Computer Aided Design of Thermal Systems (ME648)

Transcription

1 Computer Aided Design of Thermal Systems (ME648) PG/Open Elective Credits: 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. Lecture-by-Lecture Break-up (Three 50 min Lectures per Week) 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.

2 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 y i 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.

3 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) Non- Axisymmetric 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.

4 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 Two- Variable Problem). Geometric Programming: Introduction. Form of Objective Function and Constraints. Degree of Difficulty. Solution Methodology for Single Variable Unconstrained Optimization Problem.

5 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, McGraw- Hill, New York. 2. Deb, Kalyanmoy, 2006, Optimization for Engineering Design, Prentice-Hall, New Delhi.