Updated Syllabus:

Introduction: Applications of boiling and condensation. Difference between evaporation and boiling. Comparison of Nucleate and Convective (or Flow) boiling. Pool boiling: Nukiyama Experiment. Theory of vapour bubble formation: Homogeneous and Heterogeneous Nucleation. Bubble Growth Models. Mechanism of Critical Heat Flux (CHF). Various models and correlations. Pool Boiling of Binary Mixture. Flow Boiling: homogeneous and heterogeneous models. Flow Boiling in Microchannels. Flow Boiling of Binary Mixtures. Boiling enhancement techniques. Film and dropwise condensation. Nusselt’s analysis of laminar film condensation on vertical plate, single horizontal tube and vertical array of tubes. Laminar-wavy and turbulent film condensation. Film condensation inside horizontal tubes. Condensation enhancement techniques. Special topics (Suggested): Boiling in Microgravity Environment. Boiling of Nanofluids. Liquid Metals Boiling. Boiling on Structured Surfaces. Effect of Non-condensable Gases in Vapour on Condensation. Numerical Modelling of Boiling and Condensation Heat Transfer. Special topics: Boiling of Nanofluids. Computer Simulation of Pool Boiling by the Coupled Map Lattice Method.

Lecture-by-Lecture Break-up (Three 50 min lectures per week)

Lecture # 1: Introduction:

• Applications of Boiling and Condensation: Thermal Power Plant Cycle.  Ideal Vapour-Compression Refrigeration Cycle.  Immersion Cooling of Computers.  Heat Pipe.

Lecture # 2:

• Difference between Evaporation and Boiling.  Evaporation:  Benard Convection.  The typical temperature profile in the evaporating liquid.    Definition of ‘h’.  Why Tsat is used in the definition of ‘h’?  Nucleate Boiling:  Bubble Nucleation.  Temperature Profile in Water.  Comparison of h vs.q// plots for evaporation and nucleate boiling of water at 1 atm.

Lecture # 3:

• Convective Boiling:  Various flow regimes in a vertical heated tube.  Comparison of nucleate boiling and convective boiling.

Lecture # 4:

• Review of Thermodynamics of Phase Change of Pure Substances:  subcooled liquid, saturated liquid, saturated liquid-vapour mixture, saturated vapour, superheated vapour, critical point.  Psat vs. Tsat plot: Clapeyron Equation and ClausiusClapeyron Equation.  Triple Point.  Superheated liquid: Definition.  Application in boiling.  Concept of metastable equilibrium of vapour bubble and superheated liquid.

Lecture # 5:

• Interfacial Tension: Explanation from Molecular Point of View.  Formation of Vapour Bubbles:  Derivation of the expression for the diameter of a spherical vapour bubble in thermal and mechanical equilibrium with its superheated liquid.  Theory of heterogeneous nucleation (to be continued).

Lecture # 6:

• Heterogeneous Nucleation.Expression of Mikic and Rohsenow (1969) for Activation Superheat of a Cavity.  Homogeneous Nucleation.  Spinodal lines and metastable states on a p-v diagram.  Bubble Growth near a Heated Surface: Liquid Inertia Controlled Growth and Heat Transfer Controlled Growth.

Lecture # 7:

• Mathematical Modelling of heat-transfer controlled bubble growth in the non-uniform temperature field near a superheated wall: Model of Mikic and Rohsenow (1969):  Basic assumptions.  Expression for the waiting time.  Expression for the rate of growth of bubble (to be continued).

Lecture # 8:

• Expression for the rate of bubble growth (completed).  Example Problem.  Bubble Departure Diameter and the Frequency of Bubble Release:  Definition of the frequency of bubble release.  Various mechanisms of bubble release.  Sample Correlations for Departure Diameter: Fritz (1935), Zuber (1959) and Cole (1967).

Lecture # 9:

• Frequency of Bubble Release: Influencing factors.  Correlations for frequency of bubble release (valid in the intermediate regime between inertia and heattransfer controlled growth): Jacob and Fritz (1931), Peebles and Garber (1953), Zuber (1963).  Basic forms of correlations given by Ivey (1967) for inertia controlled growth and heat-transfer controlled growth.  Favourable conditions for inertia controlled growth and heat-transfer controlled growth.  Example Problem.

Lecture # 10:

• Pool Boiling: Definition.  Applications.  Temperature Controlled Saturated Pool Boiling Curve for a Large Horizontal Surface: Various regimes.  Maximum or Critical heat flux (CHF).  Minimum heat flux.  Points of difference between heating and cooling curves: (a) Contact angle hysteresis in transition regime; (b) near onset of nucleation condition.  Heat Flux Controlled Curve: Various regimes.  Points of difference between heating and cooling curves: hysteresis effect (Missing transition regime).

