Experimental Procedures: Calculate Temperature-time profiles

General Parameters and Procedures

1. With either a calculator or computer program (see Appendix A), calculate the temperature profile for a cup of coffee from t=0 to t=75 minutes using the finite difference method (equation 1) and the exact solution (equation 2).
2. Vary Dt according to the directions in each exercise.
3. For all experiments, let the cup have an insulation value, a, of 0.1, the starting temperature is 100 ° C and room temperature (T_room) is 20 ° C.
4. Make a scatter (x-y) plot of the data with temperature, T, on the y-axis and time, t, on the x-axis.

Exercise 1 Temperature-time profiles

For this experiment, use a time interval, Dt, of 1 minute.

Exercise 2 Temperature-time profiles

For this experiment, use a time interval, Dt, of 5 minutes.

Exercise 3 Temperature-time profiles

For this experiment, use a time interval, Dt, of 15 minutes.

Exercise 4 Computational cost

1. For exercises 1, 2, and 3, how many points were needed to calculate the temperature-time profiles for a 75 minute period?
2. How long of a period elapses before the simulation result matches with exact solution?

The Sample Problem

Experimental Results