Consider the thermal system given figure, with three thermal masses $C_1,C_2$ and $C_3$ with

corresponding temperatures $T_1,T_2$ and $T_3.$ Heat is input into the system at two points: $q_{h1}$ into

thermal mass $1$ and $q_{h2}$ into thermal mass $2.$ The system exchanges heat with the environment at

temperature $T_0$ through thermal resistances $R_1,R_2$ and $R_3.$

Using the principles of thermal capacitance and resistance, derive and simplify the system of

equations governing the dynamics of this system with respect to inputs $T_0,q_{h1},$ and $q_{h2}.$