# BME350 WNE Biotransport Processes Problem Set 2 Exercise

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BME 350 Biotransport Processes Issued: Thursday, January 24, 2019 Due: Tuesday, February 5, 2019 Problem Set #2 PART 1: First Order Differential Equations The function y(t) obeys the differential equation 3 dyt  1  yt   2u 1 t  dt 2 for both negative and positive times. Given the initial condition y(0) = 0 you are required to find an expression for y(t) for t > 0. Recall that the function u-1(t) is a unit step function, defined by u-1(t) = 0 ; t < 0 u-1(t) = 1 ; t > 0 or t = 0. i) Write down the differential equation for t > 0. ii) Solve the differential equation in i). iii) Provide a rough sketch of the solution. 1 PART 2: Continuity in three dimensional Cartesian coordinates In three dimensional Cartesian coordinates the continuity equation is of the form  C x, y, z, t     x, y, z, t    t where     x, y, z, t    x x, y, z, t i   y x, y, z, t  ˆj   z x, y, z, t k and   x, y, z, t   y x, y, z, t   z x, y, z, t     x, y, z, t   x   . x y z Outline a derivation of this equation. PART 3: Exercise 3.18 From Weiss PART 4: Problems 3.1 and 3.2 From Weiss 2 ...
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School: Rice University

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