Engineering Relations from Second Law

1. Engineering Relations from Second Law P M V Subbarao Professor Mechanical Engineering Department An Equation to Regulate Manufacturing Processes …..

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 Capability of Resources Utilization by a Manufacturing Processes

4. Rate Equations for Manufacturing Systems Conservation of Mass: First Law of Thermodynamics:

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

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.

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

8. Analysis of SSSF Adiabatic Work Transfer CVs SSSF: Conservation of mass First Law : First Law :

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

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. 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 Creation of Energy Sources for Manufacturing System Manufacturing System Material Processing System Creation of Energy Sources for Material Processing System

14. Material Processing System Manufacturing System

15. Manufacturing System as a Rate Process

16. Auxiliaries (to Manufacturing System) as a Thermodynamic CV

17. Power Plant for A Manufacturing System & Material Processing System Power Plant for Manufacturing System & Material Processing System

18. Heat Source for A Manufacturing System & Material Processing System Heat Generation Unit for Manufacturing System & Material Processing System