Lecture # 11:

• Single Composite Pool Boiling Curve showing heating and cooling for both temperature and heat flux controlled modes.  Definition of CHF for temperature controlled and heat flux controlled modes.  Definition of Minimum Heat Flux.  Experiment of Nukiyama (1934): Saturated Pool Boiling of Water at Atmospheric Pressure (to be continued).

Lecture # 12:

• Details of Nukiyama Experiment: Equipments used.  Experimental Procedure.  Sources of Experimental Error.  Results.  Maximum and Minimum heat fluxes.  High speed video camera pictures of heat flux controlled saturated pool boiling showing regimes till CHF.

Lecture # 13:

• h vs. ∆Tw plot in Pool Boling: Explanation.  Heat Transfer Mechanism during Nucleate Boiling: Rohsenow’s Model and its basis.  Rohsenow (1952) Correlation.

Lecture # 14:

• Stephan and Abdelsalam Correlation (1980): Basis.  Correlations for water, hydrocarbons, cryogenic fluids, and refrigerants.  Unified correlation valid for all fluids (lower accuracy).  Simpler and easy-to-use correlations.  Surface roughness correction.  Comparison of q//vs.∆Tw graphs on log-log plot for boiling of water at 1 bar using Rohsenow (1952) and, Stephan and Abdelsalam (1980) correlations.

Lecture # 15:

• Basic approaches used in the making of pool boiling correlations.  Applicability of pool boiling correlations for horizontal tubes/surfaces to other geometries/orientations.  Example Problems.  Liquid Metals Pool Boiling: Physics.  Basic differences with respect to boiling of normal fluids.  Subbotin et al. (1970) Correlation.

Lecture # 16:

• Transition Boiling and Taylor Instability.  Helmholtz Instability.  Mechanism of CHF: Derivation of Zuber (1959) Correlation using Taylor instability and Helmholtz instability theories.

Lecture # 17:

• Summary of Zuber’s Hypothesis.  Drawbacks of Zuber’s Model.  Effect of geometry on CHF:  Correlations given by Lienhard and co-workers for square and round heated surfaces of finite size.  Example Problem.

Lecture # 18:

• Accuracy of CHF Correlations given by Lienhard and co-workers.  CHF Correlation for Liquid Metals.  CHF as a Function of Pressure:  Explanation for the nature of the curve.  Stephan (1992) Correlation for organic fluids and water.  Example Problem.

Lecture # 19:

• Criticisms on Zuber’s Model of CHF.  Effect of Surface Wetting Characteristics:  Pool boiling on a completely non-wetted surface.  Alternative Model of Kandlikar (2001) for predicting CHF: Postulate.  Basic Mechanism.  Model Description.  Derivation of CHF.  Kandlikar’s expression of CHF for saturated pool boiling of pure liquids.  Validation with earlier experiments.

Lecture # 20:

• Kandlikar’s Model of CHF (Contd.):  Effect of bubble contact angle and plate inclination on CHF.  Difficulties in the use of Kandlikar’s correlation.

Lecture # 21:

• Minimum Heat Flux: Zuber(1959) theory and correlation, and modification by Berenson (1961) for Infinite Plate.  Lienhard and Wong (1963) Correlation for Horizontal Cylinder.  Film Boiling: Bromley (1950) Correlations for horizontal cylinder and sphere.  Berenson (1961) Correlation for Infinite Horizontal Surface.  Effect of Radiation on Film Boiling:  Correction by Bromley (1950).  Film Boiling on Finite Horizontal Surface.

Lecture # 22:

• Example Problem on Film Boiling.  Summary of Saturated Pool Boiling.

Lecture # 23:

• Parametric Effects on Pool Boiling: Effect of Subcooling.  Kutateladze(1952) correlation for CHF in Subcooled Boiling.  Effect of Gravity (to be continued).

Lecture # 24:

• Effect of Gravity (Completed).  Effect of Size and Wettability.  Effect of Surface Roughness.  Flow Boiling: Introduction.

Lecture # 25:

• Basic Terms and Definitions in Two-Phase Flows.  Basic Model and Governing Equations (Conservation of Mass and Momentum) for One-dimensional TwoPhase Flow: Assumptions and derivations.  Expression of total axial pressure gradient in terms of frictional effect at the wall, gravitational head effect and acceleration (or deceleration) of the flow.

Lecture # 26:

• Calculation of Frictional Pressure Gradient:Definition of Two-Phase Multipliers, φl ,φlo ,φv .  Homogeneous Flow: Basic definition and idealizations. Derivation of the expression for φlo2 .  Heterogeneous Flow: Basic definition.  Method of Lockhart and Martinelli (1949):  Basic philosophy.  Concept of Correction factor or Martinelli parameter, X.  To be continued.

