final - ME 608 Numerical Methods in Heat, Mass, and...

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ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Final Examination Date: April 30, 2008 8:00-10:00 AM Instructor: J. Murthy Open Book, Open Notes Total: 50 points Use the finite volume method in all problems. NAME: Problem Points Score 1 25 2 25 TOTAL 50 1
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1. Consider one-dimensional steady laminar incompressible flow in a porous medium in the domain shown in Fig. 1. The flow is described by the following governing equations: u x = 0 0 = - μ u κ - p x + x p u x P All properties may be considered constant, with = 10 - 3 kg / ( m - s ) and the permeability = 10 - 2 m 2 . The length of the domain, L , is 0 . 3 m . The inlet velocity is given as u 1 = 0 . 5 m / s and the outlet velocity is u 4 = 0 . 5 m / s . You are asked to solve for the velocity and pressure field in the 3-cell computational domain shown in Figure 1 using the finite volume method and the SIMPLE algorithm. Use a staggered mesh, and perform only one iteration of SIMPLE . Start with an initial guess of p = 0 Pa everywhere. Use under-relaxation factors of α u = 1 . 0 and p = 1 . 0. (a) Develop the appropriate discrete momentum equations, first showing the analytical expressions for the various
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final - ME 608 Numerical Methods in Heat, Mass, and...

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