Discuss the relevant stability criterion

Assignment Help Simulation in MATLAB

Reference no: EM133913698

Applied Heat and Mass Transfer

Prac 1: Transient Conduction

Theory
Transient conduction prediction via the finite difference method and semi-infinite solid method
Setup for the simulation
3 different metal strips (Aluminium, Gold and Copper) of 10 cm in length, of unit area cross section with one end immersed in water at 98°C, the other end and sides insulated.
4 thermocouples placed along each metal strip 25mm apart
1 thermocouple to measure water temperature
1 data logger to record the temperature at the thermocouple

Assume the conductivity values for the metals.

Students are encouraged to refer to Sections 5.7 to 5.10 in the prescribed textbook for a comprehensive understanding of the concepts needed to address this prac. A thorough analysis is expected, and students should also consult additional sources and include appropriate references in their assignment.

Tasks - Predict the transient heat conduction of the three metals and predict the temperature at the 4 thermocouple points for the first 200 seconds.

Using Excel/Matlab, implement one of the following equations:

a. Use initial conditions of 26°C and dt = 1sec or dx = 0.1cm Assume suitable boundary conditions as needed.

Finite difference method - explicit

Question 1. Create a plot of the temperature at the 4 thermocouple locations for the first 200 sec when the hot water is brought in contact with the setup.

Question 2. 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. Get top-rated assignment help now.

Question 3. 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

1. Consider another method to find the same results:
MATLABs PDE solver (PDEPE), OR
attempt to implement an implicit method. Please provide the relevant references.

2. Compare these results to the results for the first method

Semi-infinite solid method - Refer to Section 5.7 of the text

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 200 sec when the hot water is brought in contact with the setup.

3. Discuss how you evaluated the ERF function and the validity of that choice

Method comparison

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
Plot the sample observation 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).
Also, discuss how the thermal diffusivity of Aluminum, Gold, and Copper affects the temperature distribution along the strip. Provide a comparison and discuss the significance of thermal diffusivity in transient heat conduction.
Please present a professional analysis i.e. error, variance, etc. Use this information in your discussion and analysis.

Reference no: EM133913698

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