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Question:

Two rods A and B of different materials are welded together as shown in the figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be:

K1+K2/2

2(K1+K2)

3(K1+K2)/2

K1+K2

Solution:

R1=d/k1A
R2=d/k2A
Req=R1R2/(R1+R2)
d/keq(2A)=(d/k1A)(d/k2A)/(d/k1A+d/k2A)
1/2keq=1/(k1k2/(k1+k2))
1/2keq=(k1+k2)/(k1k2)
k1k2=2(k1+k2)
keq=k1k2/2(k1+k2)
keq=(k1+k2)/2