Modeling the Temperature of a Cooling Cup of Coffee
The model is set to run for 60 minutes with 1-minute time steps. Run the model and open the result element ‘Coffee Temperature Results’ to see the time history of the coffee temperature.
The internal energy of the coffee (in calories) is modeled using an Integrator element. An equation of the following form is used for the cooling rate: k*(T1-T2), where ‘k’ represents a generic heat conduction coefficient with units, cal/K-min and T1 and T2 are respectively the coffee temperature and the room temperature. The heat transfer rate is, therefore, proportional to the difference in temperature between the coffee and the surrounding air. This results in the coffee temperature asymptotically approaching room temperature.
Hypothetical coffee temperature data is stored in a Time Series element ('Temperature_Data') in the model. A simple optimization was used to obtain a value for ‘Conduction_Coefficient’ (6.94 cal/K-min) that results in an optimum fit of the simulation results to the data. The objective function is 'Cumulative_Temp_Difference'. To run an optimization, go to Run|Optimization... and press the Optimize! button.