Seven identical rods of material of thermal conductivity k are connected as shown in the given figure. All the rods are of identical length l and cross-sectional area A. If the one end A is kept at 100°C and the other end  A is kept at 0°C, what would be the temperatures of the junctions C, D and E (θC,θD and θE) in the steady state?

This problem can be solved like electric current problem.Let R1, R2, R3, R4, R5, R6, and R7, be the rates of heat flow through AE, EB, AC, CD, CE, ED and DB, respectively. R1=R2,         R5=R6, R3=R4+R5=R7   .........(ii)  To find θE: rate of heat flow along AB= rate of heat flow along AE100-02l=100-θElθE=50°C          rate of heat flow= kAθc−50l=kAl50−θD          kAl100−θc=kAlθc−50+kAlθc−θD=kAlθD      2θC−2θD=50⇒θC=62.5∘C     θD=37.5∘C∴     θC>θE>θD