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Question:

Two conductors having the same width and length, thickness d1 and d2, and thermal conductivity k1 and k2 are placed one above the other. Find the equivalent thermal conductivity.

(d1+d2)(k1d2+k2d1)/2(k1+k2)

(d1−d2)(k1d2+k2d1)/2(k1+k2)

k1d1+k2d2/d1+d2

k1+k2/d1+d2

Solution:

We have,

(T1−T2) / (L/keq(d1+d2)b) = (T1−T2) / (Lk1d1b) + (T1−T2) / (Lk2d2b).

This gives,

keq = (k1d1 + k2d2) / (d1 + d2)