I'm trying to calculate the new temperature of an object when the air temperature around it changes, given a period of time.
Basically I get periodic readings from an air temperature sensor in a refrigerator. In some cases these readings are every 5 minutes, in others every 1 minute, so the time between readings is variable.
For each reading I get, I'd like to also calculate the approximate temperature of food at its core; something like a chicken for example (I know that part is vague, but if there is a variable I can tweak then that is fine).
The result should be a "damped" version of the actual air temperature, as obviously any objects will slowly change temperature to eventually meet the air temperature.
Initially there used to be "food simulant" put around the sensor, so the temperature would automatically be damped, but this is no longer the case.
I do not know much about thermodynamics. I'm not sure if I can just add a percentage of the temperature change to the previous damped value, or if I need a calculation based on the last few air temperature readings, or what.
I guess I'm looking for a result a bit like:
10:00 2 degrees (air), 2 degrees (product)
10:05 2.5 degrees (air), 2.1 degrees (product)
10:10 2.5 degrees (air), 2.2 degrees (product)
10:20 2.7 degrees (air), 2.5 degrees (product)
I could do something really cheap like averaging the readings over the last 30 minutes but I don't think that will cut it!
I'd appreciate any help – thanks very much.
Best Answer
The method of modelling the chicken as a sphere, as mentioned on your other forum, might work something like this. Model the chicken as a sphere and use the heat equation, treating the surface as your boundary. The way to do this is discussed here. To obtain an approximate thermal diffusivity for a chicken you could use the equations you discovered above, which look like they are dependent on temperature only. This translates into the thermal diffusivity via:
$$ \alpha = \frac{k}{\rho c_p} $$
where $k$ is the thermal conductivity, $\rho$ is the density of the chicken, and $c_p$ is the specific heat capacity, which can be found for a number of different meats here.
Even if this method doesn't sound quite like what you're looking for, you may still find using the heat equation in some way useful. It's often used for measuring heat and temperature changes in objects.