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 ${\mathsf{F}}_{\mathsf{1}}$ and ${\mathsf{F}}_{\mathsf{2}}$, and assume they are volumetric flow rates
   • An irreversible reaction occurs, $\mathsf{A}\mathsf{+}\mathsf{3}\mathsf{B}\stackrel{\mathsf{r}}{\to }\mathsf{2}\mathsf{C}$
   • The reaction rate for A = $\mathsf{-}{\mathsf{r}}_{\mathsf{A}}\mathsf{=}\mathsf{-}\mathsf{k}{\mathsf{C}}_{\mathsf{\text{A}}}{\mathsf{C}}_{\mathsf{\text{B}}}^{\mathsf{3}}$
   1. Derive the time-varying component mass balance for species B.
      • $V\frac{d{C}_B}{dt}=F_1^{\mathrm{i}\mathrm{n}}{C}_{\mathsf{B}\mathsf{,}\mathsf{1}}^{\mathrm{i}\mathrm{n}}+F_2^{\mathrm{i}\mathrm{n}}{C}_{\mathsf{B}\mathsf{,}\mathsf{2}}^{\mathrm{i}\mathrm{n}}-F^{\mathrm{o}\mathrm{u}\mathrm{t}}{C}_{\mathsf{B}}+0-3k{C}_{\mathsf{A}}{C}_{\mathsf{B}}^{3}V$
   2. What is the steady state value of ${\mathsf{C}}_{\mathsf{B}}$? Can it be calculated without knowing the steady state value of ${\mathsf{C}}_{\mathsf{A}}$?
      • $F_1^{\mathrm{i}\mathrm{n}}{C}_{\mathsf{B}\mathsf{,}\mathsf{1}}^{\mathrm{i}\mathrm{n}}+F_2^{\mathrm{i}\mathrm{n}}{C}_{\mathsf{B}\mathsf{,}\mathsf{2}}^{\mathrm{i}\mathrm{n}}-F^{\mathrm{o}\mathrm{u}\mathrm{t}}{\bar{C}}_{\mathsf{B}}-3k{\bar{C}}_{\mathsf{A}}{\bar{C}}_{\mathsf{B}}^{3}V$ - we require the steady state value of $C_{\mathsf{A}}$, denoted as ${\bar{C}}_{\mathsf{A}}$, to calculate ${\bar{C}}_{\mathsf{B}}$.

More exercises available here