CHBE 2120 Spring 2006 Exam 1

CHBE 2120 Spring 2006 Exam 1 - NAME_ CHBE 2120A Professor...

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NAME__________________________ CHBE 2120A Professor Gallivan Exam 1 February 9, 2006 For any problem that requires an iterative method, perform two iterations. = = a c b d bc ad A d c b a A 1 1
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(1) The diffusion of mass from high concentration to low concentration is described by a differential equation called the diffusion equation: 0 2 2 = dx c d D , where c(x) is the concentration along a pipe and D is a constant called the diffusivity. This differential equation can be approximated by algebraic equations, which represent c(x) at fixed positions along the pipe: 2 1 1 2 2 ) ( 2 x c c c dx c d i i i Δ + + . Use the positions shown in the picture to solve for the concentration at 4 equally spaced points ( Δ x=1) along the pipe. The equation can be evaluated at each point in the interior, but additional information must be known at the boundary points, in order to solve for the concentrations. In this problem, the left end is closed, implying that
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CHBE 2120 Spring 2006 Exam 1 - NAME_ CHBE 2120A Professor...

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