Updated Syallabus:

Introduction. Basic Considerations in Design. Modelling of Thermal Systems. Numerical Modelling and Simulation. Acceptable Design of a Thermal System: A Synthesis of Different Design Steps. Optmization. Special Topics.

Lecturewise Breakup (based on 75min per lecture)

• Lec # 1: Introduction: Definition of Engineering Design. Design Vs. Analysis- Examples. Engineering Design: Decisions in an Engineering Undertaking- A Flow Chart.
• Lec # 2: Thermal Systems: Basic Characteristics. Definitions of System, Subsystem, Component and Process. Basic Considerations in Design: Formulation of the Design Problem-(i) Requirements: Illustration by Examples. To be continued.
• Lec # 3: Formulation of Design Problem (Contd): (ii) Specifications. (iii) Given Quantities. (iii) Design Variables: Hardware and Operating Conditions. (iv) Constraints and Limitations. Example Problem showing a design problem and how to come up with a problem statement: Air-conditioning of a house.
• Lec # 4: Steps in Design Process: A Flow Chart. Example: Design of a Simple Counterflow Heat Exchanger-Acceptable Designs and Optimal Design. Example: Design of a Refrigerator: Acceptable Designs and Optimal Design.
• Lec # 5: Example: Design of a Quenching System for Hardening of a Steel Piece: an Example illustrating main steps in the design of a thermal system. Material Selection: Properties and Applications of Metals and Alloys, Ceramics, Polymers, Composite Materials. To be continued.
• Lec # 6: Material Selection (Contd): Liquids and Gases. Selection and Substitution of Materials: Criteria. Various Examples of Material Selection. Modelling of Thermal Systems: Importance of Modelling in Design. Basic Features of Modelling.
• Lec # 7: Types of Models. Interaction between Models. Other Classifications.
• Mathematical Modelling: Transient/Steady State: Time Scales: Response Time of the Material or Body; Characteristic Time of Variation of the Ambient or Operating Conditions. To be continued.
• Lec # 8: Time Scales (Completed). Spatial Dimensions: How to determine dimensionality? Lumped Mass Approximation. Simplification of Boundary Conditions. Negligible Effects: When do we neglect a particular effect? Idealizations.
• Lec # 9: Material Properties. Conservation Laws. Example Problem.
• Lec #10: Example Problem. Curve Fitting: Exact Fit and Best Fit: Applications. Exact Fit: (a) General form of a polynomial. To be continued.
• Lec # 11: Exact Fit (Contd):(b) Newton’s Divided-Difference Interpolating Polynomial. (c) Lagrange Interpolation.
• Lec # 12: Numerical Interpolation with Splines. Best Fit: Basic Considerations. Method of Least Squares- (i) Linear Regression. Concept of Correlation Coefficient.
• Lec #13: Best fit with a Polynomial. Nonpolynomial form. Linearisation: Exponential, Power law and other functions. Function of two or more independent variables: Exact Fit: y = f(x1, x2)-demonstration of the method using a second order polynomial.
• Lec # 14: Best Fit: y = f(x1, x2)-demonstration of the method using multiple regression analysis. Extension to function of more than two independent variables. Polynomial regression. Linearisation of non-linear functions. Numerical Modelling and Simulation: General Features. Accuracy. Solution of Linear Simultaneous Algebraic Equations: Direct Methods: (1) Gaussian Elimination: Basic method. Advantages and Disadvantages. Zero pivot element: Swapping of rows. Small Pivot element: Example Problem. Swapping with row having maximum pivot element. To be continued.
• Lec # 15: Ill-conditioned and Well-conditioned System: Example. (2) Gauss-Jordon Elimination Method: Basic Method. Example. (3) Matrix Decomposition Method.
• Lec # 16: (d) Matrix Inversion Method: Use of Gauss-Jordon method for matrix inversion. Iterative Methods: (a) Jacobi Method. (b) Gauss-Seidel Iterative Method. Scarborough Criterion for Convergence.
• Lec # 17: Relaxation Method: Successive Over-relaxation and Under-relaxation. Concept of Relaxation Factor. Optimum Relaxation Factor. Finite-Difference Method: Derivation of Central, Forward and Backward difference expressions for yi/ and yi// using Taylor series approach. Concept of truncation error. Finite-difference expressions of higher order accuracy.
• Lec # 18: Applications of finite-difference to Conduction Heat Transfer Problems: Steady 1 D heat transfer from a rectangular fin: Problem statement. Governing Differential Equation. Non-dimensionalisation of GDE and B.C’s. Discretization. Image Point Technique: Handling of non-Dirichlet boundary conditions. Matrix equations for 4 grid points at which temperatures are calculated. Tri-diagonal coefficient matrix (TDM). Tri-diagonal matrix algorithm (TDMA) or Thomas algorithm.
• Comparison of the numerical solution with analytical solution of the fin problem. Numerical errors and accuracy: Round-off error, Truncation error and Total error. Minimum total error. Grid Independence Test.
• Lec # 19: 1D Fin with Convective Tip: Handling of tip boundary condition using image point technique. 2D Steady State Heat Conduction in a heat generating square block: Governing equation and boundary conditions. Non-dimensionalization. Discretization. Handling of Corner Points. Matrix equations for 4 x 4 grid points. Advantage of having a banded coefficient matrix. Method of Solution: Choice between G-E and G-S. Justification for using G-S. Line-by-Line method. 3D Problems: Handling of corner and edge points.
