Difference between revisions of "Modelling and scientific computing"
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class_date = 16 September 2010 (slides 16 to | class_date = 16 September 2010 (slides 16 to 19)<br>20 September 2010 (slides 20 to the end) | ||
button_label = Create my course notes! | button_label = Create my course notes! | ||
show_page_layout = 1 | show_page_layout = 1 | ||
show_frame_option = 1 | show_frame_option = 1 | ||
pdf_file = A-Modelling- | pdf_file = A-Modelling-20-Sept-2010.pdf | ||
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* The reaction rate for A = \(\sf -r_A = -kC_\text{A} C_\text{B}^3\) | * The reaction rate for A = \(\sf -r_A = -kC_\text{A} C_\text{B}^3\) | ||
# Derive the time-varying component mass balance for species B. | # Derive the time-varying component mass balance for species B. | ||
#* \( V\frac{dC_B}{dt} = F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} C_{\sf B} + 0 - 3 kC_{\sf A} C_{\sf B}^3 \) | |||
# What is the steady state value of \(\sf C_B\)? Can it be calculated without knowing the steady state value of \(\sf C_A\)? | # What is the steady state value of \(\sf C_B\)? Can it be calculated without knowing the steady state value of \(\sf C_A\)? | ||
#* \( F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} \overline{C}_{\sf B} - 3 k \overline{C}_{\sf A} \overline{C}^3_{\sf B} \) - we require the steady state value of \(C_{\sf A}\), denoted as \(\overline{C}_{\sf A}\), to calculate \(\overline{C}_{\sf B}\). | |||
</ol> | </ol> | ||
''More exercises to come'' | ''More exercises to come'' | ||
Revision as of 19:01, 20 September 2010
Course slides
<pdfreflow> class_date = 13 September 2010 (slides 1 to 8) button_label = Create my course notes! show_page_layout = 1 show_frame_option = 1 pdf_file = A-Modelling-12-Sept-2010.pdf </pdfreflow>
<pdfreflow>
class_date = 15 September 2010 (slides 9 to 15)
button_label = Create my course notes!
show_page_layout = 1
show_frame_option = 1
pdf_file = A-Modelling-15-Sept-2010.pdf
</pdfreflow>
<pdfreflow>
class_date = 16 September 2010 (slides 16 to 19)
20 September 2010 (slides 20 to the end)
button_label = Create my course notes!
show_page_layout = 1
show_frame_option = 1
pdf_file = A-Modelling-20-Sept-2010.pdf
</pdfreflow>
Practice questions
- 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?
- 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 = \(\sf -r_A = -kC_\text{A} C_\text{B}^3\)
- Derive the time-varying component mass balance for species B.
- \( V\frac{dC_B}{dt} = F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} C_{\sf B} + 0 - 3 kC_{\sf A} C_{\sf B}^3 \)
- What is the steady state value of \(\sf C_B\)? Can it be calculated without knowing the steady state value of \(\sf C_A\)?
- \( F^{\rm in}_1 C^{\rm in}_{\sf B,1} + F^{\rm in}_2 C^{\rm in}_{\sf B,2} - F^{\rm out} \overline{C}_{\sf B} - 3 k \overline{C}_{\sf A} \overline{C}^3_{\sf B} \) - we require the steady state value of \(C_{\sf A}\), denoted as \(\overline{C}_{\sf A}\), to calculate \(\overline{C}_{\sf B}\).
More exercises to come