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sample-mid-term - ME 608 Numerical Methods in Heat Mass and...

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ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Mid-Term Examination Date: March 5, 2008 6:00 – 7:30 PM Instructor: J. Murthy Open Book, Open Notes Total: 50 points Use the finite volume method in all problems. NAME: Problem Points Score 1 30 2 20 TOTAL 50 1
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1. Consider laminar hydrodynamically and thermally fully-developed flow in a 2D parallel plate channel, as shown in Fig. 1. There is a constant heat generation S in the channel. Neglecting axial diffusion, the energy equation may be written as: x ( ρ C p u ( y ) T ) = y parenleftbigg k T y parenrightbigg + S The walls of the channel are perfectly insulated. The velocity field u ( y ) is the classical parabolic profile, given by: u ( y ) u m = 3 2 parenleftbigg 1 - parenleftBig y D parenrightBig 2 parenrightbigg Here u m is the mean velocity at any x location. All properties are assumed constant in keeping with the concept of fully-developed flow and heat transfer. You are given the following information: ρ = 1 kg / m 3 , C p = 1000 J / kgK , u m = 0 . 1 m / s , k = 0 . 5 W / mK ,
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