Two rods A and B of different materials are welded together as shown in Figure. If their thermal conductivities are k1and k2, the thermal conductivity of the composite rod will be
If the ends of the rods are maintained at temperatures , the rate of flow of heat through each rod is given by Q1=k1A(θ1−θ2)dand Q2=K1A(θ1−θ2)d Where A is the cross – sectional area of each rod and d is the length of each rod. Now the cross sectional area _ of the composite rod is 2A. If k is the thermal conductivity of the composite rod, the rate of heat flow is
Q=k(2A)(θ1−θ2))dbut Q=Q1+Q2. therefore(2A)(θ1−θ2)d=K1A(θ1−θ2)d+K1A(θ1−θ2)dOr k=12(k1+k2)