Two identical metal wires of thermal conductivities k1 and k2 respectively are connected in series. The effective thermal conductivity of the combination is:

In series combination the effective thermal resistance R=R1+R2⇒l'k1A=l1k1A1+l2k2A2here l'=l1+l2=l+l=2l As l1=l2=lAlso, A1=A2=A⇒2lk'A=lk1A+lk2A ⇒2k'=1k1+1k2 ∴k'=2k1k2k1+k2