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Term End Examination - November 2012

Course : MEE405 - Computational Fluid Dynamics Slot: D1

Class NBR : 4835

Time : Three Hours Max.Marks:100

(Symbols and Notations have their usual meaning)

PART A (5 X 5 = 25 Marks)

Answer ALL the Questions

1. The governing equations of fluid dynamics could be derived by the Eulerian and

Lagrangian formulation. What do you understand by these terms and when these

formulations are helpful.

2. Differentiate the various approaches by which the governing equations of

computational fluid dynamics could be discretized.

3. Differentiate between implicit and explicit formulations.

4. Explain the significance of Peclet number and its impact on discretization scheme

selection.

5. What is a staggered grid and why is it required for the solution of pressure velocity

coupled problems?

PART B (5 X 15 = 75 Marks)

Answer ALL the Questions

6(a) Derive the equation of momentum for the three dimensional viscous fluid in Cartesian

conservative form.

OR

6(b) Discuss in detail the classification of partial differential equations with reference to

CFD and mention their applications.

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7(a) Derive the discretized equation for the two dimensional diffusion problem using finite

volume method.

OR

7(b) The ends of an insulated metal rod are maintained at constant temperatures of 100C

and 500C respectively. Calculate the steady state temperature distribution for source

free heat conduction through the rod of 6 cm length at 5 nodes apart from boundary

nodes. The thermal conductivity of the rod is 1000 W/m K and cross sectional area is

10 x10-3

m2.

8(a) Derive the transformed equation used in converting the physical domain intocomputational domain.

OR

8(b) Analyze the various grid generation techniques used to discretize the physical domain

for CFD analysis.

9(a) Derive the explicit and implicit discretized forms of the unsteady one-dimensional heat

conduction equation and analyze their advantages and disadvantages.

OR

9(b) An iron rod of length 5 cm, diameter 2 cm and thermal conductivity of 50 W/mC,

protruding from a wall is exposed to ambient temperature of 30C. The heat transfer

coefficient between the rod surface and the ambient air is 100 W/m2

C. The base of

the rod is kept at a constant temperature of 330C. If the governing equation is given

by d2T/dx

2 hP (T - T)/KA and assuming one dimensional steady state heat flow,

develop equations for finding temperature profile at 5 equally spaced nodes, where P isthe perimeter and A is cross sectional area of the rod.

10(a) Explain the various discretization schemes used for convection diffusion problems by

FVM and analyze them in terms of their characteristics.

OR

10(b) Explain the SIMPLE algorithm for getting solutions for pressure velocity coupled

problems and state when it is preferred.