This verification example compares the current and the Joule heat generated in conductor calculated by the Ohm's law and Joule's law, and calculated in QuickField using three formulations: DC conduction, AC conduction and Transient electric.
Engineering question
How to find joule lenz law conductor heating?
Answer Set up a plane-parallel QuickField DC Conduction problem for a conductor and evaluate Joule–Lenz heating from computed field results.
Problem Type Plane-parallel problem of DC conduction.
Geometry
Given V = 0.1 V - voltage applied; f = 50 Hz - frequency in time harmonics and transient magnetics problems; g = 1 MS/m - conductivity of conductor material. L = 0.4 m - conductor length. A = 0.02*0.005 m² - conductor cross-section area.
Task
Calculate the current and Joule heat inside the conductor and compare with the value given by the Joule-Lenz law.
Solution
To maintain the same value of Joule heat across all formulations the voltage value is adjusted:
In the time harmonics problem peak amplitude value of voltage is set √2·V.
In the transient electric voltage is set via formula V(t) = √2·V · sin(2·180·50·t).
According to the Joule-Lenz law* the power of heating generated by an electrical current I:
W = R*I²,
where the conductor resistance is R = (1/g) * (L/A).
The electric current value could be calculated I = V / R [A],
