3. (20 pts). The Calrod heating element transfers heat largely by a radiation mechanism. If the rate of electrical energy input to the heater is Q and the rot temperature and ambient temperatures are T and Ta, respectively, then an appropriate unsteady-state model for the system is:
Find the transfer functions relating T' to Q' and T' to Ta'. (Be sure they are both in standard form.)
The first thing we realize here is that the equation is non-linear. We will have to linearize the equation to get the transfer functions into standard form.
No linearize the equation:
Invert into the Laplace domain:
Now the transfer functions can be written down directly: