Modelling and scientific computing

Process modelling slides

Please download the lecture slides. 13 September 2010 (slides 1 to 8)
15 September 2010 (slides 9 to 15)
16 September 2010 (slides 16 to 19)
20 September 2010 (slides 20 to the end)

Approximation and computer representation

Please download the lecture slides. 22 and 23 September (updated)

• More about the Ariane 5 rocket 16-bit overflow
• Python code used in class for ...

Calculating relative error

Working with integers

Working with floats

Special numbers

Practice questions

1. From the Hangos and Cameron reference, (available here] - accessible from McMaster computers only)
   • Work through example 2.4.1 on page 33
   • Exercise A 2.1 and A 2.2 on page 37
   • Exercise A 2.4: which controlling mechanisms would you consider?
2. Homework problem, similar to the case presented on slide 18, except
   • Use two inlet streams \(\sf F_1\) and \(\sf F_2\), and assume they are volumetric flow rates
   • An irreversible reaction occurs, \(\sf A + 3B \stackrel{r}{\rightarrow} 2C\)
   • The reaction rate for A = \(\sf -r_A = -kC_\text{A} C_\text{B}^3\)
   1. Derive the time-varying component mass balance for species B.
      • \( V\frac{dC_B}{dt} = F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} C_{\sf B} + 0 - 3 kC_{\sf A} C_{\sf B}^3 V \)
   2. What is the steady state value of \(\sf C_B\)? Can it be calculated without knowing the steady state value of \(\sf C_A\)?
      • \( F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} \overline{C}_{\sf B} - 3 k \overline{C}_{\sf A} \overline{C}^3_{\sf B} V \) - we require the steady state value of \(C_{\sf A}\), denoted as \(\overline{C}_{\sf A}\), to calculate \(\overline{C}_{\sf B}\).

More exercises available here