Hello, I am tesing a simple heat model using both the joule heating and heat transfer modules. My objective of the simulation is to estimate the temperature increase in box surface as a function of the voltage applied to the top surface of a box with a dimension: W=300um, H=100um, and D=500um. Assuming the material parameters of electrical conductivity (200S/m), relative permittivity (10), and thermal conductivity (10W/m/K) and the applied voltage of 1V on the top surface, I can estimate the current density J of 2e6A/m^2 ( or I=0.3A). Then, the dissipated heat will be 0.3 W. Based on the thermal conductivity of the material and the reference temperature(Tref) of 300 K set on the bottom of the box, the estimated temperature increase in the top surface is Qarea*D+Tref= 20+300=320K. Heat source in Volume Qheat will be Qarea/D=2e10 W/m^3.
Now, I apply it to the Joule heating module. The top surface was biased with 1 V and the bottom was set as the ground plane. The side walls were set as a insulating layer. The simulated current density is 2e6A/m^2, as expected, and the electric field (Ez) is 1e4 V/m (=1V/100um). Thus, heat source value is Qheat=J*E=2e10 W/m^3. However, the temperature increase is 10K not 20K.
Using only the heat transfer module (by setting the potention to zero, one can use the heat transfer module only), we can also estimate the temperature, where the top surface was set as a boundary heat source with either a general source (Qarea in W/m^2) or Power, in this case, 0.3W. In this simulation, I obtain the expected temperature increase, 20 K.
Can anyone help me why I am getting twice lower value in Joule heating simulation? The model is attached for your reveiw. Thanks,