1. 02 October 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 13 – Partial Differential Equations 02 October 2007 8.00 am – 9.00 am

2. 02 October 2007 Week 13 Page 2 Topics

3. 02 October 2007 Week 13 Page 3 Tutorial Example 1 (adapted courtesy of ref. [1]) [1] KQ3013 Lecture Notes & Excercise A boiler is supported by four 6cm tall steel legs. Initially, the temperatures on the legs are 20 o C. The boiler is then filled with boiling 100 o C water, while at the base of its legs, the temperature is constantly cooled to 20 o C. If the coefficient of thermal diffusivity k = 0.835 cm 2 /s, using the Crank-Nicolson method, determine the temperatures at T 1 and T 2 from t = 1s to t = 5s. Plot the graph of temperature vs. time. (Use a timestep  t = 1s) What happens as t  ∞ (i.e. steady state) ? Boiler filled with 100 o C water Boiler base

4. 02 October 2007 Week 13 Page 4 Tutorial Example 1 (adapted courtesy of ref. [1]) [1] KQ3013 Lecture Notes & Excercise What we have here, is a case of transient 1-D heat conduction problem : where : with boundary and initial condition : At x = 0 and all time t, T = 100 o C At x = 6 and all time t, T = 20 o C At all x and at time t = 0 (initially), T = 20 o C

5. 02 October 2007 Week 13 Page 5 Tutorial Example 1

6. 02 October 2007 Week 13 Page 6 Tutorial Example 1

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8. 02 October 2007 Week 13 Page 8 Tutorial Example 1

9. 02 October 2007 Week 13 Page 9 Tutorial Example 1

10. 02 October 2007 Week 13 Page 10 Tutorial Example 1 Plot of variation in temperature at point 1 and 2 with time (using Crank-Nicolson method)