• Lec #20: 1D Transient Heat Conduction in a Plane Wall: Governing equation, initial and boundary conditions. Non-dimensionalization. Explicit or Euler Scheme: Basis. Finitedifference expressions for the case of four grid points. Crank-Nicolson and Pure Implicit Schemes.
• Lec # 21: Definition of Stability. von Neumann Stability Analysis for each scheme.
• Lec # 22: 2D Transient Conduction Problems: Applications of Euler, Pure Implicit, Crank-Nicolson and Alternating Direction Implicit (ADI) Method. 1D Transient Heat Conduction in Composite Media: Handling of the Interface by Taylor Series Approach.
• Lec # 23: Problems in Cylindrical Geometry: (a) Axisymmetric Problems (b) NonAxisymmetric Problems.
• Lec # 24: Non-linear GDE: Variable Thermal Conductivity. Non-linear Boundary Condition: Radiation boundary Condition.
• Lec # 25: Numerical Model for a System: Isolating System parts. Mathematical
• Modelling. Numerical Modelling. Merging of Different Models. System Simulation. Importance of Simulation: Evaluation of design. Off-design condition. Optimization. Improving or modifying existing systems. Sensitivity tests. Acceptable Design of a Thermal System: Steps leading to acceptable design.
• Lec # 26: Commonly used methods for obtaining an initial design. Example Problem: Initial design of a Refrigerator.
• Lec # 27: Example Problem (Acceptable design not based on initial design): Design of a Solar Energy driven Water Heating System. Iterative Redesign Procedure. Example Problem: Design of Cooling of an Electronic Equipment: Statement of the Problem. To be continued.
• Lec # 28 Example Problem (Completed). Heat Exchanger Design Problem: Given quantities, Requirements, Constraints, Design variables and Operating Conditions of a typical heat exchanger design problem.
• Lec # 29: Example Problem: Design of a Counterflow Double-Pipe Heat Exchanger: Statement of the Problem.
• Lec # 30: Problem Formulation for Optimization: Optimization in Design. Basic Concepts: Objective Function. Constraints: Equality Constraints and Inequality Constraints. Conversion of Inequality Constraints to Equality Constraints by the use of
• Slack Variables. Steps involved in the formulation of an optimization problem. List of Important Optimization Methods. Calculus Methods: Basic Concepts. Maxima, Minima and saddle point for one variable and two variable problems. Optimization involving objective function having more than two variables: Lagrange Multiplier Technique: Basic Method of Lagrange Multipliers for Constrained Optimization. The Concept of Gradient Vector. Lagrange Multiplier Equations.
• Lec # 31: Visualization of Lagrange Multiplier Method in Two Dimensions. Unconstrained Optimization: Application of Lagrange Multiplier Method when there is no constraint. Example Problems (Conversion of a Constrained Optimization Problem into an Unconstrained Optimization Problem).
• Lec # 32: Example Problem: Solution by Lagrange Multiplier Method for Constrained Optimization. Sensitivity Coefficients. Search Methods: Single Variable Problems: Uniform Exhaustive Search Method: Basic Concepts. Expression for the Final Interval of Uncertainty. Unimodal Functions: Examples of Continuous, Non-differentiable and Discontinuous Functions. Use of Search Methods for Optimizing Non-Unimodal Functions.
• Lec # 33: Eliminating a section based on two tests. Dichotomous Search: The basic method. The expression for the Final Interval of Uncertainty. Fibonacci Search: Fibonacci Series. The Steps in a Fibonacci Search. Example Problem: Demonstration of the application of Fibonacci Search method to obtain the maxima of a function. Comparison of Effectiveness of Three Search Methods in terms of Reduction Ratio (RR).
• Lec # 34: Multivariable, Unconstrained Optimization: (a) Lattice Search; (b) Univariate Search. Example Problem (Demonstration of Univariate Search for a Two-variable Problem).
• Lec # 35: (c) Steepest Ascent/Descent Method: Basis. Basic Approach. Algorithm. Example Problem (Demonstration of Steepest Ascent/Descent Method for a Twovariable Problem).
• Lec # 36: Constrained Optimization: Penalty Function Method: Introduction. Solution
• Methodology. Example Problem (Demonstration of Penalty Function Method for a TwoVariable Problem). Geometric Programming: Introduction. Form of Objective Function and Constraints. Degree of Difficulty. Solution Methodology for Single Variable Unconstrained Optimization Problem.
• Lec # 37: Mathematical Proof of Geometric Programming for Single Variable Unconstrained Optimization (with zero degree of difficulty). Example Problem. Example of a Difficult Expression of y* (containing a negative number raised to a negative non-integer): How to get around the problem?
• Lec # 38: Unconstrained, Multivariable Optimization (with Zero Degree of Difficulty): Methodology. Example Problem. Constrained, Multivariable Optimization (with Zero Degree of Difficulty): Methodology. Example Problem.
• Lec #39: Genetic Algorithm: Fundamentals.
• Lec # 40-41: Special Topics (Suggested): 1. Optimization of Performance of a Power Cycle based on Exergy Analysis. 2. Any other topic of the instructor’s choice.

Textbooks:

1. Jaluria, Yogesh, 1998, Design and Optimization of Thermal Systems, McGrawHill, New York.

2. Deb, Kalyanmoy, 2006, Optimization for Engineering Design, Prentice-Hall, New Delhi.