1Thermal Domain
When power is dissipated by resistor elements in other domains, the power is transferred into the Thermal Domain which deals in temperature and moving heat.
1.1Thermal Constant: Thermal Conductivity
Amount of heat a material can transfer due to a temperature difference across the material. Behave like the resistivity in the Electric Domain. Longer element causes lower transfer of heat. Thicker element causes higher transfer of heat. Different material causes different transfer.
Phase change of material causes non linearity, which is not accounted for in the GST model. Example: Working with water close to 100 [°C] will causes a deviation from this model.
1.2Thermal Constant: Specific Heat
Amount of energy required to increase the temperature of a unit of mass of a material by one unit of temperature. Specific heat capacity can be measured two ways:
Constant Volume: Material cannot expand. Stress goes into pressure causing stronger specific heat.
Constant Pressure: Material expands, the expansion does work which must come from the incoming heat. Weaker specific heat. More energy is required to achieve the same thermal increase.
2Formulation
Compute the formulation for the Thermal Domain consistent to GST
2.1Effort and Flow
First step in any domain is to found an effort and a flow variables whose product is power in watt.
Materials have two relevant constants:
Thermal conductivity [W/m/°K]
Specific Heat [J/Kg/°K]
Now, the thermal conductivity looks a lot like the resistivity of a material [Ohm*m]. I also know that the temperature difference is what moves heat. I can start from here to compute what the effort and flow are in the Thermal Domain.
Illustration 1 - Compute thermal effort and thermal flow
2.2Resistor and Capacitor
With effort and flow obtained, the resistive and capacitive elements of the Thermal Domain can be computed.
Unlike other domains, the thermal resistor does not dissipate power, but instead transfers it.
The capacitive element behave like in other domains, storing the flow.
There is no inductive element because the flow is energy and is not massive. Effort cannot be stored in the thermal domain.
Illustration 2 - Compute thermal resistor and thermal capacitor
2.3Energy Storage
The thermal capacitor stores energy. Like all other GST capacitors, storage is half square of effort over capacitor terminals by capacitor value. There is no way to store effort in the thermal domain.
2.4Generators
Like all other GST domains, there is an effort and a flow generator in the Thermal Domain.
The effort generator is a constant temperature, it can be used to model the environment temperature if the thermal capacity of the ambient is large compared to the system.
The flow generator can be used to model the losses from a resistive element in another domain to the thermal domain.
Take into account that the effort of the thermal domain is the square of absolute temperature. This models the fact that pumping heat at different absolute temperatures achieves different temperature increases.
3Recap
Recap of the General System Theory Thermal Domain equations.
3.1Definitions
Illustration 3 - GST Thermal Domain Equations
3.2Materials Thermal Constants
Illustration 4 - Thermal Domain Material Constants
Specific heat is related to the number of atoms and modes of vibrations of that atom. Thermal conductivity is often related to electrical conductivity, and an electrical conductor is will also be good thermal conductor.
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