MEL 807 Computational Heat Transfer (2-0-4) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

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1 MEL 807 Computational Heat Transfer (2-0-4) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

2 Time and Venue Course Coordinator: Dr. Prabal Talukdar Room No: III, Course webpage: Pre-requisite: Fluid Mechanics and Heat Transfer Fortran or C Programming Lectures: Tuesday & Friday, a.m. (Room: V 315) Lab: Tuesday: 1-5 p.m.

3 Syllabus Mathematical Description of the Physical Phenomena- Governing equations mass, momentum, energy, species, General form of the scalar transport equation, Elliptic, parabolic and hyperbolic equations, Behavior of the scalar transport equation with respect to these equation type (2 lectures) Discretization Methods- Methods for deriving discretization equations-finite difference, finite volume and finite element method, Method for solving discretization equations, Consistency, stability and convergence (4 lectures) Diffusion Equation- 1D-2D steady diffusion, Source terms, nonlinearity, Boundary conditions, interface diffusion coefficient, Underrelaxation, Solution of linear equations (preliminary), Unsteady diffusion, Explicit, Implicit and Crank-Nicolson scheme, Two dimensional conduction, Accuracy, stability and convergence revisited (5 lectures)

4 Syllabus (cont d) Convection and Diffusion- Steady one-dimensional convection and diffusion, Upwind, exponential, hybrid, power, QUICK scheme, Two-dimensional convection-diffusion, Accuracy of Upwind scheme; false diffusion and dispersion, Boundary conditions (6 lectures) Flow Field Calculation- Incompressibility issues and pressurevelocity coupling, Primitive variable versus other methods, Vorticitystream function formulation, Staggered grid, SIMPLE family of algorithms (5 lectures) Numerical Methods for Radiation- Radiation exchange in enclosures composed of diffuse gray surfaces, Finite volume method for radiation, Coupled radiation-conduction for participating media (3 lectures) Projects- presentation (3 lectures) Total: 28 lectures, 15 labs

5 Grading Evaluation: Assignment: 50% Minor Test I: 7.5% Minor Test II: 7.5% Major Test: 15% Project: 20% Total: 100% Textbook: Numerical Heat Transfer and Fluid Flow: Suhas V. Patankar Reference book: Computational Fluid Dynamics: Jr. Anderson Computational Fluid Mechanics and Heat Transfer: Anderson, Tanehil and Pletcher Computational Methods for Fluid dynamics: Ferziger and Peric Projects: Complexity of the problem, report and presentation

6 CFD? Computational Fluid Dynamics is the use of computers and numerical techniques to solve problems involving fluid flow Being it s a computational heat transfer (CHT) course, we will emphasize in heat transfer with and without fluid flow.

7 Overview of the course Finite volume method, Finite difference method Conduction Diffusion-convection Fluid flow computation SIMPLE algorithm Radiation

8 What is CFD? Applied Mathematics Numerical analysis& Programming Problem formulation and analysis Engineering, Biological and Physical Science Visualization & Data Processing Computer Science

9 Applications Aerodynamics of aircraft and vehicles: lift & drag Turbomachinery: flows inside rotating passages, diffusers etc. Power plant: combustion in IC Engines and gas turbines Fluid-structure interaction Hydrodynamics of ships Electrical and electronic engineering: cooling of equipment including micro circuits Reacting flows, Combustion Meteorology and weather prediction Biomedical engineering: blood flows through arteries and veins Impossible to solve Navier-Stokes equations analytically for these applications!

10 Applications CFD simulation of Honda

11 Applications Water droplets dispersing from an Audi car

12 Applications

13 Applications Male CFD simulation of a swimmer showing the contours of Shear stress on the swimsuit region Female

14 Applications Turbo-machinery Application Fluid-structure interaction Axial inducer with CFD velocity vectors and metal stress calculation

15 Flow past a square cylinder CFD Animations

16 History Earliest CFD work by L. F. Richardson (1910) Iterative solution of Laplace equation using finite difference method Error estimates, extrapolate to zero error Relaxation methods (1920 s-50 s) Landmark paper by Courant, Friedrichs and Lewy for hyperbolic equations (1928) Von Neumann stability criteria for parabolic problems (1950) Harlow and Fromm (1963) computed unsteady vortex street using a digital computer. They published a Scientific American article (1965) which ignited interest in modern CFD and the idea of computer experiments

17 History (cont d) Boundary-layer codes developed in the s (GENMIX by Patankar and Spalding in 1972 for e.g.) Solution techniques for incompressible flows published through the 1970 s (SIMPLE family of algorithms by Patankar and Spalding for eg.) Jameson computed Euler flow over complete aircraft (1981) Unstructured mesh methods developed in 1990 s

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