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Question

The figure shows the face and interface temperature of a composite slab consisting of four materials, of identical thickness, through which the heat transfer is steady. Which material has minimum thermal conductivity?



A
a
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B
b
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C
c
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D
d
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Solution

The correct option is C c
Rate of heat transfer i.e thermal current is given by

ith=kAΔTΔx

ith==kATbigTsmallΔx

k=(ith×ΔxA)(1TbigTsmall)

In steady state, ith is the same for all slabs. Since all the slabs have the same thickness and cross-sectional area, Δx and A are constant.

i.e k=CTbigTsmall for constant C.

Therefore, ka=C2515=C10
kb=C1510=C5
kc=C10(5)=C15
kd=C5(10)=C5

So. the minimum thermal conductivity is kc.


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