Page 54 - Entrophy Analysis in Thermal Engineering Systems

46 Entropy Analysis in Thermal Engineering Systems

4.2 Heat flow

The first and simplest example of irreversible process, which may lead
to a production of entropy, is the flow of heat Q from a warmer body at
temperature T 1 to a cooler body at temperature T 2 . The two bodies may
also represent two different locations in a single system. The change in
the entropy of each body is obtained as follows.
ð
δQ Q
ΔS 1 ¼ ¼ (4.1)
T 1
T
ð
δQ Q
ΔS 2 ¼ ¼ (4.2)
T 2
T
The net change in the entropy is
Q Q
Φ ¼ (4.3)
T 2 T 1
Because the warmer body loses heat, the change in its entropy is Q/T 1 ,
whereas the change in the entropy of the cooler body is Q/T 2 as it receives
the same quantity of heat. Because T 1 >T 2 , we conclude that Q/T 2 >Q/T 1 .
So, the net change in entropy (of both bodies) is positive. Thus, the heat
flow is a source of entropy increase (generation).
In the example, each body is assumed to have a constant temperature
during the heat transfer process. However, if the temperature varies, one
must find a relation between the amount of heat and the temperature to
perform integration in Eqs. (4.1) and (4.2). In this case, Eq. (4.3) is rewritten
as follows.

ð
1 1
Φ ¼ δQ (4.4)
T 2 T 1

4.3 Pressure drop

Entropy generation may take place due to pressure drop on the path of
a fluid flow. The amount of work wasted due to the friction on the flow path
is dissipated in the form of heat. A problem of this kind was analyzed by