The University of SydneyFaculty of Engineering and ITAMME 2000 Engineering AnalysisThis examination paper contains 4 questionsEach question is on a separate page.All questions carry equal marks.Candidates should answer any 3 out of 4 questionsThere are a total of 5 pages including this cover sheet.These pages must be handed in with the examination script.A simple calculator (programmable versions and PDA’s not allowed) may be taken into theexam room.Take care to write legibly. Write your nal answers in ink, not pencil.Name:SID:Closed Book Duration: 2 hour 00 minutes + 10 minutes reading time10:00 Tuesday XXth June 2XXX1Question 1.Consider a uniform rod with ends at x = 0, 1, and with a temperature distribution T(x, t) thatsatises the diusion equation Tt = Txx. Suppose that at t = 0 rod’s temperature is a constant T0for 0 ≤ x ≤ 1, and that for t > 0 the left end is kept at temperature T0 and the right at 0. Thusthe boundary conditions can be stated as T(0, t) = T0, T(1, t) = 0 for t > 0 and initial conditionsT(x, 0) = T0 , 0 < x < 1.(a) Sketch the variation of the solution at the initial time and two later time, highlighting thephysical behaviour of the system. [Ans: Sketch the initial condition, the late time steady linearsolution ,and a curve showing the solution at a time 0
