The thermal properties of aluminum are:
Aluminium
The thermal properties of aluminum are:
Density (): 2700 kg/m
Specific heat capacity (Cp): 900 J/(kgK)
Thermal conductivity (k): 237 W/(mK)
Silver
The thermal properties of silver are:
Density (): 10500 kg/m
Specific heat capacity (Cp): 235 J/(kgK)
Thermal conductivity (k): 429 W/(mK)
Lead
The thermal properties of lead are:
Density (): 11340 kg/m
Specific heat capacity (Cp): 129 J/(kgK)
Thermal conductivity (k): 35.3 W/(mK)
ENG581 Applied Heat and Mass Transfer
Prac 1: Transient Conduction
Theory
Transient conduction prediction via the finite difference method and semi-infinite solid method
Setup
3 different metal strips (Aluminium, Silver and Lead) of 12cm in length, one end immersed in water at 950C, 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
Measurement
Temperature of each thermocouple is measured and recorded.
Tasks
Using Excel, implement one of the following equations:
Use boundary conditions of 95C at x = 0 end and 25C at x = l
Use initial conditions of 25C and dt = 1sec or dx = 0.1cm
Finite difference method explicit (20%)
Create a plot of the temperature at the 4 thermocouple locations for the first 300 sec after the water at 950C has been added.
Discuss the relevant stability criterion and how your choice of delta t and delta x fits with the relevant stability criterion
Using your spreadsheet, demonstrate what happens if the stability criterion is not followed.
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%)
Consider another method to find the same results:
Maybe try the textbooks accompanying software IHT OR
MATLABs PDE solver (PDEPE), OR
attempt to implement an implicit method. Please provide the relevant references.
Compare these results to the results for the first method
Semi-infinite solid method - Refer to Section 5.7 of the text (10%)
Implement the semi-infinite solid formulae for the experimental conditions
Create a plot of the temperature at the 4 thermocouple locations for the first 300 sec after the water at 950C has been added.
Discuss how you evaluated the ERF function and the validity of that choice
Method comparison (25%)
Compare the results obtained from each of the methods you used (at least the finite-difference method and the semi-infinite solid method)
Which do you think is the more accurate?
What factors will affect the difference between these two methods?
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.
