal but opposite heat transfer rates. It can also be analyzed as a steady state, steady flow, doubleinlet,<br />

double-outlet system that has no (assuming it is insulated) external heat transfer. In both cases it is common<br />

to neglect any changes in flow stream specific kinetic or potential energy across the system. The general<br />

ERB (Eq. (6.4)) for the latter case reduces to<br />

_Q + _m 1 h 1 + _m 3 h 3 − _m 2 h 2 − _m 4 h 4 = 0<br />

The conservation of mass law requires that _m 1 = _m 2 = _m a and that _m 3 = _m 4 = _m b , where the subscripts a and b<br />

refer to the two different fluids. Therefore, the ERB becomes<br />

_Q + _m a ðh 1 − h 2 Þ + _m b ðh 3 − h 4 Þ = 0 (6.27)<br />

and if the heat exchanger is insulated, then _Q = 0 and this equation further reduces to<br />

_m a ðh 1 − h 2 Þ = _m b ðh 4 − h 3 Þ (6.28)<br />

If both fluids a and b are incompressible (e.g., liquids), then Eq. (6.19) can be used to give<br />

_m a ½c a ðT 1 − T 2 Þ + v a ðp 1 − p 2 ÞŠ = _m b ½c b ðT 4 − T 3 Þ + v b ðp 4 − p 3 ÞŠ<br />

where c a and c b are the specific heats of fluids a and b, respectively. For liquids, not only are v a and v b small numbers,<br />

but the pressure drops p 1 − p 2 and p 3 − p 4 across the heat exchanger are also small. Therefore, it is common to ignore<br />

the pressure terms in the previous equation, giving the final incompressible fluid heat exchanger ERB as<br />

ERB when both fluids are incompressible liquids<br />

_m a c a ðT 1 − T 2 Þ = _m b c b ðT 4 − T 3 Þ<br />

If both fluids are ideal gases with constant specific heats, then the use of Eq. (6.22) gives<br />

ERB when both fluids are ideal gases<br />

_m a ðc p Þ a<br />

ðT 1 − T 2 Þ = _m b ðc p Þ b<br />

ðT 4 − T 3 Þ<br />

where (c p ) a and (c p ) b are the constant pressure specific heats of gases a and b, respectively.<br />

System<br />

boundary<br />

Fluid a<br />

Fluid b<br />

1<br />

3<br />

Q i<br />

2<br />

4<br />

m a<br />

m b<br />

Assumptions:<br />

1. Steady state, steady flow,<br />

2. W = 0,<br />

3. Q = 0 (unless otherwise stated),<br />

4. Negligible changes in ke and pe<br />

on all flow steams.<br />

(Q i is the internal heat transfer rate)<br />

FIGURE 6.8<br />

Typical heat exchanger operating characteristics.

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