ENG481 Applied Heat and Mass Transfer
Prac 1: Transient Conduction
Transient conduction prediction via the finite difference method and semi-infinite solid method

  • 3 different metal strips (Aluminium, Copper and Stainless Steel) of 12cm in length, one end immersed in boiling water, the other end and sides insulated
  • 4 thermocouples placed along each metal strip 30mm apart
  • 1 thermocouple to measure water temperature
  • 1 data logger to record the temperature at the thermocouple

Temperature of each thermocouple is measured and recorded.
Using Excel, implement one of the following equations:

  1. Use boundary conditions of 90°C at x = 0 end and 27°C x = l
  2. Use initial conditions of 27°C and dt = 1sec or dx = 0.1cm

Finite difference method – explicit (20%)

  1. Create a plot of the temperature at the 4 thermocouple locations for the first 300 sec after the boiling water has been added
  2. Discuss the relevant stability criterion and how your choice of delta t and delta x fits with the relevant stability criterion
  3. Using your spreadsheet, demonstrate what happens if the stability criterion is not followed.
  4. What other limitations are there for the explicit method? Do some research and demonstrate these limitations using your spreadsheet results.

Challenge to the finite difference method (20%)

  1. Consider another method to find the same results:
  • Maybe try the textbook’s accompanying software IHT OR
  • MATLABs PDE solver (PDEPE), OR
  • attempt to implement an implicit method. Please provide the relevant references.
  1. Compare these results to the results for the first method

Semi-infinite solid method – Refer to Section 5.7 of the text (10%)

  1. Implement the semi-infinite solid formulae for the experimental conditions
  2. Create a plot of the temperature at the 4 thermocouple locations for the first 300 sec after the boiling water has been added
  3. Discuss how you evaluated the ERF function and the validity of that choice

Method comparison (25%)

  1. Compare the results obtained from each of the methods you used (at least the finite-difference method and the semi-infinite solid method)
  2. Which do you think is the more accurate?
  3. What factors will affect the difference between these two methods?
  4. Do you have any control of these factors?

Data analysis (25%)
Plot the experimental results and the theoretical results on one plot. Discuss potential reasons for any differences between the experimental results and the theoretical results (consider validity of boundary conditions, initial conditions, material properties).
Please present a professional analysis i.e. error, variance, etc. Use these information in your discussion and analysis.



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