53206-mt----computational Fluid Dynamics

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Code No: 53206/MT

M.Tech. – II Semester Regular Examinations, September, 2008 COMPUTATIONAL FLUID DYNAMICS (Common to Machine Design/ CAD/CAM) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

Explain the basis and history of FEM. Consider a steady compressible flow and write down the continuity equation. Discretize the governing equations in conservative and non conservative form and show the consequence of it for 1 – D flow.

2.a) b)

Explain the method of treating Neumann Boundry conditions. Solve the following equations using Gauss – siedel iterative method. 4 x1 + 8 x2 + 3 x3 = 15 7 x1 + 5 x2 + x3 = 13 x1 + 3 x2 + 10 x3 = 14

3.a) b)

What are the different types of numerical grids and illustrate them with figures. Explain the advantages and disadvantages of explicit and implicit methods applied to the linear parabolic equations.

4.

A long cylinder with an initial temperature of Ti is immersed into a not oil bath at temperature Tb. Assuming that the cylinder surface immediately reaches the bath temperature, formulate the nodal equations for temperature with in the cylinder with second order discretization error.

5.

Develop the stream function-vorticity formulation (equations and boundary conditions) for steady axisymmetric flow in a circular tube in r-z co-ordinates. Contd…2.,

Code No: 53206/MT 6.a) b)

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Explain the approximations in the discretization techniques in finite volume method. Derive the expression for the stability criterion for the finite difference solution of the one dimensional unsteady heat conduction using Von Neumann analysis.

7.

Obtain the temperature distribution in the slab with transient heat conduction through it assuming it as a rectangular one in any of the finite difference applications.

8.

Write short notes on: a) Explicit scheme for parabolic equations. b) Convergence requirements c) Finite volume method for three dimensional flows. *****