JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisite

Heat Transfer, Fluid Mechanics

Course Objective

To apply the principles of Heat Transfer and Fluid Mechanics to solve simple heat

transfer and fluid flow problems using different numerical techniques

Course Outcomes

At the end of the course, the student should be able to

• Differentiate between different types of Partial Differential Equations and to be able to apply appropriate numerical techniques
• Solve the simple heat transfer and fluid flow problems using different numerical techniques
• Understand and to appreciate the need for validation of numerical solution

UNIT - I

Review of Governing Equations in Heat Transfer and Fluid Flow: Conservation Laws – Differential Form of Equations – Characteristics of Governing Equations - Solution Methods: Analytical, Experimental and Numerical Methods – Review of Boundary Conditions Introduction to Numerical Methods - Brief about Finite Difference, Finite Element and Finite Volume Methods – Solution of Linear Algebraic Equations – Direct and Iterative Approaches Mathematical Behavior of Partial Differential Equations: Classification of Partial Differential Equations – Illustrations Finite Difference Method: Taylor’s series – Derivation of Finite Difference Formulae for Partial Derivative Terms - FD formulation of 1D Elliptic PDEs - 1D steady state heat transfer problems – Cartesian, cylindrical and spherical co-ordinate systems –- boundary conditions

UNIT - II

Finite Difference Method: 2D Elliptic PDEs – 2D Steady State Heat Conduction Problems. Parabolic PDEs - Transient heat conduction – Errors and Stability - Explicit Method – Stability Analysis – Implicit and Crank Nickolson method – 2-D Parabolic PDEs - Finite Difference formulation – ADI Method and explicit Method – Finite Difference Formulation of 1D Hyperbolic PDEs - Wave Equation

UNIT - III

Finite Volume Method: Formation of Basic rules for Finite Volume approach – General Nodal Equation - Interface Thermal Conductivity -– Treatment of Source Term and Treatment of Nonlinearity. Solution of 1D and 2D Elliptic PDEs - Heat conduction problems - Solution of 1D Parabolic PDEs – Explicit Method and Implicit Methods- Transient Heat conduction problems

UNIT - IV

FVM to Convection and Diffusion: General Form of Governing Equations for Fluid Flow and Heat transfer – Burger’s equation - Steady 1D Convection Diffusion – Discretization Schemes and their assessment – Treatment of Boundary Conditions

UNIT - V

Calculation of Flow Field: Vorticity & Stream Function Method – Advantages and Disadvantages – Treatment of Boundary Conditions - Staggered Grid as Remedy for representation of Flow Field - Pressure Velocity Coupling - SIMPLE & SIMPLER (revised algorithm) Algorithms. Compressible Flows: Introduction - Pressure, Velocity and Density Coupling.

TEXT BOOKS:

• 1. Numerical heat transfer and fluid flow – S.V. Patankar (Hemisphere Pub. House)
• 2. An Introduction to Computational Fluid Dynamics – FVM Method – H.K. Versteeg, W. Malalasekhara (PHI)
• 3. Computational Fluid Flow and Heat Transfer by Muralidharan & Sundarajan (Narosa Pub)
• 4. Computational Fluid Dynamics and Heat Transfer by P. S. Ghoshdastidar, Centage Pub

REFERENCE BOOKS:

• 1. Computational Fluid Dynamics by Hoffman and Chiang, Engg Education System
• 2. Computational Fluid Dynamics by Anderson, TMH
• 3. Computational Methods for Fluid Dynamics by Ferziger, Peric, Springer
• 4. Computational Fluid Dynamics by T.J. Chung, Cambridge University
• 5. Computational Fluid Dynamics by A Practical Approach – Tu, Yeoh, Liu, Elsevier
• 6. Text Book of Fluid Dynamics by Frank Chorlton, CBS Publishers M.Tech, I Year, II Sem