To verify the validity of the solutions produced by the manual simulation, I've calculated the relative error between the results from the manual code and the results produced by COMSOL normally.

The plot for the relative error in the defocus at r = 0 and r = 54 mm is shown below, in the case where only the ring heater is turned on at a total power of 5 W.

The following indicates that the maximum error is less than 0.01% (in percent error format).