# Thermal Systems

• User to model heat transfer
• For example in a house
• Or in electronic components
• Determine efficiency of elements
• Determine thermal operating ranges for components

## Variables

• Rate of heat flow in watts ()

• Temperature, in Kelvins (K)

• Analogous to current and voltage in electrical systems

## Elements

### Thermal Capacitor

• Stores heat energy in a reversible way

Elemental equation:

Where is the net heat flowing in, ie .

### Thermal Resistor

• Dissapates heat
• Non-reversible

Any object that restricts heat flow when heat flows from on medium to another can be modelled as a resistor. Elemental equation:

Where is the flow of heat from the temperature on one side of the resistor to the temperature on the other.

## Interconnection Laws

Compatibility Law:

• Temperatures are identical where elements touch,

Equilibrium Law:

• Elemental heat flow rates sum to zero at connection points

## Examples

Develop a thermal model for someone doing winter sports. Assume:

• Ambient temperature
• Body temperature
• Thermal resistance between body and ambient (the person is wearing a coat)
• Heat generated by body

The rate of heat flow out is the difference in ambient and body temperature accross the resistor:

In the thermal capacitor, the net input heat is proportional to the rate of change of temperature:

Combining the two equations gives: