This document discusses applying concepts from thermodynamics, such as entropy and efficiency, to manufacturing systems. It presents equations to model manufacturing systems as control volumes and rate processes. Entropy generation rates are used to characterize irreversibilities within manufacturing processes. Isentropic efficiency is defined as the ratio of actual to reversible performance and can be used to quantify process efficiency. The modeling approach is applied to various components of manufacturing systems, including material processing, auxiliary systems, power plants, and heat sources.

1. Engineering Relations from Second Law
P M V Subbarao
Professor
Mechanical Engineering Department
AnEquationtoRegulateManufacturingProcesses…..

2. Industrial Use of Entropy Generation
• Entropy is negative concept emerged from negative laws.
• Low quality devices lead to high entropy generation and
vice versa.
• Cost of any operation is proportional to energy transactions
involved in the operation.
• Quality of a device is characterized by amount of entropy
generation, which cannot be directly translated into energy
transactions.
• Another qualifying parameter, which is proportional to
energy transactions with a positive nature is essential.

3. Manufacturing System as a Rate Process
mat
mat
mat
h
m
H 
 

pro
pro
pro
h
m
H 
 

scrap
scrap
scrap
h
m
H 
 

loss
env
MF
Q 

in
MF
PP
W 

in
MF
HS
Q 

mat
mat
mat
s
m
S 
 

scrap
MF
scrap
MF
scrap
MF s
m
S 
 

pro
pro
pro
s
m
S 
 

Capability of Resources Utilization by a
Manufacturing Processes

4. Rate Equations for Manufacturing Systems
scrap
pro
mat
MF
m
m
m
dt
dM


 


Conservation of Mass:
First Law of Thermodynamics:
in
MF
PP
pro
pro
scrap
scrap
MF
mat
mat
loss
env
MF
in
MF
HS
W
h
m
h
m
dt
dE
h
m
Q
Q



















5. Entropy as A Rate Equation
• The second law of thermodynamics was used to write the
balance of entropy for a infinitesimal variation for a finite
change.
• Here the equation is needed in a rate form so that a given
process can be tracked in time.
• Take the incremental change and divide by dt.
• We get
t
S
t
Q
T
t
dS gen
cm
d
d
d
d
d


1

6. • For a given control mass we may have more than one source of
heat transfer, each at a certain surface temperature (semi-
distributed situation).
The rate of entropy change is due to the flux of entropy into
the control mass from heat transfer and an increase due to
irreversible processes inside the control mass.
t
S
T
Q
t
dS gen
i
i
cm
d
d
d

 


7. Entropy Rate Equation for CV
Rate of change in entropy of a CV = Entropy in flow rate –Entropy
out flow rate + the flux of entropy into the control mass from heat
transfer + Rate of Entropy generation
gen
e
e
i
i
CV
S
T
Q
s
m
s
m
dt
dS 


 


 



8. Analysis of SSSF Adiabatic Work Transfer CVs
0


 
 gen
e
e
i
i
S
s
m
s
m 


CV
out
out
in
in W
gz
V
h
m
gz
V
h
m


























 
 2
2
2
2
SSSF: Conservation of mass




 out
in m
m
First Law :
First Law :
gen
i
i
e
e
S
s
m
s
m 

 
 

irr
i
i
e
e
S
s
m
s
m 

 
 


9. Visualization of Irreversibilities in Turbine
(Power Generating Machine)
h
s
Ideal work ws = hin – herev
Actual work wa = hin – heirr
pinlet
pExit

10. Process Efficiency of A Thermodynamic Device
• A device following a Reversible process will produce
maximum benefits for a specified amount of resources.
• Irreversible or actual devices generate relatively lower
magnitude of benefits.
• The level of this process irreversibility is also defined as
efficiency of a process or machine.
• Conventional thermodynamics used various such
parameters.
• For example, a machine is expected to follow an Isentropic
process. However, due to friction it may be following an
irreversible adiabatic or irreversible and heat loss process.
• This irreversibility is defined as Isentropic Efficiency.

11. Isentropic Efficiency of a Device
• Isentropic efficiency is defined for a process.
• This is the ratio of actual performance to Isentropic
performance of a machine.
• For power generation machines:
• Isentropic efficiency = Actual power output/Isentropic
power output.
• For Power consuming machines:
• Isentropic efficiency = Isentropic power input/Actual
Power input.
erev
in
eirr
in
turbine
iso
h
h
h
h



,

These definitions are case dependent and a separate definition is
to be developed for each application.

12. Power Consuming Device

13. A Generalized Model Of A Manufacturing System
Material Processing
System
Creation of Energy
Sources for Material
Processing System
Creation of Energy
Sources for
Manufacturing System
Manufacturing System

14. Material Processing
System Manufacturing System

15. Manufacturing System as a Rate Process
mat
MF
mat
MF
mat
MF h
m
H 
 

pro
MF
pro
MF
pro
MF h
m
H 
 

scrap
MF
scrap
MF
scrap
MF h
m
H 
 

loss
env
MF
Q 

in
MF
PP
W 

in
MF
HS
Q 

mat
MF
mat
MF
mat
MF s
m
S 
 

scrap
MF
scrap
MF
scrap
MF s
m
S 
 

pro
MF
pro
MF
pro
MF s
m
S 
 


16. Auxiliaries (to Manufacturing System) as a Thermodynamic
CV
raw
Mp
raw
MP
raw
MP h
m
H 
 

mat
MP
mat
MP
mat
MP h
m
H 
 

scrap
MP
scrap
MP
scrap
MP h
m
H 
 

loss
env
MP
Q 

in
MP
PP
W 

in
MP
HS
Q 

raw
Mp
raw
MP
raw
MP s
m
S 
 

scrap
MP
scrap
MP
scrap
MP s
m
S 
 

mat
MP
mat
MP
mat
MP s
m
S 
 


17. Power Plant for A Manufacturing System & Material
Processing System
Power Plant for
Manufacturing System &
Material Processing System
in
MP
PP
W 

in
MF
PP
W 

fuel
PP
fuel
PP
fuel
PP h
m
H 
 

air
PP
air
PP
air
PP h
m
H 
 

exhaust
PP
exhaust
PP
exhaust
PP h
m
H 
 

loss
env
PP
Q 

air
PP
air
PP
air
PP s
m
S 
 

fuel
PP
fuel
PP
fuel
PP s
m
S 
 

exhaust
PP
exhaust
PP
exhaust
PP h
m
S 
 


18. Heat Source for A Manufacturing System & Material
Processing System
Heat Generation Unit for
Manufacturing System &
Material Processing System
fuel
HS
fuel
HS
fuel
HS h
m
H 
 

air
HS
air
HS
air
HS h
m
H 
 

exhaust
HS
exhaust
HS
exhaust
HS h
m
H 
 

loss
env
HS
Q 

in
MP
HS
Q 

in
MF
HS
Q 

air
HS
air
HS
air
HS s
m
S 
 

fuel
HS
fuel
HS
fuel
HS s
m
S 
 

exhaust
HS
exhaust
HS
exhaust
HS s
m
S 
 