Lecture # 27:

• Heterogeneous Flow (Completed): Details of the method and its accuracy and limitations.  Profile of (dp/ dz)fr vs. z: Physical Explanation. Example Problem. (Homogeneous Flow).

Lecture # 28:

• Variation of φl and φv as well as αwith X: Physical Explanation.  Basic Procedure for obtaining Pressure Drop in a Two-Phase Flow.  Example Problem. (Heterogeneous Flow).  To be continued.

Lecture # 29:

• Example Problem (Completed).

Lecture # 30:

• Regimes of Convective Boiling in Round Tubes.  Method of Calculating Heat Transfer Coefficient in Two-Phase Flows: Chen (1966) Correlation for vertical tube.  Example Problem (to be continued).

Lecture # 31:

• Example Problem (Completed).  Modification to Chen’s Correlation: Bennett and Chen (1980) Correlation.  Condition of applicability of Chen’s Correlation to flow boiling in horizontal tubes.  Correlation for stratified flow boiling in horizontal tubes.  Gungor and Winterton (1986) Correlation for vertical tube flow boiling.  Boiling Regime Map for Constant Wall Flux Condition: Departure from nucleate boiling and dryout.  Why is thermodynamic quality negative in subcooled boiling and greater than 1 in drop flow regime?  To be continued.

Lecture # 32:

• Real Quality vs. Thermodynamic Quality (Completed).  Critical Boiling States:  Definition of CHF in flow boiling.  Boiling Crisis at low quality and at high quality.  Plot of CHF vs. Quality. Condensation: Definition.  Dropwise and Film Condensation.  Nusselt’s Analysis of Laminar Film Condensation on a Vertical Flat Plate: Basic Assumptions.  To be continued.

Lecture # 33:

• Nusselt’s Analysis (Completed): Derivation of expression of average heat transfer coefficient and average Nusselt number.

Lecture # 34:

• Expression for mass rate of condensation.  Effect of Subcooling:  Derivation of the expression for modified latent heat of condensation h/fg .  Turbulent Film Condensation over a Vertical Plate:  Definition of film condensation Reynolds number.  Various regimes of film condensation flow such as laminar, laminar-wavy and turbulent and transition criteria.  Experimental correlations for average heat transfer coefficient for laminar-wavy and turbulent regimes.  Basic method of solution of film condensation problems: Why are iterations required?  Example Problem (to be continued).

Lecture # 35:

• Example Problem (Completed).  Laminar Film Condensation over a Single − Horizontal Tube (Nusselt’s Approach): Derivation of the expression for hD .

Lecture # 36:

• Laminar Film Condensation on a Vertical Tier of n tubes: Nusselt’s Analysis.  Chen (1961) Correlation: Modification of Nusselt’s correlation.  Calculation of total condensation rate on a square array of tubes.  Staggered Tube Arrangement.  Effect of vapour velocity and non-condensable gases in the vapour.

Lectures # 37-40:

• Special Topics: Boiling of Nanofluids. Computer Simulation of Pool Boiling by the Coupled Map Lattice Method

Reference Books:

1. Stephan K, 1992, Heat Transfer in Condensation and Boiling, Springer-Verlag, Berlin.

2. Carey, V.P., 2008, Liquid-Vapor Phase-Change Phenomena, 2nd edn, Taylor & Francis, New York.

Course Syllabus:

Review of classical thermodynamics; introductory electrochemistry; principles of chemical and electrochemical kinetics; transport phenomena in electrochemical system, Classical thermodynamic analyses of fuel cell systems; analyses of fuel cell kinetics; quantification of fuel cell performance, Conservation and rate equations; approximate analytical treatment of fuel cell systems; scope and limitations of one-dimensional analyses; introduction to computational fluid mechanics of fuel cell systems; measurement of fuel cell performance; lab visits; introduction to electrochemical impedance spectroscopy, Direct methanol fuel cell; microbial fuel cell; hydrogen generation and storage; limitations, recent advances and challenges in fuel cell research.

Course Contents (approximate number of lectures in brackets):

I. Fundamentals: Review of classical thermodynamics; introductory electrochemistry; principles of chemical and electrochemical kinetics; transport phenomena in electrochemical systems [14].

II. Analyses of fuel cells: Classical thermodynamic analyses of fuel cell systems; analyses of fuel cell kinetics; quantification of fuel cell performance [14].

III. Computational/experimental techniques: Conservation and rate equations; approximate analytical treatment of fuel cell systems; scope and limitations of one-dimensional analyses; introduction to computational fluid mechanics of fuel cell systems; measurement of fuel cell performance; lab visits; introduction to electrochemical impedance spectroscopy [10].

IV. Special topics: Direct methanol fuel cell; microbial fuel cell; hydrogen generation and storage; limitations, recent advances and challenges in fuel cell research [4].

