**Computational Fluid Dynamics**

**Paper Code: CHE 804 C**

Introduction to Computational Fluid Mechanics and Heat Transfer – Modeling of Transport Phenomena

Transport Equations – Equations of Continuity, Motion, Energy in dimensional and non-dimensional forms – Lagrangian and Eulerian forms

Conservative and Non-conservative forms of transport equations

Equations – Elliptic, Parabolic and Hyperbolic

Understanding the convection and diffusion terms

Generalized Advection-Diffusion Equation with source term

Initial condition and Boundary conditions – three kinds

Concept of discretization – Taylor series FDM and CV based FVM – one-dimensional unsteady state heat diffusion equation - Treatment of boundary conditions

Numerical solution of PDE - Explicit method – Stability – Convergence – Consistency

Thomas (Tri-diagonal Matrix) Algorithm - Implicit method

Discretization of two-dimensional unsteady state heat diffusion equation – Numerical solution - ADI method – Line-by line

solution for multi-dimensional problem

Vorticity-Stream function approach

Primitive variable approach - Staggered grid

Discretization of the convection term - Upwind scheme - Central Difference scheme - Hybrid scheme - Power law scheme

Evaluation of pressure from Equation of Continuity

Pressure correction - Velocity correction

SIMPLE Algorithm – Residues in solution – Relaxation

Iterative scheme – Over and under relaxation - quick updation

Discussion on SIMPLER, SIMPLE-C

Solution of coupled equations – Thermal buoyancy

Validation of code and results – Benchmarking - Benchmark cases - Lid driven cavity - Flow in pipe - Estimation of

location of vena contracta in orifice flow – Rayleigh-Benard convection

**Test Books/ References:**

- Numerical Heat Transfer and Fluid Flow: S V Patankar. Taylor & Francis (Paperback Ed)
- Computational Fluid Mechanics and Heat Transfer: J C Tannehill, D A Anderson and R H Pletcher. Taylor & Francis (1997)
- Computational Methods for Fluid Dynamics: J H Ferziger and M Peric. Springer-Verlag (1999)
- Computational Fluid Dynamics: P J Roache
- Applied Numerical Methods: B Carnahan, H A Luther and J O Wilkes. John Wiley. NY.
- Handbook of Numerical Heat Transfer: Ed. W J Minkowycz, E M Sparrow, G E Schneider and R H Pletcher. Wiley InterScience (Paperback Ed)
- Physical and Computational Aspects of Convective Heat Transfer: Tuncer Cebecci and Peter Bradshaw. Springer (Paperback Ed)

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