1. Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras Advanced Transport Phenomena Module 1 Lecture 1 Overview & “Bulb Blackening” Example

2. COURSE OUTLINE This advanced course in “Transport Phenomena” deals with the transport of:  Energy,  Mass, and  Momentum in chemically reacting fluids.  The basic principles of these fields are here generalized and reformulated so as to be able to deal with chemically-reacting flow systems of current and future Engineering interest.

3.  Principles are developed and illustrated here for the rational design of Engineering equipment  chemical reactor analysis,  separation processes,  multiphase transport, etc.  Emphasis is placed on the use of fundamental laws, and on a judicious blend of experimental, analytical and numerical methods to develop:  required understanding, and  necessary mathematical models  for solving Engineering problems involving transport processes. COURSE OUTLINE CONTD…

4. CONTENTS  Introduction: Examples; Types/Uses of Control Volumes; Notion of Conservation Principles and Constitutive Laws; Illustrations of Use  Conservation Principles: Mass, Momentum, Energy, Entropy; Alternative Forms; statement of Assumptions  Constitutive Laws: Diffusion Flux Laws/ Coefficients, general constraints; Momentum/ Energy/ Mass Diffusion Laws; Multi-component mass diffusion; Reaction rates, mechanisms, time-scales

5.  Momentum Transport Mechanisms, Rates & Coefficients in Chemically Reacting Flow Systems (CRFS)  Energy Transport Mechanisms, Rates & Coefficients in CRFS  Mass Transport Mechanisms, Rates & Coefficients in CRFS  Analogies & Similitude Analyses with Application to CRFS  Problem-Solving Techniques, Aids, Philosophy CONTENTS CONTD…

6.  Textbook:  “Transport Processes in Chemically Reacting Flow Systems”, Rosner, Daniel E., Dover 2000  References:  “Chemically Reacting Flow: Theory and Practice”, Robert J. Kee, Michael E. Coltrin, Peter Glarborg, Wiley, 2003  “Transport Phenomena”, R. Byron Bird, Warren E. Stewart and Edwin N Lightfoot, 2nd Edition, Wiley, 2001 TEXTBOOKS AND REFERENCES

7. STUDY OF TRANSPORT PHENOMENA: WHY?

8.  In the known universe, systems and surroundings co- exist in dynamic equilibrium, from macro-scale to molecular-scale.  The fundamental quantities of mass, momentum, energy and entropy are constantly being generated and consumed, and being exchanged between the system and its surroundings  To characterize and quantify these “exchange rates”, we need to study the underlying transport processes.  EXAMPLES… IMPORTANCE OF STUDYING TRANSPORT PHENOMENA

9. BULB BLACKENING

10. INCANDESCENT LAMPS  Oldest known light source  e.g., candle, kerosene lamp, gas lights  High temperature achieved by chemical reaction  Light emitted by particles brought to incandescence  1879: Edison constructs carbon filament lamp  Filament electrically heated  Carbon evaporates at a high rate  Bulb blackens within days

11. CARBON FILAMENT LAMP

12. Tungsten FILAMENT LAMP  1906: Tungsten used first in vacuum lamps  Tungsten has lower melting point than carbon, but has a vapor pressure lower than that of carbon by 5000X at filament temperatures  Evaporation rate further reduced by operating filament in gaseous atmosphere  e.g., nitrogen, inert gases

13. Tungsten FILAMENT IG BULB COMPONENTS 1.Outline of Glass bulb 2.Low pressure inert gas (argon, neon, nitrogen) 3.Tungsten filament 4.Contact wire (goes out of stem) 5.Contact wire (goes into stem) 6.Support wires 7.Stem (glass mount) 8.Contact wire (goes out of stem) 9.Cap (sleeve) 10. Insulation 11. Electrical contact

14. HALOGEN CYCLE LAMPS  Conceived in order to bring evaporated Tungsten back to filament  Suitable reactive environment provided  Tungsten depositing on bulb wall reacts with halogen,  Forms a volatile Tungsten halide,  Circulates back through bulb, and  Decomposes to W and halogen near or at hot filament  Perfect cycle results in absence of bulb-blackening, infinite lifetime of filament  Till it breaks!  All current incandescent bulbs have the halogen cycle

15. XENON HALOGEN LAMP

16. BULB BLACKENING: TRANSPORT PHENOMENA INVOLVED  Mass transfer:  Tungsten to bulb wall, Tungsten halide back to filament  Heat transfer:  From hot filament to cold bulb wall, setting up a temperature distribution  Momentum transfer:  Collision of evaporated Tungsten atoms with inert-gas & halogen molecules  Entropy transfer:  As a result of chemical reactions that drive towards a thermodynamic equilibrium  All are intricately coupled, and must be solved simultaneously

18. Tungsten EVAPORATION PROCESS Vapor pressure of Tungsten is given by: (Elenbaas, 1972) Simple model of halogen cycle: W + X  WX (low T) WX  W + X (high T) Simplified condition for zero Tungsten flux:

19. HEAT-TRANSFER MODELING IN INERT GAS INCANDESCENT LAMPS Langmuir heat-conduction model: where and power-law heat conductivity with boundary conditions: Temperature distribution in annular geometry is given by: where r’s represent cylindrical radii.

20. MASS-TRANSFER MODELING IN INERT GAS INCANDESCENT LAMPS Mass diffusion of Tungsten vapor is described by: with where

21. For the bulb geometry, the solution is found to be: where A’ and B’ are constants evaluated by applying the bc’s: With this, mass loss of Tungsten wire per unit length may be estimated. MASS-TRANSFER MODELING IN INERT GAS INCANDESCENT LAMPS CONTD…

22. MASS-TRANSFER MODELING IN HALOGEN INCANDESCENT LAMPS: SPECIES VIEW Equation to be satisfied by chemical species becomes: with where and are Fick and thermal diffusion coefficients, respectively, of species i

23. Assumption of local thermo-chemical equilibrium (LTCE) leads to law of mass action: where are number of atoms of type in compound Resulting system of highly nonlinear PDE’s are solved numerically using a finite-difference procedure. MASS-TRANSFER MODELING IN HALOGEN INCANDESCENT LAMPS: SPECIES VIEW CONTD…

24. For each element, we have: where MASS-TRANSFER MODELING INHALOGEN INCANDESCENT LAMPS: ELEMENT VIEW

25. with element diffusivities being weighted sums of bearer species diffusivities: Element mass concentrations can be solved for as: where A’ and B’ can be obtained by applying bc’s MASS-TRANSFER MODELING IN HALOGEN INCANDESCENT LAMPS: ELEMENT VIEW CONTD…

26. Radial diffusion flux of k th element is given by: When this is equated to zero, we obtain the “zero element flux” (i.e., no bulb blackening) condition: MASS-TRANSFER MODELING IN HALOGEN INCANDESCENT LAMPS: ELEMENT VIEW CONTD…

27. REMARKS  This case-study from everyday life is a classic illustration of the interplay between various transport phenomena in chemically-reactive environments.  A seemingly-complex problem can be greatly simplified by identifying conserved and invariant quantities in such systems, and focusing our analysis on such quantities.  In the next lecture, we’ll review another illustration of these principles.