Problem+set+5 - the directional migratory velocity of the...

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BIM 107 Winter 2010 Problem Set 5 (Partial Differential Equations) 1. Consider a one-dimensional heated rod that occupies the region 0 x L. Temperatures at both the edges of the rod (x=0 and x=L) are kept at zero. The temperature of the rod at t=0 is also fixed and is given by f(x). Solve the heat equation to determine the temperature distribution of the heated rod T(x,t). Find the steady state temperature T(x) of the rod. 2. The flow and migration of human polymorphonuclear leukocytes on prosthetic material surfaces can be modeled by the diffusion equation (Assuming that the value of
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Unformatted text preview: the directional migratory velocity of the cells is insignificant) Solve this problem numerically using a finite difference scheme using the initial/ boundary conditions given below (Note: Neumann boundary condition on the right boundary) Initial condition: t = 0 all z > 0 C = 0 Boundary condition: t > 0 z = 0 C = 1 x 10 6 z = 0.2 ∂ C/ ∂ z = 0 Assume the random migration coefficient is μ D = 1 x 10-4 cm 2 /s. Integrate the equation for a period of 100 seconds. ! C ! t = μ D ! 2 C ! z 2...
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