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Computational Fluid Dynamics (October 2009)

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Total No. of Questions : 12] P1206 [Total No. of Pages : 3 [3664]-136 B.E. (Mech.) (Part - II) COMPUTATIONAL FLUID DYNAMICS Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Assume suitable data, if necessary. SECTION - I Unit - I Q1) a) b) For model of infinitesimally small element fixed in space, obtain continuity equation and state whether it is conservation or non conservation form. [10] Write the equation of divergence of velocity with its significance. [6] OR Q2) Derive an expression for momentum equation in conservation form. [16] Unit - II Q3) For the matrix equation Ax = b, Write down the conjugate gradient algorithm for A being symmetric and positive definite. What is the strategy of using preconditioning? [16] OR Q4) For the set of following equations : a11x1 + a12x2 + a13x3 = b1 a21x1 + a22x2 + a23x3 = b2 a31x1 + a32x2 + a33x3 = b3 explain various methods to solve it. [16] P.T.O. Unit - III Q5) For large rectangular slab, initially at temperature Ti is suddenly dropped in [18] liquid both at temperature To (Ti > To) write down a) Governing equation with boundary conditions. b) Present in discretised form. c) Methods to solve these equations. OR Q6) Consider first order wave equation u u +C =0 t x Present above equation in discretised form and obtain condition for stability of its numerical solution. [18] SECTION - II Unit - IV Q7) For one dimensional steady state heat conduction equation obtain solution by [16] a) Explicit method. b) Semi-Implicit. c) Implicit method. OR Q8) For thermally developing flow and hydrodynamically fully developed flow inside circular pipe, obtain [16] a) Governing equation with boundary condition. b) Discretised form with probable solution method. Unit - V Q9) Describe the Lax-Wendroff technique for evaluating x-component of velocity at node (i, j) at a time step of t + t. [16] [3664]-136 2 OR Q10)Explain predictor and corrector step used in Mac Cormak s method to find energy at time step t + t for node (i, j) [16] Unit - VI Q11)Out line the MAC algorithm and show how the in compressible flow field is obtained. [18] OR Q12)Obtain an expression for continuity equation, momentum equation and energy equation for converging-diverging nozzle for one dimensional compressible flow. [18] vvvv [3664]-136 3

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