References:

1. Fuel Cell Systems Explained, J. Larminie and A. Dicks (John Wiley & Sons, 2003, USA)

2. Fuel Cell Fundamentals, R. O’Hayre, S-W. Cha, W. Colella, F. B. Prinz (John Wiley and Sons, 2005, USA)

3. Fuel Cell Engines, M. M. Mench (John Wiley and Sons, 2008, USA)

4. Fuel Cells: From Fundamental to Applications, S. Srinivasan (Springer, 2006, USA)

5. Principles of Fuel Cells, X. Li (CRC Press, 2005, USA)

6. Fuel Cells: Principles and Applications, B. Viswanathan and M. A. Scibioh (Universities Press, 2006, India)

7. PEM Fuel Cells: Theory and practice, F. Barbir (Elsevier Academic Press, 2005, USA)

8. High-Temperature Solid Oxide Fuel Cells: Fundamental, Design and Applications, S. C. Singhal, K. Kendall (Elsevier Science, 2004, USA)

9. Transport Phenomena in Fuel cells, Ed. B. Sunden and M. Faghri (WIT Press, 2005, UK) 10. Fundamentals of Electrochemistry, V. S. Bagotsky (John Wiley & Sons, 2006, USA)

Introduction to Turbulence, review of turbulence models: RANS, LES, DNS, simple closure of chemical source terms, mixture fraction based modeling of turbulent nonpremixed combustion: flamelet model and CMC method, PDF and Monte Carlo methods, scalar mixing models, turbulent premixed flames, droplet and spray combustion.

Lecture­wise breakup (considering the duration of each lecture is 50 minutes)

I. Introduction (6 lectures):

• Objectives and outline of the course

• Review of thermodynamics

• Review of chemical kinetics: elementary and overall reactions, reaction rate, combustion of hydrocarbons, reaction mechanisms

• Turbulence theory: Characteristics of turbulence, examples of turbulent flows

• Complexities associated with turbulent combustion, statistical description of turbulent flows

II. Review of Turbulence Models (6 lectures):

• Derivation of the Reynolds and Favre averaging of Navier­Stokes equations

• Turbulence models, length/time scales of turbulent flows, Kolmogorov hypotheses

• Turbulence closure: zero equation, one equation and two­equation models

• Transport equation for kinetic energy and dissipation rate

• Large eddy simulation, models for the subgrid stress tensor, examples

• Transport equation for reactive scalars, closure issues for the chemical source terms

• Simple closure for the chemical source terms: EBU, EDC models

III. Turbulent non­premixed combustion (9 lectures):

• Introduction: flame structure, definition of conserved scalar, mixture fraction

• Characteristics of turbulent nonpremixed flame, functional dependencies of reactive scalars with mixture fraction: infinite fast chemistry, equilibrium chemistry, frozen chemistry, shape of the PDF for nonpremixed combustion

• Derivation of transport equations for mean and variance of mixture fraction

• Closure models for the unclosed terms, model for the scalar dissipation rate

• Flamelet concept, derivation of the flamelet equations

• Functional dependence of the reactive scalars with mixture fraction and scalar dissipation rate

• Estimation of the averaged quantities, overall solution algorithm, some applications of the flamelet models

• Conditional moments and its usefulness, introduction to conditional moment closure (CMC) method

• Some examples of CMC method and its short­comings

IV. Probability Density Function based approaches for turbulent combustion (6 lectures):

• Introduction to statistics: probability, mean, variance, skewness and flatness of a random variable, probability density function, cumulative distribution function, Bayes theorem, joint PDF, marginal PDF, conditional PDF, conditional expectation

• Derivation of the transport equation for the PDF

• Closure of various unclosed terms: chemical source terms, conditional velocity

• Mixing models: IEM, CURL

V. Turbulent premixed combustion (7 lectures):

• Introduction: turbulent premixed flames, turbulent flame speed, structure and characteristics of turbulent premixed flame, different regimes of turbulent premixed flame

• Modeling of turbulent premixed flames: BML model

• G equation / level­set approach and closure models

VI. Droplet evaporation and spray combustion (6 lectures):

• Applications, simple model of droplet evaporation

• Simple model for burning droplet, burning rate constant and droplet lifetime

• Droplet burning in convective environments

• Real­world effects on droplet burning rate

• Spray phenomena

• Modeling of turbulent sprays

References:

1. Turbulent Combustion, N. Peters, Cambridge University Press

2. Computational models for turbulent reacting flows, R. O. Fox, Cambridge University Press

3. An Introduction to Combustion: Concepts and Applications by S. R. Turns, McGraw­Hill Science/Engineering/Math; 3 edition (January 24, 2011)

4. Combustion by I. Glassman, Academic Press; 4 edition (September 8, 2008)

5. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation by J. Warnatz, U. Mass and R. W. Dibble, Springer;  4th edition (November 9, 2010)