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


  • Rate of heat flow in watts ()

  • Temperature, in Kelvins (K)

  • Analogous to current and voltage in electrical systems


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


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: