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as2 - ME 608 Numerical Methods in Heat Mass and Momentum...

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ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Assignment No: 2 Due Date: February 7, 2010 Instructor: J. Murthy Unless otherwise stated, use the finite volume method for discretization . Please submit an appropriately annotated printout of any code you write. 1. Write a function or subroutine which can solve a tri-diagonal set of linear algebraic equations using the TDMA. Verify that the code is working correctly. Now write a line-by-line TDMA solver using the TDMA solver you wrote. Ensure that you sweep in both I and J directions so as to allow you to solve two-dimensional linear systems for single-block structured meshes. Verify that the code is working correctly. 2. Consider the case of hydrodynamically and thermally fully developed flow in a square duct of side D. Assume that the walls have a heat flux q specified on them. Assume that the velocity field can be represented by a uniform flow profile u(y,z)= U. The energy equation takes the form: x ( ρ UC p T ) = · ( k T ) Neglect axial diffusion. Assume all properties are constant. (a) Derive an expression for the axial temperature gradient T x by doing a heat balance on a control volume spanning the cross section of the duct.
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